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Axial load behavior of square CFT stub column with binding bars
Journal of Constructional Steel Research 62 (2006) 472–483 www.elsevier.com/locate/jcsr
Axial load behavior of square CFT stub column with binding bars Jian Cai ∗ , Zhen-Qiang He Department of Civil Engineering, South China University of Technology, Guangzhou 510641, China Received 8 March 2005; accepted 28 September 2005
Abstract This paper is concerned with the axial load behavior of square concrete filled steel tubular (S-CFT) stub columns with binding bars provided to improve the mechanical behavior of S-CFT columns. Ten specimens with binding bars and 5 specimens without binding bars were tested to examine the effects of width-to-thickness ratios and binding bars on ultimate strength, stiffness and ductility of S-CFT columns. A method for calculating ultimate strength is proposed based on a constitutive model of confined concrete and a simplification corresponding to this method is conducted. Finally, the method proposed in this paper is verified with experimental results in this test program and data from other experiments. Corresponding values of ultimate strength calculated by EC4(1996) and GJB(2000) are given respectively for comparison. For S-CFT stub columns with binding bars, the results predicted by the method proposed herein agree well with the experimental results while that predicted by the methods of EC4(1996) and GJB(2000) scatter from the experimental results; for S-CFT without binding bars, the results given by the three methods mentioned above are all reasonable. c 2005 Elsevier Ltd. All rights reserved. Keywords: Square CFT stub column; Binding bars; Ultimate strength; Load-bearing capacity
1. Introduction Square concrete filled steel (CFT) columns are used gradually more and more as one of the main structural elements for resisting both vertical and lateral loads in multistory and tall building columns due to their advantages compared to circular CFT columns such as: (1) the cross-section shape agreeing well with the design need of the architecture plane of buildings; (2) more convenient construction measures at beam–column joints resulting in easy connection and less cost; (3) large moment of inertia of cross-section which leads to higher capacity of resisting lateral load. However, the axial load-bearing capacity of square CFT columns is lower than that of circular CFT columns because of the little effect of concrete confinement. It is commonly known that circular CFT columns have high strength, ductility and large energy absorption owing to their consistently symmetrical confinement on a concrete core supplied by a steel tube under axially compressive loading, in which state the concrete core is subjected to three-dimensional compression so that the unit axial strength of concrete is enhanced greatly. The effect is shown in Fig. 1. But for square ∗ Corresponding author. Tel.: +86 020 87112437; fax: +86 020 87112437.
E-mail address: [email protected] (J. Cai). c 2005 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2005.09.010
CFT columns, it is not the case. Zhang [1] investigated the stress distribution in the cross-section of stub square CFT columns with a finite element method and found that effective confinement of concrete lies in the corner regions, decreases quickly beyond these regions and eventually vanishes at the center of the side walls as the hoop tension developed along the side walls is not constant. Furlong [2] conducted a test on 13 specimens with width-to-thickness ratio D/t ranging from 29 to 98. Results showed that confinement of the concrete core contributed nothing to the load-bearing capacity. Knowles and Park [3] investigated 12 circular and 7 square composite columns with D/t of 15, 22 and 59, and L/D ratios > 11. It was concluded that the confinement of the concrete core contributed only to increasing the overall load-bearing capacity of the short circular CFT columns owing to the increase of concrete strength resulting from tri-axial confinement effect. Tomii et al. [4] investigated about 270 circular, octagonal and square CFT columns. Concrete confinement was observed in circular and many octagonal specimens at high axial loads, but square tubes provided very little confinement of the concrete because the wall of the square tube resisted the concrete pressure by plate bending, instead of the membrane-type hoop stresses. Schneider [5] tested 3 circular, 5 square and 6 rectangular specimens with D/t ratios ranging from 17 to 47,
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Nomenclature Aa As Ac D Ea Es Ec f cu f ck f ay fy as bs ds t L Nno Nuc Nue φ1 φ2 σ ε ξ ζ
area of steel cross-section area of binding bar (steel bar) area of concrete cross-section width of square steel tube elastic modulus of steel elastic modulus of steel bar elastic modulus of concrete characteristic 28-day cubic strength of concrete characteristic strength of concrete defined as f ck = 0.67 f cu yield strength of steel yield strength of steel bar transverse space of binding bar arrangement longitudinal space of binding bar arrangement diameter of binding bar wall thickness of steel tube length of steel tube nominal strength of the composite columns, defined as Nno = f ay Aa + fck Ac predicted ultimate strength of composite columns experimental ultimate strength of composite columns strength coefficient of steel strength coefficient of concrete stress strain constraining factor (= fay Aa /( f ck Ac )) constraining factor of binding bar (= f y As /( f ck as bs ))
and L/D ratios of 4.3(4.4), 4.8 and 4.0. A finite element method with program ABAQUS was applied to nonlinear analytical modeling. It was shown that circular steel tubes offered much more post-yield axial ductility than square or rectangular tube sections. All circular tubes were classified as strainhardening, while only the small D/t ratios, approximately D/t < 20, exhibited strain-hardening characteristics for square or rectangular tubes. Significant confinement was not present for most specimens until the axial load reaches almost 92% of the yield strength of the column. Furthermore, the square and rectangular tube walls, in most cases, did not offer significant concrete core confinement beyond the yield load of the composite column. Local wall buckling for square and rectangular tubes occurred earlier than that for circular tubes. Li et al. [6] studied experimentally 14 square specimens including 6 CFT, 2 square steel tube and 6 plain concrete columns. Results indicated that square CFT stub columns exceeded the nominal load-bearing capacity in a range of 5%–30% due to the concrete confinement even though the D/t ratios were large. To improve the behavior of square CFT columns, some stiffening measures have been proposed. Ge and Usami [7] adopted the method of welding a longitudinal steel strip on the internal surface of a steel tube (as shown in Fig. 2(b)). The experimental results indicated that the significant stiffening
Fig. 1. Stresses in circular CFT column.
Fig. 2. Cross-sections of square CFT columns with different stiffened measures. (a) Normal cross-section; (b) with stiffened strips; (c) with shear studs; and (d) with inclined tie bars.
effects of longitudinal stiffeners on the strength could be expected in both the steel column and concrete-filled column because of stiffening effects against the buckling mode of the plate panels and the stiffeners sharing the axial load. But this method also causes a severe strength loss after local buckling occurred. Lin et al. [8] adopted the approach of welding shear studs (shown in Fig. 2(c)). It was found that the shearing studs did enhance the ductility of square CFT columns though they contributed nothing to strength. The two stiffening schemes mentioned previously primarily aim at enhancing the strength of the steel tube and the bond of interface between the steel tube and concrete core except for improving the concrete confinement. Shear studs are used as shear connectors to ensure reliable stiffness of the composite cross-section even in the region of elastic behavior [9]. Huang et al. [10] proposed a new stiffening scheme of welding a set of four inclined steel bars (so-called tie bars) at regular spacing along the longitudinal axis of the steel tube to actively strengthen the confinement of the concrete core provided by the steel tube (shown in Fig. 2(d)). According to their study, the tie bars help enhancing the behavior of square CFT columns in terms of ultimate strength and ductility. However, the layout of tie bars is complicated for construction due to its inclined setting in cross-section and stress may concentrate severely at the joins of tie bars and steel plate. Aiming at overcoming the shortcoming of weak concrete confinement at the center of side walls of square steel tubes,
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Fig. 3. (a) Test setup; and (b) test specimens.
a novel stiffening scheme is presented herein and the scheme involves level orthotropic binding bars arranged at spacings along the longitudinal axis of the steel tube. The typical stiffener arrangement is displayed in Fig. 3(b). In order to obtain an optimization of concrete confinement, the amount of binding bars can be conveniently adjusted to match with the steel plate and the concrete core by varying the binding bars’ level and longitudinal spacing. To investigate the effect of the proposed stiffening scheme, a test was carried out on 15 square CFT stub columns, including 10 with binding bars and 5 without as contrast. The primary parameters considered in this test program are as follows: (1) width–thickness ratio B/t; (2) level spacing as and longitudinal spacing bs of the binding bars; (3) diameters of binding bars; and (4) strength of steel tube. These factors were experimentally investigated to assess their influence on ultimate strength, initial stiffness, and ductility. Finally, a method is proposed and verified herein for calculating the ultimate strength of S-CFT stub columns under axial loading. 2. Experimental program The square steel tubes were fabricated by welding together four pieces of flat plates. Before assembling the tube, holes on the steel plates were made by drilling where the binding bars are arranged. Each binding bar joins together with the steel tube through two square stiffening steel plates on its two ends by welding, which is detailed in Fig. 4. The material properties of the steel tubes were obtained from tensile tests of coupons taken from each batch of steel plates before manufacturing. Properties of all specimens are summarized in Table 1. The compression tests were carried out in a 15 000 kN universal testing machine shown in Fig. 3. Average longitudinal
Fig. 4. Detail of binding bar construction.
strains were obtained from four linear variable differential transducers that measured axial shortenings between the two end plates. The wire strain gages were located as shown in Fig. 3(b) to measure level and vertical strains of the steel panels nearby the two ends and at the middle of the tubes. Two gages were used to measure the tension strain in binding bars arranged at the middle of the specimens. All data were collected by an Automatic-Switching-Box. Axial loads were applied to the specimen at a rate of 100 kN/min in the initial elastic stage. After the load–displacement curve came to a bifurcation from a straight line, it was turned to a displacement–load control at a rate of 0.5 mm/min. It was controlled by computer automatically during the two loading stages. 3. Experimental results and discussion 3.1. Load–deformation relationship and failure mode It was observed that the specimen C1 failed in the early loading stage because of a sudden blowout of one of the seam welds at corners that formed the steel tube due to welding deficiencies so that the result obtained is not true, which tells us
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Table 1 Properties for square concrete-filled steel tube components Test no.
Specimen
D × t × L (mm)
as × bs × ds (mm)
D/t
f ay (MPa)
f sy (MPa)
f ck (MPa)
Nue (kN)
Nno (kN)
Nue /Nno
Nuey /Nuen
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500
— 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 150 × 150 × 16
50 50 50 75 75 75 37.5 37.5 37.5 25 25 25 50 50 50
382.5 382.5 382.5 341.93 341.93 341.93 387.98 387.98 387.98 345.04 345.04 345.04 292.48 292.48 382.5
344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 365.49
39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82
– 6600 8654 5300 6243 7255 5600 7878 8170 6588 8436 9749 4370 6140 7375
– 6002 6002 5015 5015 5015 6837 6837 6837 7803 7803 7803 5367 5367 6002
– 1.100 1.442 1.057 1.245 1.447 0.819 1.152 1.195 0.844 1.081 1.245 0.814 1.144 1.229
– – – 1.000 1.178 1.369 1.000 1.407 1.459 1.000 1.281 1.480 1.000 1.405 1.272
Note: — means no binding bars available.
Fig. 5. Typical local buckling of steel tube wall: (a) specimen C4 and (b) specimen C5.
that it is important for square CFT formed by welding that the quality of welds be guaranteed to ensure failure is not owing to cracks of the weld seam. Thus the result of C1 is removed and not included herein. The failure of the other specimens was caused by local and post-local buckling, whose typical modes are shown in Fig. 5. The measured ultimate strength of each specimen is given in Table 1. The test load (N) versus average longitudinal strain (ε) curves are shown in Fig. 6. The test load (N) is plotted against hoop strain (εh ) at the center (noted as “cent” following the serial number) and that at the extreme (noted as “extr” following the serial number) of the side wall of the steel tube at mid-span of specimens in Fig. 7, while the test load (N) against strain (εs ) at the end (noted as “#1”) and at the middle (noted as “#2”) of the binding bar in Fig. 8.
the same. Moreover, the ultimate strength and corresponding strain of specimens increase while the spacing of binding bars decreases. Compared with the specimens without binding bars in Table 1, the specimens with binding bars have higher ultimate strengths, which are beyond the nominal strength in a top range of about 40%–50%, owing to the binding bars constraining the lateral deformation of the steel tube and concrete core more effectively. It is clearly shown in Fig. 8 that the binding bars contribute to improving the axial-loaded behavior of square CFT columns. The tension strain of binding bars develops gradually with the load increasing and almost all reaching its yield strain while the load reaches a peak value. Fig. 7 also shows that the hoop strain of steel tubes develops more quickly and sufficiently with the spacing of binding bars decreasing, which means that confinement of the concrete core is strengthened and leads to an increase of the ultimate strength of specimens. However, for the specimens without binding bars, the hoop strain of steel tubes develops inadequately even though the load reaches an ultimate value. In this case, the confinement of concrete is very weak and can be ignored. It is considered that there exists no interaction between the concrete core and steel tube and the two components of the column work respectively. 3.3. Thickness of steel tube Fig. 6(g)–(h) show that the thickness of the steel tube has an important influence on axial load behavior of square CFT stub columns. With the thickness of steel tube increasing, i.e. the D/t ratio decreasing, the ultimate strength and the corresponding strain increases and the columns become more ductile.
3.2. Binding bars
3.4. Yield strength of steel
It can be observed from Fig. 6(a)–(e) that ultimate strength of the specimens with binding bars is higher than that of the specimens without binding bars as the other parameters are
It can be seen in Fig. 6(f) that the higher yield strength of steel helps in improving the ultimate strength of a specimen, but the value of improvement is quite small. The specimens
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(a) Varial parameter: as (t = 6 mm).
(b) Varial parameter: as (t = 4 mm).
(c) Varial parameter: as (t = 8 mm).
(d) Varial parameter: as (t = 12 mm).
(e) Varial parameter: ds .
(f) Varial parameter: strength of steel.
(g) Varial parameter: t (as = 150 mm).
(h) Varial parameter: t (as = 100 mm).
Fig. 6. Axial load (N ) versus average longitudinal strain (ε).
C14 and C2 are in usage of steel with yield strengths of 292.48 N/mm2 and 382.50 N/mm2 respectively. The ultimate strength of C2 is only somewhat higher than that of C14 in about 7%. It implies that the yield strength of steel contributes nothing to the confinement of concrete and the increase of ultimate strength is not owing to the confinement of concrete but the increase of the yield strength of steel only. Both cross-
sections containing steel ratios ρa , defined as Aa /(Aa + Ac ), are 7.84%, that is in a normal range of engineering in practice. 4. Confinement effects of binding bars The confinement effects of binding bars on the behavior of CFT stub columns with binding bars can be summarized in two aspects as follows.
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Fig. 7. Axial load (N ) versus hoop strain of steel tube (εh ).
4.1. Constraining lateral deformation of concrete core The interaction among the components of CFT stub column with binding bars is illustrated in Fig. 9. Assuming that a separate part with the depth along the longitudinal axis is equal to the longitudinal spacing of binding bars (bs ), it can result from Fig. 9 according to the equilibrium of forces as follows D − 1 Fs = 0 (1) fl bs (D − 2t) − σh bs · 2t − as Fs = E s εs As . (2) Substituting Eq. (2) into Eq. (1) produces fl =
σh +
D−as As 2t as bs
E s εs
D/(2t) − 1
.
(3)
It was observed from Fig. 8 that the binding bars yielded when the specimens came to ultimate strength. So Eq. (3) can be rewritten as fl =
D−as As 2t as bs
fy σh + D/(2t) − 1 D/(2t) − 1
(4)
where the second part on the right hand side indicates the contribution of binding bars to lateral pressure on concrete, which shows that the lateral confining stress of the concrete core fl increases while the spacing as and bs decreases. 4.2. Effect on local buckling of steel tube The local buckling of a steel plate of the CFT column with or without binding bars is shown in Fig. 10. The concrete in-fill is considered as a rigid medium, restraining the free formation of buckles and forcing them to form away from the concrete. He et al. [11] applied an energy formulation to calculate the critical stress in a plate assuming that the displacement is a cosine function. The critical stress is expressed as 2 π 2 Ea t σcr = k (5) 12(1 − µ2 ) b where the buckling parameter k is given by 2 6 2 k= + 6φ + 4 3 φ2
(6)
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(a) C2.
(b) C3.
(c) C5.
(d) C6.
(e) C8.
(f) C9.
(g) C11.
(h) C12. Fig. 8. Axial load (N ) versus tension strain of binding bar (εs ).
in which the wavelength parameter φ is defined as: φ = a/b. It is observed that the half wavelength of local buckling a is nearly equal to the width b [12]. So it is reasonable to assume a = b for specimens without binding bars. Substituting a = b into Eq. (6) results in k = 10.67. But for specimens
with binding bars, it can be observed from this experiment that all of the buckling takes place at the spacing between two adjacent rows of level binding bars. It is considered clamped where the rows of level binding bars are located, i.e., a = bs . For specimens with binding bars in this experimental program,
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(i) C14.
479
(j) C15. Fig. 8. (continued)
Fig. 9. Lateral confinement of concrete. (a) Local buckling for steel plate of CFT column without binding bars.
bs = D/2 and b = D. Applying bs = D/2 and b = D to Eq. (5) results in k = 19.67, which is 1.84 times that of specimens without binding bars. It indicates that the local buckling of the steel plate can be delayed or even avoided by an appropriate longitudinal spacing of binding bars. 5. Calculation of ultimate strength 5.1. Primary methods in current codes and specifications Methods for calculating the ultimate strength of normalsectioned square CFT stub columns under axial compressive loading are included in many current codes and specifications such as AIJ [13], EC4 [14], LRFD [15] and GJB41422000 [16]. The confining effect of the steel tube on the concrete core is ignored in the methods of AIJ, EC4 and LRFD. GJB4142-2000 takes into account the contribution of the confinement effect to the ultimate strength of square CFT stub columns, regarding the concrete in-fill and the steel tube in a column as an entity and taking into account concrete confinement with the so-called constraining factor ξ . The ultimate strength can be expressed as Nu = Asc f scy
(7)
Asc = Aa + Ac
(8)
fscy = (2.212 + Bξ + Cξ ) fck 2
(9)
where B = 0.1381 f y /235 + 0.7646; C = −0.0727 f ck /20 + 0.0216. The formulae described above also do not consider the contribution of binding bars to the ultimate strength of CFT columns with binding bars. A new method is proposed for predicting the ultimate strength of CFT stub columns with binding bars in Section 5.2 based on the experimental results.
(b) Local buckling for steel plate of CFT column with binding bars. Fig. 10. Local buckling for steel plates of CFT column.
5.2. Model It is noted that the methods existing in Ref. [13–15] assume that the steel tube is in a state of uniaxial compressive stress and the concrete obtains its uniaxial ultimate strength while steel yields. Actually the steel tube is subjected to lateral compression after the Poisson’s ratio of concrete exceeds that of steel in the upward loading stage, which leads to the steel tube being in a state of hoop tension and longitudinal compression and the concrete core being in a triaxial compressive state. The longitudinal compressive strength of the concrete core increases due to such a triaxial compression state. However, the increase in concrete strength outweighs the reduction in the yield strength of steel in vertical compression due to the confinement tension needed to contain the concrete [17]. The formulae for calculating the strength of square CFT stub columns with binding bars are expressed as Nu = Aa fa + Ac f cc
(10)
where f a is the longitudinal strength of steel and fcc the longitudinal strength of concrete.
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Then, from Eq. (13) the confinement effectiveness coefficient is given by
n bs tan θ 2 (as /D)2 tan θ 1− . (20) ke = 1 − 6 2(D − 2t) i=1
Fig. 11. Effectively confined regions for square CFT with binding bars.
In order to determine f cc , the constitutive model of confined concrete proposed by Mander et al. [18] is modified and applied herein. The ultimate uniaxial strength of confined concrete is given by 7.94 f l fl f cc = f ck −1.254 + 2.254 1 + (11) −2 fck f ck where fl is equivalent lateral confined stress, given herein by fl = ke fl
(12) fl
is calculated from Eq. (4). The confinement in which effectiveness coefficient ke is divided into ke1 , the level confinement effectiveness coefficient, and ke2 , the longitudinal confinement coefficient, i.e. ke = ke1 · ke2
(13)
where ke1 and ke2 take the form [18] as Ae1 Acc1 Ae2 = Acc2
ke1 =
(14)
ke2
(15)
where Ae1 and Ae2 are the level area of an effectively confined concrete core and longitudinal area of an effectively confined concrete core, while Acc1 and Acc2 are the level area of a concrete core and the longitudinal area of a concrete core respectively. The arching action shown in Fig. 11 is assumed to occur in the form of a second-degree parabola with an initial tangent angle θ . So that Ae1 and Acc1 are given by Ae1 = (D − 2t)2 −
n [(D − 2t)/(D/as )]2 tan θ i=1
6
Acc1 = (D − 2t)2 and applying Eqs. (16) and (17) to Eq. (14) produces n (as /D)2 tan θ ke1 = 1 − . 6 i=1
(16) (17)
(18)
ke2
θ=
π (13 + 9.2as /100) (rad). 180
(21)
It is shown that specimens with binding bars failed in postlocal buckling mode. The steel yielded as this type of column reached ultimate strength, supposed to obey the Von Mises criteria given by 2 f a2 − f a σh + σh2 = f ay .
(22)
For the local buckling strength of a steel plate f b in CFT columns, Ge and Usami [19] proposed a relationship as fb 1.2 0.3 − 2 ≤ 1.0 = f ay R R
(23)
which is ensured by keeping R ≥ 0.85; where R is the width–thickness ratio parameter, defined as D 12(1 − ν 2 ) f ay R= . (24) t Ea 4π 2 Then from Eq. (23), the stress states of steel tubes can be determined in the two cases as follows. For R ≥ 0.85 applying fa = fb to Eqs. (23) and (22) results in 1.2 0.3 − 2 f ay (in compression) (25) fa = R R 2 −3f2 f a − 4 f ay a (in tension). (26) σh = 2 For R < 0.85, the effects of local buckling can be ignored [19]. Sakino et al. [20] deduced a relationship between stress coefficient au and bu , which represent hoop stress to yield strength of steel ratio and longitudinal stress to yield strength of steel ratio respectively, based on a large number of results of experiments for circular CFT short columns. The value of coefficients au and bu given as −0.19 and 0.89 respectively are adopted herein to assume the value of hoop stress and longitudinal stress for steel in the case of R < 0.85. Therefore, σh and f a are expressed as follows σh = 0.19 f ay
(in tension)
(27)
f a = 0.89 f ay
(in compression).
(28)
5.3. Simplification of the method proposed
Similarly it can be deduced that
bs tan θ 2 = 1− . 2(b − 2t)
It is found that the initial tangent angle θ is mainly sensitive to level spacing of binding bars. Based on a linear regression, a simple form of expression is taken as
(19)
The method presented above is somewhat complicated and a simplification is proposed below.
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Fig. 12. φ1 –R relationship.
481
(a) Relationship of φ2 and ζ .
Assumed that Eq. (10) can be expressed alternatively as Nu = φ1 f ay Aa + φ2 f ck Ac
(29)
where φ1 and φ2 are the strength coefficient of steel and that of concrete, defined as φ1 =
fa , f ay
φ2 =
fcc . f ck
(30)
Based on the regression of data from this experiment program which is shown in Fig. 12, φ1 is given as 0.89 R < 0.85 (31) φ1 = 0.897R −0.7407 R ≥ 0.85. It is found that the uniaxial strength of concrete filled in a square steel tube with binding bars primarily depends on the constraining factor of the binding bars ζ and the width-to-thickness ratio parameter R. Fig. 13(a) shows that there exists an almost linear relationship between φ2 and ζ . Fig. 13(b) presents a nonlinear relationship of φ2 and R when the constraining factor of the binding bars is equal to zero (meaning specimens without binding bars arranged). Based on a double nonlinear regression through the data in Table 1, the strength coefficient of steel φ2 is given by φ2 = 1.039R −0.0861(7.3836ς + 1.0588).
(32)
5.4. Verification The predicted ultimate strengths of S-CFT stub columns with or without binding bars calculated by Eqs. (10) and (29) respectively are given in Table 2. To make a comparison, the extensive experimental data from other research such as Chen [21] and Han and Tao [22] are adopted and results predicted by the methods of EC4 and GJB4142-2000 are also given in Table 2. For specimens with binding bars tested in this program, the results predicted by the formulae proposed herein agree well with that of experiments with mean value and covariance of Nuc /Nue given as 1.037 and 0.008 respectively. Both the value of the mean and the covariance predicted by the simplified method are somewhat larger with the mean value and covariance as 1.060 and 0.012 respectively. EC4 gives a mean of Nuc /Nue as 0.912 while GJB 1.044. Both of the covariances given by EC4 and GJB are somewhat large with the value of 0.024 and 0.031 respectively owing to the two methods cannot take into account the contribution of binding bars and thus result in the covariance being relatively larger. For the normalsectioned S-CFT stub columns from Han and Tao [22], the two
(b) Relationship of φ2 and R. Fig. 13. Relationship of φ2 and z (or R).
methods proposed in this paper can also give reasonable results as those of EC4 and GJB do. 6. Conclusions The following conclusions can be drawn based on the results of this study: (1) Under axial loading, normal-sectioned square CFT stub columns without stiffening measures are prone to failing in local buckling, whose ultimate strength, plastic deformability and ductility are relatively low. The main reason is that the concrete confinement is not consistent along the side walls of the steel tube and only exists in the corner regions. The effect of confinement is very weak and usually neglected. The potential load-bearing capacity is not adequately in usage in this type of column. (2) The proposed stiffening scheme improves the axial load behavior of square CFT columns mainly on two aspects. One is that the concrete confinement beyond the corner regions is improved since the transverse deformation of the concrete core is constrained by the binding bars. The other is that the elastic local buckling of a steel plate can be delayed or even avoided through an appropriate longitudinal spacing of binding bars owing to the local buckling only taking place between the two adjacent rows of level binding bars. (3) The spacing and diameter of binding bars have an important influence on ultimate strength and plastic deformability of square CFT columns with binding bars. With spacing of binding bars decreasing and the diameter of binding bars increasing, the ultimate strength and corresponding strain of specimens with binding bars increase remarkably and the post load–strain curve decreases slowly.
482
Table 2 Comparison among ultimate strengths from prediction and experiment for square CFT columns with or without binding bars No. Specimen
B × t × L (mm)
as × bs × ds (mm) ξ
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500
16 17
C1 GZ02a
300 × 10 × 1500 150 × 150 × 14 300 × 10 × 1500 150 × 150 × 14
— 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 150 × 150 × 16
0.625 0.817 0.817 0.477 0.477 0.477 1.129 1.129 1.129 1.572 1.572 1.572 0.625 0.625 0.817
f ck (MPa)
Nue (kN) Formulae proposed in Formulae simplified this paper in this paper Nuc (kN) Nuc /Nue Nuc (kN) Nuc /Nue
EC4(1996) [14]
GBJ(2000) [16]
Nuc (kN)
Nuc /Nue
Nuc (kN)
Nuc /Nue
292.48 382.50 382.50 341.93 341.93 341.93 387.98 387.98 387.98 345.04 345.04 345.04 292.48 292.48 382.5
39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82
5800 6600 8654 5300 6243 7255 5600 7878 8170 6588 8436 9749 4370 6140 7375
5852 6622 8209 5293 6243 7037 6745 7722 7997 8571 9239 9772 4411 6184 7308
1.009 1.003 0.949 0.999 1.000 0.970 1.204 0.980 0.979 1.301 1.095 1.002 1.009 1.007 0.991
4543 6015 6751 5460 5395 6887 7237 7327 7977 7129 8601 9338 7744 9191 9915
0.857 0.964 0.931 0.941 1.235 1.122 1.096 0.994 0.922 1.273 1.092 1.143 1.176 1.090 1.017
5367 6002 6002 5015 5015 5015 6837 6837 6837 7803 7803 7803 5367 5367 6002
0.925 0.909 0.694 0.946 0.803 0.691 1.221 0.868 0.837 1.184 0.925 0.800 1.228 0.874 0.814
6268 6946 6946 5894 5894 5894 7797 7797 7797 8704 8704 8704 6268 6268 6946
1.081 1.052 0.803 1.112 0.944 0.812 1.392 0.990 0.954 1.321 1.032 0.893 1.434 1.021 0.942
This paper
1.581 366.86 2.410 357.72
34.34 21.96
7695 6634
8293 7012
1.078 1.057
8391 7174
1.090 1.081
6948 5871
0.903 0.885
7737 6371
1.005 0.960
[21]
Mean
1.037
1.060
0.912
1.044
COV
0.008
0.012
0.024
0.031
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
sczs1-1-1 sczs1-1-2 sczs1-1-3 sczs1-1-4 sczs1-1-5 sczs1-2-1 sczs1-2-2 sczs1-2-3 sczs1-2-4 sczs2-1-1 sczs2-1-2 sczs2-1-3 sczs2-1-4 sczs2-1-5 sczs2-2-1 sczs2-2-2 sczs2-2-3 sczs2-2-4 sczs2-3-1 sczs2-3-2
120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 140 × 3.8 × 420 140 × 3.8 × 420 140 × 3.8 × 420 140 × 3.8 × 420 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 140 × 5.9 × 420 140 × 5.9 × 420 140 × 5.9 × 420 140 × 5.9 × 420 200 × 5.9 × 600 200 × 5.9 × 600
— — — — — — — — — — — — — — — — — — — —
1.69 1.479 1.479 0.936 0.879 2.437 2.334 0.714 0.714 2.462 2.462 2.863 1.407 1.407 3.793 0.791 1.132 1.132 2.36 2.36
330.1 330.1 330.1 330.1 330.1 330.1 330.1 330.1 330.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1
27.3 31.2 31.2 49.3 52.5 16 16.7 54.6 54.6 30 30 25.8 52.5 52.5 16.3 18.3 54.6 54.6 17.6 17.6
882 882 921.2 1080 1078 940.8 921.6 1499.4 1470 1176 1117.2 1195.6 1460.2 1372 1342.6 1292.6 2009 1906.1 2058 1960
915 964 964 1194 1234 964 976 1646 1646 1188 1188 1138 1453 1453 1273 1306 1912 1912 2162 2162
1.037 1.093 1.047 1.105 1.145 1.025 1.060 1.098 1.120 1.010 1.063 0.952 0.995 1.059 0.948 1.010 0.952 1.003 1.050 1.103
909.4 965.2 965.2 1224 1270 921.6 935.3 1678 1678 1183 1183 1125 1493 1493 1216 1252 1947 1947 2012 2012
1.031 1.094 1.048 1.133 1.178 0.980 1.015 1.119 1.141 1.006 1.059 0.941 1.023 1.089 0.906 0.969 0.969 1.022 0.978 1.055
928 977 977 1206 1246 964 976 1641 1641 1216 1216 1167 1479 1479 1284 1315 1914 1914 2094 2094
1.052 1.108 1.061 1.117 1.156 1.025 1.059 1.094 1.116 1.034 1.088 0.976 1.013 1.078 0.956 1.018 0.952 1.004 1.018 1.069
886.8 927.5 927.5 1123 1158 945.8 954.9 1495 1495 1159 1159 1123 1382 1382 1283 1299 1768 1768 2021 2021
1.005 1.052 1.007 1.040 1.075 1.005 1.036 0.997 1.017 0.985 1.037 0.940 0.946 1.007 0.956 1.005 0.880 0.928 0.982 1.031
Mean
1.044
1.038
1.050
0.997
COV
0.003
0.005
0.003
0.002
Note: — means specimen without binding bars.
Resource
[22]
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
f ay (MPa)
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
(4) Ultimate strength predicted by the methods proposed in this paper is reasonable for square CFT stub columns with or without binding bars, while that calculated by EC4(1996) and GJB(2000) scatters quite a bit from the experimental results of square CFT stub columns with binding bars owing to not considering the contribution of binding bars. Acknowledgements The work described in this paper is part of the project entitled “Research on behavior of abnormal-shaped CFT stub columns”, funded by Natural Science Key Foundation of Guangdong Province in China under Grant No. 012356. This support is sincerely appreciated. Additionally, special thanks to Xing Chen, senior engineer in Arch. & Civil Design Research Institute of Guangdong, for his skilled assistance. References [1] Zhang ZG. Analysis of mechanism and load-bearing capacity of square concrete-filled steel under axial load. China Ind Constr 1989;11:2–8 [in Chinese]. [2] Forlong RW. Strength of steel-encased concrete beam–columns. J Struct Div, ASCE 93(5):113–24. [3] Knowles RB, Park R. Strength of concrete-filled steel tubular columns. J Struct Div, ASCE 95(12):2565–87. [4] Tomii M, Yoshimura K, Morishita Y. Experimental studies on concrete filled steel tubular stub columns under concentric loading. In: Proc., int. colloquium on stability of structure under static and dynamic loads. p. 718–41. [5] Schneider SP. Axially loaded concrete-filled steel tubes. J Struct Eng 1998;124(10):1125–38. [6] Li XL, Yu Y et al. Study on behavior of square concrete-filled steel under axial load: experiment. China Build Struct 1999;(10):41–3 [in Chinese].
483
[7] Ge HB, Usami T. Strength of concrete-filled thin-walled steel box column: experiment. J Struct Eng, ASCE 1992;118(11):3036–54. [8] Lin TI, Huang CM, Chen SY. Concrete-filled tubular steel columns subjected to eccentric axial load. J Chin Inst Civil Hydraulic Eng 1993; 5(4):377–86 [in Chinese]. [9] Kitada T. Ultimate strength and ductility of state-of-the-art concrete-filled steel bridge piers in Japan. Eng Struct 1998;20(4–6):347–54. [10] Huang CS, Yeh YK et al. Axial load behavior of stiffened concrete-filled steel columns. J Struct Eng, ASCE 2002;128(9):1222–30. [11] He BK, Yang XB, Zhou TH. Theoretical analysis on local buckling behavior of concrete filled rectangular steel tube column subjected to axial force. J Xi’an Univ of Arch & Tech (Natural Science Edition) 2002;34(3): 210–3 [in Chinese]. [12] Uy B. Local and post-local buckling of concrete-filled steel welded box columns. J Constr Steel Res 1998;47(1–2):47–72. [13] Architectural Institute of Japan (AIJ). Recommendations for design and construction of concrete filled steel tubular structures. October 1997. [14] EC4. Design of steel and concrete structures, Part1, 1, general rules and rules for building. DD ENV 1994-1-1:1996. London WI A2BS: British Standards Institution. [15] AISC. Load and Resistance Factor Design (LRFD). Specification for structural steel buildings. Amer Inst Steel Constr, 25(4):2–16. [16] GJB4142-2000, 2001. Technical specifications for early-strength model composite structures. Peking, China [in Chinese]. [17] Shanmugam HE, Lakshmi B. State of the art report on steel–concrete composite columns. J Constr Steel Res 2001;(57):1041–80. [18] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. J Struct Eng, ASCE 1988;114(8):1807–26. [19] Ge HB, Usami T. Strength analysis of concrete filled thin-walled steel box columns. J Constr Steel Res 1994;30:259–81. [20] Sakina K, Nakahara H et al. Behavior of centrally loaded concrete-filled steel-tube short columns. J Struct Eng, ASCE 2004;130(2):180–8. [21] Chen DM. Foundational study on mechanic behavior of abnormal-shaped CFT columns with binding bars. MS thesis. Guangzhou (China): South China University of Technology; 2000. [22] Han LH, Tao Z. Study on behavior of concrete filled square steel tube under axial load. China J Civ Eng 2001;34(2):17–25 [in Chinese].
Axial load behavior of square CFT stub column with binding bars Jian Cai ∗ , Zhen-Qiang He Department of Civil Engineering, South China University of Technology, Guangzhou 510641, China Received 8 March 2005; accepted 28 September 2005
Abstract This paper is concerned with the axial load behavior of square concrete filled steel tubular (S-CFT) stub columns with binding bars provided to improve the mechanical behavior of S-CFT columns. Ten specimens with binding bars and 5 specimens without binding bars were tested to examine the effects of width-to-thickness ratios and binding bars on ultimate strength, stiffness and ductility of S-CFT columns. A method for calculating ultimate strength is proposed based on a constitutive model of confined concrete and a simplification corresponding to this method is conducted. Finally, the method proposed in this paper is verified with experimental results in this test program and data from other experiments. Corresponding values of ultimate strength calculated by EC4(1996) and GJB(2000) are given respectively for comparison. For S-CFT stub columns with binding bars, the results predicted by the method proposed herein agree well with the experimental results while that predicted by the methods of EC4(1996) and GJB(2000) scatter from the experimental results; for S-CFT without binding bars, the results given by the three methods mentioned above are all reasonable. c 2005 Elsevier Ltd. All rights reserved. Keywords: Square CFT stub column; Binding bars; Ultimate strength; Load-bearing capacity
1. Introduction Square concrete filled steel (CFT) columns are used gradually more and more as one of the main structural elements for resisting both vertical and lateral loads in multistory and tall building columns due to their advantages compared to circular CFT columns such as: (1) the cross-section shape agreeing well with the design need of the architecture plane of buildings; (2) more convenient construction measures at beam–column joints resulting in easy connection and less cost; (3) large moment of inertia of cross-section which leads to higher capacity of resisting lateral load. However, the axial load-bearing capacity of square CFT columns is lower than that of circular CFT columns because of the little effect of concrete confinement. It is commonly known that circular CFT columns have high strength, ductility and large energy absorption owing to their consistently symmetrical confinement on a concrete core supplied by a steel tube under axially compressive loading, in which state the concrete core is subjected to three-dimensional compression so that the unit axial strength of concrete is enhanced greatly. The effect is shown in Fig. 1. But for square ∗ Corresponding author. Tel.: +86 020 87112437; fax: +86 020 87112437.
E-mail address: [email protected] (J. Cai). c 2005 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2005.09.010
CFT columns, it is not the case. Zhang [1] investigated the stress distribution in the cross-section of stub square CFT columns with a finite element method and found that effective confinement of concrete lies in the corner regions, decreases quickly beyond these regions and eventually vanishes at the center of the side walls as the hoop tension developed along the side walls is not constant. Furlong [2] conducted a test on 13 specimens with width-to-thickness ratio D/t ranging from 29 to 98. Results showed that confinement of the concrete core contributed nothing to the load-bearing capacity. Knowles and Park [3] investigated 12 circular and 7 square composite columns with D/t of 15, 22 and 59, and L/D ratios > 11. It was concluded that the confinement of the concrete core contributed only to increasing the overall load-bearing capacity of the short circular CFT columns owing to the increase of concrete strength resulting from tri-axial confinement effect. Tomii et al. [4] investigated about 270 circular, octagonal and square CFT columns. Concrete confinement was observed in circular and many octagonal specimens at high axial loads, but square tubes provided very little confinement of the concrete because the wall of the square tube resisted the concrete pressure by plate bending, instead of the membrane-type hoop stresses. Schneider [5] tested 3 circular, 5 square and 6 rectangular specimens with D/t ratios ranging from 17 to 47,
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473
Nomenclature Aa As Ac D Ea Es Ec f cu f ck f ay fy as bs ds t L Nno Nuc Nue φ1 φ2 σ ε ξ ζ
area of steel cross-section area of binding bar (steel bar) area of concrete cross-section width of square steel tube elastic modulus of steel elastic modulus of steel bar elastic modulus of concrete characteristic 28-day cubic strength of concrete characteristic strength of concrete defined as f ck = 0.67 f cu yield strength of steel yield strength of steel bar transverse space of binding bar arrangement longitudinal space of binding bar arrangement diameter of binding bar wall thickness of steel tube length of steel tube nominal strength of the composite columns, defined as Nno = f ay Aa + fck Ac predicted ultimate strength of composite columns experimental ultimate strength of composite columns strength coefficient of steel strength coefficient of concrete stress strain constraining factor (= fay Aa /( f ck Ac )) constraining factor of binding bar (= f y As /( f ck as bs ))
and L/D ratios of 4.3(4.4), 4.8 and 4.0. A finite element method with program ABAQUS was applied to nonlinear analytical modeling. It was shown that circular steel tubes offered much more post-yield axial ductility than square or rectangular tube sections. All circular tubes were classified as strainhardening, while only the small D/t ratios, approximately D/t < 20, exhibited strain-hardening characteristics for square or rectangular tubes. Significant confinement was not present for most specimens until the axial load reaches almost 92% of the yield strength of the column. Furthermore, the square and rectangular tube walls, in most cases, did not offer significant concrete core confinement beyond the yield load of the composite column. Local wall buckling for square and rectangular tubes occurred earlier than that for circular tubes. Li et al. [6] studied experimentally 14 square specimens including 6 CFT, 2 square steel tube and 6 plain concrete columns. Results indicated that square CFT stub columns exceeded the nominal load-bearing capacity in a range of 5%–30% due to the concrete confinement even though the D/t ratios were large. To improve the behavior of square CFT columns, some stiffening measures have been proposed. Ge and Usami [7] adopted the method of welding a longitudinal steel strip on the internal surface of a steel tube (as shown in Fig. 2(b)). The experimental results indicated that the significant stiffening
Fig. 1. Stresses in circular CFT column.
Fig. 2. Cross-sections of square CFT columns with different stiffened measures. (a) Normal cross-section; (b) with stiffened strips; (c) with shear studs; and (d) with inclined tie bars.
effects of longitudinal stiffeners on the strength could be expected in both the steel column and concrete-filled column because of stiffening effects against the buckling mode of the plate panels and the stiffeners sharing the axial load. But this method also causes a severe strength loss after local buckling occurred. Lin et al. [8] adopted the approach of welding shear studs (shown in Fig. 2(c)). It was found that the shearing studs did enhance the ductility of square CFT columns though they contributed nothing to strength. The two stiffening schemes mentioned previously primarily aim at enhancing the strength of the steel tube and the bond of interface between the steel tube and concrete core except for improving the concrete confinement. Shear studs are used as shear connectors to ensure reliable stiffness of the composite cross-section even in the region of elastic behavior [9]. Huang et al. [10] proposed a new stiffening scheme of welding a set of four inclined steel bars (so-called tie bars) at regular spacing along the longitudinal axis of the steel tube to actively strengthen the confinement of the concrete core provided by the steel tube (shown in Fig. 2(d)). According to their study, the tie bars help enhancing the behavior of square CFT columns in terms of ultimate strength and ductility. However, the layout of tie bars is complicated for construction due to its inclined setting in cross-section and stress may concentrate severely at the joins of tie bars and steel plate. Aiming at overcoming the shortcoming of weak concrete confinement at the center of side walls of square steel tubes,
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Fig. 3. (a) Test setup; and (b) test specimens.
a novel stiffening scheme is presented herein and the scheme involves level orthotropic binding bars arranged at spacings along the longitudinal axis of the steel tube. The typical stiffener arrangement is displayed in Fig. 3(b). In order to obtain an optimization of concrete confinement, the amount of binding bars can be conveniently adjusted to match with the steel plate and the concrete core by varying the binding bars’ level and longitudinal spacing. To investigate the effect of the proposed stiffening scheme, a test was carried out on 15 square CFT stub columns, including 10 with binding bars and 5 without as contrast. The primary parameters considered in this test program are as follows: (1) width–thickness ratio B/t; (2) level spacing as and longitudinal spacing bs of the binding bars; (3) diameters of binding bars; and (4) strength of steel tube. These factors were experimentally investigated to assess their influence on ultimate strength, initial stiffness, and ductility. Finally, a method is proposed and verified herein for calculating the ultimate strength of S-CFT stub columns under axial loading. 2. Experimental program The square steel tubes were fabricated by welding together four pieces of flat plates. Before assembling the tube, holes on the steel plates were made by drilling where the binding bars are arranged. Each binding bar joins together with the steel tube through two square stiffening steel plates on its two ends by welding, which is detailed in Fig. 4. The material properties of the steel tubes were obtained from tensile tests of coupons taken from each batch of steel plates before manufacturing. Properties of all specimens are summarized in Table 1. The compression tests were carried out in a 15 000 kN universal testing machine shown in Fig. 3. Average longitudinal
Fig. 4. Detail of binding bar construction.
strains were obtained from four linear variable differential transducers that measured axial shortenings between the two end plates. The wire strain gages were located as shown in Fig. 3(b) to measure level and vertical strains of the steel panels nearby the two ends and at the middle of the tubes. Two gages were used to measure the tension strain in binding bars arranged at the middle of the specimens. All data were collected by an Automatic-Switching-Box. Axial loads were applied to the specimen at a rate of 100 kN/min in the initial elastic stage. After the load–displacement curve came to a bifurcation from a straight line, it was turned to a displacement–load control at a rate of 0.5 mm/min. It was controlled by computer automatically during the two loading stages. 3. Experimental results and discussion 3.1. Load–deformation relationship and failure mode It was observed that the specimen C1 failed in the early loading stage because of a sudden blowout of one of the seam welds at corners that formed the steel tube due to welding deficiencies so that the result obtained is not true, which tells us
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475
Table 1 Properties for square concrete-filled steel tube components Test no.
Specimen
D × t × L (mm)
as × bs × ds (mm)
D/t
f ay (MPa)
f sy (MPa)
f ck (MPa)
Nue (kN)
Nno (kN)
Nue /Nno
Nuey /Nuen
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500
— 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 150 × 150 × 16
50 50 50 75 75 75 37.5 37.5 37.5 25 25 25 50 50 50
382.5 382.5 382.5 341.93 341.93 341.93 387.98 387.98 387.98 345.04 345.04 345.04 292.48 292.48 382.5
344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 344.45 365.49
39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82
– 6600 8654 5300 6243 7255 5600 7878 8170 6588 8436 9749 4370 6140 7375
– 6002 6002 5015 5015 5015 6837 6837 6837 7803 7803 7803 5367 5367 6002
– 1.100 1.442 1.057 1.245 1.447 0.819 1.152 1.195 0.844 1.081 1.245 0.814 1.144 1.229
– – – 1.000 1.178 1.369 1.000 1.407 1.459 1.000 1.281 1.480 1.000 1.405 1.272
Note: — means no binding bars available.
Fig. 5. Typical local buckling of steel tube wall: (a) specimen C4 and (b) specimen C5.
that it is important for square CFT formed by welding that the quality of welds be guaranteed to ensure failure is not owing to cracks of the weld seam. Thus the result of C1 is removed and not included herein. The failure of the other specimens was caused by local and post-local buckling, whose typical modes are shown in Fig. 5. The measured ultimate strength of each specimen is given in Table 1. The test load (N) versus average longitudinal strain (ε) curves are shown in Fig. 6. The test load (N) is plotted against hoop strain (εh ) at the center (noted as “cent” following the serial number) and that at the extreme (noted as “extr” following the serial number) of the side wall of the steel tube at mid-span of specimens in Fig. 7, while the test load (N) against strain (εs ) at the end (noted as “#1”) and at the middle (noted as “#2”) of the binding bar in Fig. 8.
the same. Moreover, the ultimate strength and corresponding strain of specimens increase while the spacing of binding bars decreases. Compared with the specimens without binding bars in Table 1, the specimens with binding bars have higher ultimate strengths, which are beyond the nominal strength in a top range of about 40%–50%, owing to the binding bars constraining the lateral deformation of the steel tube and concrete core more effectively. It is clearly shown in Fig. 8 that the binding bars contribute to improving the axial-loaded behavior of square CFT columns. The tension strain of binding bars develops gradually with the load increasing and almost all reaching its yield strain while the load reaches a peak value. Fig. 7 also shows that the hoop strain of steel tubes develops more quickly and sufficiently with the spacing of binding bars decreasing, which means that confinement of the concrete core is strengthened and leads to an increase of the ultimate strength of specimens. However, for the specimens without binding bars, the hoop strain of steel tubes develops inadequately even though the load reaches an ultimate value. In this case, the confinement of concrete is very weak and can be ignored. It is considered that there exists no interaction between the concrete core and steel tube and the two components of the column work respectively. 3.3. Thickness of steel tube Fig. 6(g)–(h) show that the thickness of the steel tube has an important influence on axial load behavior of square CFT stub columns. With the thickness of steel tube increasing, i.e. the D/t ratio decreasing, the ultimate strength and the corresponding strain increases and the columns become more ductile.
3.2. Binding bars
3.4. Yield strength of steel
It can be observed from Fig. 6(a)–(e) that ultimate strength of the specimens with binding bars is higher than that of the specimens without binding bars as the other parameters are
It can be seen in Fig. 6(f) that the higher yield strength of steel helps in improving the ultimate strength of a specimen, but the value of improvement is quite small. The specimens
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(a) Varial parameter: as (t = 6 mm).
(b) Varial parameter: as (t = 4 mm).
(c) Varial parameter: as (t = 8 mm).
(d) Varial parameter: as (t = 12 mm).
(e) Varial parameter: ds .
(f) Varial parameter: strength of steel.
(g) Varial parameter: t (as = 150 mm).
(h) Varial parameter: t (as = 100 mm).
Fig. 6. Axial load (N ) versus average longitudinal strain (ε).
C14 and C2 are in usage of steel with yield strengths of 292.48 N/mm2 and 382.50 N/mm2 respectively. The ultimate strength of C2 is only somewhat higher than that of C14 in about 7%. It implies that the yield strength of steel contributes nothing to the confinement of concrete and the increase of ultimate strength is not owing to the confinement of concrete but the increase of the yield strength of steel only. Both cross-
sections containing steel ratios ρa , defined as Aa /(Aa + Ac ), are 7.84%, that is in a normal range of engineering in practice. 4. Confinement effects of binding bars The confinement effects of binding bars on the behavior of CFT stub columns with binding bars can be summarized in two aspects as follows.
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477
Fig. 7. Axial load (N ) versus hoop strain of steel tube (εh ).
4.1. Constraining lateral deformation of concrete core The interaction among the components of CFT stub column with binding bars is illustrated in Fig. 9. Assuming that a separate part with the depth along the longitudinal axis is equal to the longitudinal spacing of binding bars (bs ), it can result from Fig. 9 according to the equilibrium of forces as follows D − 1 Fs = 0 (1) fl bs (D − 2t) − σh bs · 2t − as Fs = E s εs As . (2) Substituting Eq. (2) into Eq. (1) produces fl =
σh +
D−as As 2t as bs
E s εs
D/(2t) − 1
.
(3)
It was observed from Fig. 8 that the binding bars yielded when the specimens came to ultimate strength. So Eq. (3) can be rewritten as fl =
D−as As 2t as bs
fy σh + D/(2t) − 1 D/(2t) − 1
(4)
where the second part on the right hand side indicates the contribution of binding bars to lateral pressure on concrete, which shows that the lateral confining stress of the concrete core fl increases while the spacing as and bs decreases. 4.2. Effect on local buckling of steel tube The local buckling of a steel plate of the CFT column with or without binding bars is shown in Fig. 10. The concrete in-fill is considered as a rigid medium, restraining the free formation of buckles and forcing them to form away from the concrete. He et al. [11] applied an energy formulation to calculate the critical stress in a plate assuming that the displacement is a cosine function. The critical stress is expressed as 2 π 2 Ea t σcr = k (5) 12(1 − µ2 ) b where the buckling parameter k is given by 2 6 2 k= + 6φ + 4 3 φ2
(6)
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(a) C2.
(b) C3.
(c) C5.
(d) C6.
(e) C8.
(f) C9.
(g) C11.
(h) C12. Fig. 8. Axial load (N ) versus tension strain of binding bar (εs ).
in which the wavelength parameter φ is defined as: φ = a/b. It is observed that the half wavelength of local buckling a is nearly equal to the width b [12]. So it is reasonable to assume a = b for specimens without binding bars. Substituting a = b into Eq. (6) results in k = 10.67. But for specimens
with binding bars, it can be observed from this experiment that all of the buckling takes place at the spacing between two adjacent rows of level binding bars. It is considered clamped where the rows of level binding bars are located, i.e., a = bs . For specimens with binding bars in this experimental program,
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
(i) C14.
479
(j) C15. Fig. 8. (continued)
Fig. 9. Lateral confinement of concrete. (a) Local buckling for steel plate of CFT column without binding bars.
bs = D/2 and b = D. Applying bs = D/2 and b = D to Eq. (5) results in k = 19.67, which is 1.84 times that of specimens without binding bars. It indicates that the local buckling of the steel plate can be delayed or even avoided by an appropriate longitudinal spacing of binding bars. 5. Calculation of ultimate strength 5.1. Primary methods in current codes and specifications Methods for calculating the ultimate strength of normalsectioned square CFT stub columns under axial compressive loading are included in many current codes and specifications such as AIJ [13], EC4 [14], LRFD [15] and GJB41422000 [16]. The confining effect of the steel tube on the concrete core is ignored in the methods of AIJ, EC4 and LRFD. GJB4142-2000 takes into account the contribution of the confinement effect to the ultimate strength of square CFT stub columns, regarding the concrete in-fill and the steel tube in a column as an entity and taking into account concrete confinement with the so-called constraining factor ξ . The ultimate strength can be expressed as Nu = Asc f scy
(7)
Asc = Aa + Ac
(8)
fscy = (2.212 + Bξ + Cξ ) fck 2
(9)
where B = 0.1381 f y /235 + 0.7646; C = −0.0727 f ck /20 + 0.0216. The formulae described above also do not consider the contribution of binding bars to the ultimate strength of CFT columns with binding bars. A new method is proposed for predicting the ultimate strength of CFT stub columns with binding bars in Section 5.2 based on the experimental results.
(b) Local buckling for steel plate of CFT column with binding bars. Fig. 10. Local buckling for steel plates of CFT column.
5.2. Model It is noted that the methods existing in Ref. [13–15] assume that the steel tube is in a state of uniaxial compressive stress and the concrete obtains its uniaxial ultimate strength while steel yields. Actually the steel tube is subjected to lateral compression after the Poisson’s ratio of concrete exceeds that of steel in the upward loading stage, which leads to the steel tube being in a state of hoop tension and longitudinal compression and the concrete core being in a triaxial compressive state. The longitudinal compressive strength of the concrete core increases due to such a triaxial compression state. However, the increase in concrete strength outweighs the reduction in the yield strength of steel in vertical compression due to the confinement tension needed to contain the concrete [17]. The formulae for calculating the strength of square CFT stub columns with binding bars are expressed as Nu = Aa fa + Ac f cc
(10)
where f a is the longitudinal strength of steel and fcc the longitudinal strength of concrete.
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Then, from Eq. (13) the confinement effectiveness coefficient is given by
n bs tan θ 2 (as /D)2 tan θ 1− . (20) ke = 1 − 6 2(D − 2t) i=1
Fig. 11. Effectively confined regions for square CFT with binding bars.
In order to determine f cc , the constitutive model of confined concrete proposed by Mander et al. [18] is modified and applied herein. The ultimate uniaxial strength of confined concrete is given by 7.94 f l fl f cc = f ck −1.254 + 2.254 1 + (11) −2 fck f ck where fl is equivalent lateral confined stress, given herein by fl = ke fl
(12) fl
is calculated from Eq. (4). The confinement in which effectiveness coefficient ke is divided into ke1 , the level confinement effectiveness coefficient, and ke2 , the longitudinal confinement coefficient, i.e. ke = ke1 · ke2
(13)
where ke1 and ke2 take the form [18] as Ae1 Acc1 Ae2 = Acc2
ke1 =
(14)
ke2
(15)
where Ae1 and Ae2 are the level area of an effectively confined concrete core and longitudinal area of an effectively confined concrete core, while Acc1 and Acc2 are the level area of a concrete core and the longitudinal area of a concrete core respectively. The arching action shown in Fig. 11 is assumed to occur in the form of a second-degree parabola with an initial tangent angle θ . So that Ae1 and Acc1 are given by Ae1 = (D − 2t)2 −
n [(D − 2t)/(D/as )]2 tan θ i=1
6
Acc1 = (D − 2t)2 and applying Eqs. (16) and (17) to Eq. (14) produces n (as /D)2 tan θ ke1 = 1 − . 6 i=1
(16) (17)
(18)
ke2
θ=
π (13 + 9.2as /100) (rad). 180
(21)
It is shown that specimens with binding bars failed in postlocal buckling mode. The steel yielded as this type of column reached ultimate strength, supposed to obey the Von Mises criteria given by 2 f a2 − f a σh + σh2 = f ay .
(22)
For the local buckling strength of a steel plate f b in CFT columns, Ge and Usami [19] proposed a relationship as fb 1.2 0.3 − 2 ≤ 1.0 = f ay R R
(23)
which is ensured by keeping R ≥ 0.85; where R is the width–thickness ratio parameter, defined as D 12(1 − ν 2 ) f ay R= . (24) t Ea 4π 2 Then from Eq. (23), the stress states of steel tubes can be determined in the two cases as follows. For R ≥ 0.85 applying fa = fb to Eqs. (23) and (22) results in 1.2 0.3 − 2 f ay (in compression) (25) fa = R R 2 −3f2 f a − 4 f ay a (in tension). (26) σh = 2 For R < 0.85, the effects of local buckling can be ignored [19]. Sakino et al. [20] deduced a relationship between stress coefficient au and bu , which represent hoop stress to yield strength of steel ratio and longitudinal stress to yield strength of steel ratio respectively, based on a large number of results of experiments for circular CFT short columns. The value of coefficients au and bu given as −0.19 and 0.89 respectively are adopted herein to assume the value of hoop stress and longitudinal stress for steel in the case of R < 0.85. Therefore, σh and f a are expressed as follows σh = 0.19 f ay
(in tension)
(27)
f a = 0.89 f ay
(in compression).
(28)
5.3. Simplification of the method proposed
Similarly it can be deduced that
bs tan θ 2 = 1− . 2(b − 2t)
It is found that the initial tangent angle θ is mainly sensitive to level spacing of binding bars. Based on a linear regression, a simple form of expression is taken as
(19)
The method presented above is somewhat complicated and a simplification is proposed below.
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
Fig. 12. φ1 –R relationship.
481
(a) Relationship of φ2 and ζ .
Assumed that Eq. (10) can be expressed alternatively as Nu = φ1 f ay Aa + φ2 f ck Ac
(29)
where φ1 and φ2 are the strength coefficient of steel and that of concrete, defined as φ1 =
fa , f ay
φ2 =
fcc . f ck
(30)
Based on the regression of data from this experiment program which is shown in Fig. 12, φ1 is given as 0.89 R < 0.85 (31) φ1 = 0.897R −0.7407 R ≥ 0.85. It is found that the uniaxial strength of concrete filled in a square steel tube with binding bars primarily depends on the constraining factor of the binding bars ζ and the width-to-thickness ratio parameter R. Fig. 13(a) shows that there exists an almost linear relationship between φ2 and ζ . Fig. 13(b) presents a nonlinear relationship of φ2 and R when the constraining factor of the binding bars is equal to zero (meaning specimens without binding bars arranged). Based on a double nonlinear regression through the data in Table 1, the strength coefficient of steel φ2 is given by φ2 = 1.039R −0.0861(7.3836ς + 1.0588).
(32)
5.4. Verification The predicted ultimate strengths of S-CFT stub columns with or without binding bars calculated by Eqs. (10) and (29) respectively are given in Table 2. To make a comparison, the extensive experimental data from other research such as Chen [21] and Han and Tao [22] are adopted and results predicted by the methods of EC4 and GJB4142-2000 are also given in Table 2. For specimens with binding bars tested in this program, the results predicted by the formulae proposed herein agree well with that of experiments with mean value and covariance of Nuc /Nue given as 1.037 and 0.008 respectively. Both the value of the mean and the covariance predicted by the simplified method are somewhat larger with the mean value and covariance as 1.060 and 0.012 respectively. EC4 gives a mean of Nuc /Nue as 0.912 while GJB 1.044. Both of the covariances given by EC4 and GJB are somewhat large with the value of 0.024 and 0.031 respectively owing to the two methods cannot take into account the contribution of binding bars and thus result in the covariance being relatively larger. For the normalsectioned S-CFT stub columns from Han and Tao [22], the two
(b) Relationship of φ2 and R. Fig. 13. Relationship of φ2 and z (or R).
methods proposed in this paper can also give reasonable results as those of EC4 and GJB do. 6. Conclusions The following conclusions can be drawn based on the results of this study: (1) Under axial loading, normal-sectioned square CFT stub columns without stiffening measures are prone to failing in local buckling, whose ultimate strength, plastic deformability and ductility are relatively low. The main reason is that the concrete confinement is not consistent along the side walls of the steel tube and only exists in the corner regions. The effect of confinement is very weak and usually neglected. The potential load-bearing capacity is not adequately in usage in this type of column. (2) The proposed stiffening scheme improves the axial load behavior of square CFT columns mainly on two aspects. One is that the concrete confinement beyond the corner regions is improved since the transverse deformation of the concrete core is constrained by the binding bars. The other is that the elastic local buckling of a steel plate can be delayed or even avoided through an appropriate longitudinal spacing of binding bars owing to the local buckling only taking place between the two adjacent rows of level binding bars. (3) The spacing and diameter of binding bars have an important influence on ultimate strength and plastic deformability of square CFT columns with binding bars. With spacing of binding bars decreasing and the diameter of binding bars increasing, the ultimate strength and corresponding strain of specimens with binding bars increase remarkably and the post load–strain curve decreases slowly.
482
Table 2 Comparison among ultimate strengths from prediction and experiment for square CFT columns with or without binding bars No. Specimen
B × t × L (mm)
as × bs × ds (mm) ξ
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 4 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 8 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 12 × 1500 300 × 6 × 1500 300 × 6 × 1500 300 × 6 × 1500
16 17
C1 GZ02a
300 × 10 × 1500 150 × 150 × 14 300 × 10 × 1500 150 × 150 × 14
— 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 100 × 150 × 14 — 150 × 150 × 14 150 × 150 × 16
0.625 0.817 0.817 0.477 0.477 0.477 1.129 1.129 1.129 1.572 1.572 1.572 0.625 0.625 0.817
f ck (MPa)
Nue (kN) Formulae proposed in Formulae simplified this paper in this paper Nuc (kN) Nuc /Nue Nuc (kN) Nuc /Nue
EC4(1996) [14]
GBJ(2000) [16]
Nuc (kN)
Nuc /Nue
Nuc (kN)
Nuc /Nue
292.48 382.50 382.50 341.93 341.93 341.93 387.98 387.98 387.98 345.04 345.04 345.04 292.48 292.48 382.5
39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82 39.82
5800 6600 8654 5300 6243 7255 5600 7878 8170 6588 8436 9749 4370 6140 7375
5852 6622 8209 5293 6243 7037 6745 7722 7997 8571 9239 9772 4411 6184 7308
1.009 1.003 0.949 0.999 1.000 0.970 1.204 0.980 0.979 1.301 1.095 1.002 1.009 1.007 0.991
4543 6015 6751 5460 5395 6887 7237 7327 7977 7129 8601 9338 7744 9191 9915
0.857 0.964 0.931 0.941 1.235 1.122 1.096 0.994 0.922 1.273 1.092 1.143 1.176 1.090 1.017
5367 6002 6002 5015 5015 5015 6837 6837 6837 7803 7803 7803 5367 5367 6002
0.925 0.909 0.694 0.946 0.803 0.691 1.221 0.868 0.837 1.184 0.925 0.800 1.228 0.874 0.814
6268 6946 6946 5894 5894 5894 7797 7797 7797 8704 8704 8704 6268 6268 6946
1.081 1.052 0.803 1.112 0.944 0.812 1.392 0.990 0.954 1.321 1.032 0.893 1.434 1.021 0.942
This paper
1.581 366.86 2.410 357.72
34.34 21.96
7695 6634
8293 7012
1.078 1.057
8391 7174
1.090 1.081
6948 5871
0.903 0.885
7737 6371
1.005 0.960
[21]
Mean
1.037
1.060
0.912
1.044
COV
0.008
0.012
0.024
0.031
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
sczs1-1-1 sczs1-1-2 sczs1-1-3 sczs1-1-4 sczs1-1-5 sczs1-2-1 sczs1-2-2 sczs1-2-3 sczs1-2-4 sczs2-1-1 sczs2-1-2 sczs2-1-3 sczs2-1-4 sczs2-1-5 sczs2-2-1 sczs2-2-2 sczs2-2-3 sczs2-2-4 sczs2-3-1 sczs2-3-2
120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 120 × 3.8 × 360 140 × 3.8 × 420 140 × 3.8 × 420 140 × 3.8 × 420 140 × 3.8 × 420 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 120 × 5.9 × 360 140 × 5.9 × 420 140 × 5.9 × 420 140 × 5.9 × 420 140 × 5.9 × 420 200 × 5.9 × 600 200 × 5.9 × 600
— — — — — — — — — — — — — — — — — — — —
1.69 1.479 1.479 0.936 0.879 2.437 2.334 0.714 0.714 2.462 2.462 2.863 1.407 1.407 3.793 0.791 1.132 1.132 2.36 2.36
330.1 330.1 330.1 330.1 330.1 330.1 330.1 330.1 330.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1 321.1
27.3 31.2 31.2 49.3 52.5 16 16.7 54.6 54.6 30 30 25.8 52.5 52.5 16.3 18.3 54.6 54.6 17.6 17.6
882 882 921.2 1080 1078 940.8 921.6 1499.4 1470 1176 1117.2 1195.6 1460.2 1372 1342.6 1292.6 2009 1906.1 2058 1960
915 964 964 1194 1234 964 976 1646 1646 1188 1188 1138 1453 1453 1273 1306 1912 1912 2162 2162
1.037 1.093 1.047 1.105 1.145 1.025 1.060 1.098 1.120 1.010 1.063 0.952 0.995 1.059 0.948 1.010 0.952 1.003 1.050 1.103
909.4 965.2 965.2 1224 1270 921.6 935.3 1678 1678 1183 1183 1125 1493 1493 1216 1252 1947 1947 2012 2012
1.031 1.094 1.048 1.133 1.178 0.980 1.015 1.119 1.141 1.006 1.059 0.941 1.023 1.089 0.906 0.969 0.969 1.022 0.978 1.055
928 977 977 1206 1246 964 976 1641 1641 1216 1216 1167 1479 1479 1284 1315 1914 1914 2094 2094
1.052 1.108 1.061 1.117 1.156 1.025 1.059 1.094 1.116 1.034 1.088 0.976 1.013 1.078 0.956 1.018 0.952 1.004 1.018 1.069
886.8 927.5 927.5 1123 1158 945.8 954.9 1495 1495 1159 1159 1123 1382 1382 1283 1299 1768 1768 2021 2021
1.005 1.052 1.007 1.040 1.075 1.005 1.036 0.997 1.017 0.985 1.037 0.940 0.946 1.007 0.956 1.005 0.880 0.928 0.982 1.031
Mean
1.044
1.038
1.050
0.997
COV
0.003
0.005
0.003
0.002
Note: — means specimen without binding bars.
Resource
[22]
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
f ay (MPa)
J. Cai, Z.-Q. He / Journal of Constructional Steel Research 62 (2006) 472–483
(4) Ultimate strength predicted by the methods proposed in this paper is reasonable for square CFT stub columns with or without binding bars, while that calculated by EC4(1996) and GJB(2000) scatters quite a bit from the experimental results of square CFT stub columns with binding bars owing to not considering the contribution of binding bars. Acknowledgements The work described in this paper is part of the project entitled “Research on behavior of abnormal-shaped CFT stub columns”, funded by Natural Science Key Foundation of Guangdong Province in China under Grant No. 012356. This support is sincerely appreciated. Additionally, special thanks to Xing Chen, senior engineer in Arch. & Civil Design Research Institute of Guangdong, for his skilled assistance. References [1] Zhang ZG. Analysis of mechanism and load-bearing capacity of square concrete-filled steel under axial load. China Ind Constr 1989;11:2–8 [in Chinese]. [2] Forlong RW. Strength of steel-encased concrete beam–columns. J Struct Div, ASCE 93(5):113–24. [3] Knowles RB, Park R. Strength of concrete-filled steel tubular columns. J Struct Div, ASCE 95(12):2565–87. [4] Tomii M, Yoshimura K, Morishita Y. Experimental studies on concrete filled steel tubular stub columns under concentric loading. In: Proc., int. colloquium on stability of structure under static and dynamic loads. p. 718–41. [5] Schneider SP. Axially loaded concrete-filled steel tubes. J Struct Eng 1998;124(10):1125–38. [6] Li XL, Yu Y et al. Study on behavior of square concrete-filled steel under axial load: experiment. China Build Struct 1999;(10):41–3 [in Chinese].
483
[7] Ge HB, Usami T. Strength of concrete-filled thin-walled steel box column: experiment. J Struct Eng, ASCE 1992;118(11):3036–54. [8] Lin TI, Huang CM, Chen SY. Concrete-filled tubular steel columns subjected to eccentric axial load. J Chin Inst Civil Hydraulic Eng 1993; 5(4):377–86 [in Chinese]. [9] Kitada T. Ultimate strength and ductility of state-of-the-art concrete-filled steel bridge piers in Japan. Eng Struct 1998;20(4–6):347–54. [10] Huang CS, Yeh YK et al. Axial load behavior of stiffened concrete-filled steel columns. J Struct Eng, ASCE 2002;128(9):1222–30. [11] He BK, Yang XB, Zhou TH. Theoretical analysis on local buckling behavior of concrete filled rectangular steel tube column subjected to axial force. J Xi’an Univ of Arch & Tech (Natural Science Edition) 2002;34(3): 210–3 [in Chinese]. [12] Uy B. Local and post-local buckling of concrete-filled steel welded box columns. J Constr Steel Res 1998;47(1–2):47–72. [13] Architectural Institute of Japan (AIJ). Recommendations for design and construction of concrete filled steel tubular structures. October 1997. [14] EC4. Design of steel and concrete structures, Part1, 1, general rules and rules for building. DD ENV 1994-1-1:1996. London WI A2BS: British Standards Institution. [15] AISC. Load and Resistance Factor Design (LRFD). Specification for structural steel buildings. Amer Inst Steel Constr, 25(4):2–16. [16] GJB4142-2000, 2001. Technical specifications for early-strength model composite structures. Peking, China [in Chinese]. [17] Shanmugam HE, Lakshmi B. State of the art report on steel–concrete composite columns. J Constr Steel Res 2001;(57):1041–80. [18] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. J Struct Eng, ASCE 1988;114(8):1807–26. [19] Ge HB, Usami T. Strength analysis of concrete filled thin-walled steel box columns. J Constr Steel Res 1994;30:259–81. [20] Sakina K, Nakahara H et al. Behavior of centrally loaded concrete-filled steel-tube short columns. J Struct Eng, ASCE 2004;130(2):180–8. [21] Chen DM. Foundational study on mechanic behavior of abnormal-shaped CFT columns with binding bars. MS thesis. Guangzhou (China): South China University of Technology; 2000. [22] Han LH, Tao Z. Study on behavior of concrete filled square steel tube under axial load. China J Civ Eng 2001;34(2):17–25 [in Chinese].