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Creep of high strength concrete filled steel tube columns
Thin-Walled Structures 53 (2012) 91–98
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Creep of high strength concrete filled steel tube columns Yi Shuo Ma, Yuan Feng Wang n School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
a r t i c l e i n f o
abstract
Article history: Received 19 May 2011 Accepted 2 December 2011 Available online 31 January 2012
High strength concrete filled steel tube (HSCFT) members have found wide applications. However, there are few reports on the test and model of their creep. This paper investigates the creep of axially loaded HSCFT columns by testing eight specimens for 380 day. A creep model, considering the state of triaxial stress and autogenous shrinkage of the high strength concrete core, has been proposed and validated against the test data. Parametric analysis demonstrates that there exists an obvious difference in the creep between HSCFT columns and normal strength concrete filled steel tube columns, additionally, concrete composition influences the creep of HSCFT columns considerably. & 2011 Elsevier Ltd. All rights reserved.
Keywords: High strength concretes Concrete filled steel tube Columns Creep Model studies Tests
1. Introduction Mechanical characteristics superior to conventional reinforced concrete columns in terms of stiffness, strength, ductility and energy absorption capacity promote the use of concrete filled steel tube (CFT) columns as a competitive composite system [1,2]. In modern CFT structures, mineral and supplementary cementitious materials, such as silica fume, are commonly added into the concrete core to enable the concrete to have higher strength and better performances. CFT columns prepared in this way can be referred to as high strength concrete filled steel tube (HSCFT) columns. For HSCFT columns, the composite action between the two constituent elements, which means that the concrete prevents the wall of the steel tube from buckling inwards and the steel tube acts as reinforcements as well as provides confining pressure to the concrete, effectively reduces the brittleness of the high strength concrete (HSC) core and provokes the enhancement of the mechanical properties [3,4]. Nevertheless, as to the long-term performances of CFT columns, the creep and shrinkage of the concrete core would weaken the interface bond between the steel tube and concrete, affect the composite interaction [5], cause a decrease in the ultimate strength [6,7] and consequently induce serviceability problems. These highlight the need for a thorough observation on the creep and shrinkage behaviors of CFT columns, along with the development of an effective model. In this context, the extensive use in practice and the particularity of HSCFT
n
Corresponding author. Tel.: þ86 10 51685552; fax: þ86 10 62221591. E-mail address: [email protected] (Y.F. Wang).
0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.12.012
columns especially necessitate a comprehensive understanding on their time-dependent behavior. However, most experimental as well as theoretical research performed to date on the creep behavior of CFT columns is to deal principally with normal strength concrete, with various affecting parameters being investigated, including cross-sectional shape [6], level of sustained loading [8], concrete strength [8,9], loading age [8–10], eccentricity [10,11], loading case [12,13], specimen dimension [13], steel ratio (the ratio of the cross-sectional areas of the steel tube to the concrete core) [8,9,12,14] and interface bond condition [15]. On the theoretical plane, the creep behaviors of circular or square normal strength concrete filled steel tube (NSCFT) columns subjected to axial or eccentric compressive loads were analyzed by means of regression on the experimental creep data of NSCFT members [10,12] or combining the creep model for normal strength concrete either into the section analysis based on the conditions of the mechanical equilibrium and geometric compatibility [7,16–18] or into the finite element model of NSCFT columns [13,19]. The available test data concerning the creep behavior of HSCFT columns are too limited so far to provide a solid research basis. To be specific, only Uy [7] conducted experiments to ascertain the creep and shrinkage characteristics of 6 HSCFT column specimens with the 28-day compressive strength of the HSC core being 52 MPa, presenting the conclusion that the final creep coefficient for HSCFT columns was significantly lower than that for HSC cylinders, however, no comparison on the creep between HSCFT columns and NSCFT columns. The insufficiency of the research on the creep behavior of HSCFT columns lies in not only the weak experimental support but also the incomplete theoretical analysis, which is limited to utilizing the creep model calibrated for normal strength concrete directly to consider the creep of HSCFT
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columns at present [7]. Instead, this issue demands a deep insight into the special long-term property of HSC, which is considerably different from that of normal strength concrete because of the significant influence of various admixtures and pozzolanic materials on the creep [20–27]. Therefore, a rational creep model for HSC is the primary concern in the framework of analyzing the creep of HSCFT columns theoretically. As to this point, regression equations based on test data [20,22,26,27] and a modified B3 Model based on solidification theory [28] have been proposed, which are of much significance for the creep of HSCFT columns. This paper investigates the creep behavior of HSCFT columns under axial loads by experimental and theoretical analysis. Four specimens were tested for 380 day to measure their creep behavior under sustained axial compression, and other four companion specimens were tested for shrinkage at the same time. In addition, on the basis of modified B3 Model [28], which is suitable for predicting the creep of HSC, considering the autogenous shrinkage, the state of triaxial stress, and the composite action between the steel tube and the HSC core, an analytical model is presented to predict the creep of axially loaded HSCFT columns.
2. Materials and experiments
steel ratio a, the sustained axial load N, the ultimate capacity Nu calculated according to CECS 104:99 [29], the initial axial stress in the concrete sc1 ðt 0 Þ calculated based on the measured initial axial strain, and the ratio ac of sc1 ðt 0 Þ to the 28-day cylindrical compressive strength of concrete fc, 28. 2.2. Materials and mix proportions The cementitious materials of the concrete core used in the test were ordinary Portland cement and an amount of silica fume corresponding to 5% of the weight of the total cementitious materials. The minimum compressive strengths of the cement at the ages of 3 d and 28 d are 17.0 MPa and 42.5 MPa, respectively, and its minimum folding strengths at the ages of 3 d and 28 d are 3.5 MPa and 6.5 MPa, respectively. River sand and crushed granite stone were used as the fine and coarse aggregates, respectively. The densities of the fine and coarse aggregates were 2.65 103 kg/m3 and 2.74 103 kg/m3, respectively. The composition and properties of the HSC adopted in the test are outlined in Table 2, where fcu,28 represents the measured 28-day cube compressive strength. Cold-formed, mild steel tubes were used in the present investigation, with the elastic modulus and yielding strength of 2.06 105 MPa and 235 MPa, respectively.
2.1. Specimen design 2.3. Specimen preparation A total of eight HSCFT columns with circular cross-section were tested in the laboratory for the research of the long-term deformation. The primary variables in this investigation are the composition and compressive strength of HSC. Two series of concrete which were mixed from two batches with the designed cube compressive strengths of 60 MPa and 80 MPa were used, designated as concrete A and B. Correspondingly, HSCFT columns are also divided into two groups, labeled as HSCFT-A and HSCFT-B, respectively. Two specimens in each group were used to perform the creep study. The parallel shrinkage tests were carried out on the other two specimens, which were kept unloaded for the whole duration of the long-term tests and had the same materials, age, dimensions and environmental conditions as the loaded ones. The actual creep strains were calculated by subtracting the shrinkage values from the total timedependent strains of the corresponding specimens under loading. Three cube specimens with the side length of 150 mm for each concrete series were prepared to measure the compressive strength of the HSC. The summary of the specimen test matrix is given in Table 1. The following give the tabulated variables: the outer diameter D and thickness t of the steel tube, the length of the specimen L, the Table 1 Specimen test matrix. Specimen
D L t (mm)
a
N (kN)
Nu (kN)
sc1 ðt0 Þ (MPa)
ac
HSCFT-A1 HSCFT-A2 HSCFT-B1 HSCFT-B2
150 450 5 150 450 5 150 450 5 150 450 5
0.148 0.148 0.148 0.148
503 549 598 644
1372.5 1372.5 1418.2 1418.2
17.69 23.08 29.28 27.27
0.26 0.34 0.35 0.32
The steel tubes used in this test, being manufactured from mild steel sheet, were wire brushed to remove rust and loose debris in the insides, and were kept ungreased on the outer surfaces to reflect the common site practice. The bottom end of each steel tube was welded to a circular steel base plate with the thickness of 10 mm. The well-mixed HSC for filling in the steel tubes was poured from the top and vibrated to ensure the compactness, with the steel tubes being kept in an upright position. Meanwhile, the corresponding HSC cube specimens, with the side length of 150 mm, were cast for concrete strength tests. The specimens were then cured for 28 day, under the controlled temperature of 20 72 1C and the relative humidity of 95% above. Prior to testing, the top surface of each HSCFT specimen, being trimmed off by a trowel, was welded with another circular steel cover plate with the thickness of 10 mm, in order that the load could be applied evenly across the cross-section. 2.4. Instrumentation and test setup For measuring the deformations of the specimens, creep and shrinkage specimens were all instrumented at their mid-height with an embedded vibrating wire strain gage (DI-25) in the axial direction. At the age of 28 day, the creep specimens were subjected to sustained axial stresses, with the stress level in the concrete core varying from 0.26fc,28 to 0.35fc,28, for a load duration of 380 day. And shrinkage specimens were maintained unloaded for the whole duration of the long-term tests. The centering of the loaded specimens was necessary to avoid eccentric loading before the test. The loaded specimen is illustrated in Fig. 1.
Table 2 Composition and properties of HSC. Concrete
A B
fcu,28 (MPa)
70.5 85.5
Slump (mm)
37 37
Composition (kg/m3) Cement
Silica fume
Water
Fine aggregate
Coarse aggregate
478.2 478.2
25.17 25.17
151 151
881.43 672.58
881.43 1097.37
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The stress-relaxation coefficient instrument, a specialized laboratory apparatus for testing creep and temperature stress of concrete, which consists of computer, hydraulic servo system, strain-measuring system and loading system, was used for the axial creep test, as shown in Fig. 2. Companion specimens corresponding to the creep ones were tested for their free shrinkage strains. All creep and shrinkage specimens were kept in a controlled temperature of 20 1C throughout the test duration, so that the influence of temperature gradient could be kept to minimum values. 3. Creep model for axially loaded HSCFT 3.1. Creep and shrinkage model for HSC The most useful prediction models for concrete creep at present include ACI 209 Model [30], CEB 90 Model [31], GL
Fig. 1. Loaded specimen for creep test.
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2000 Model [32] and B3 Model [33], which are all developed based on normal strength concrete. Among these four creep models, B3 Model takes account of the most comprehensive parameters including the concrete composition, concrete compressive strength, relative humidity of environment, member dimension and so on, and is calibrated by a computerized data bank comprising practically all the relevant test data obtained in various laboratories throughout the world [33]. The coefficients of variation of the deviations of the Model B3 from those data have been evaluated to be distinctly smaller than those for CEB 90 Model and ACI 209 model [25,33,34]. But the model cannot consider the effects of admixtures and pozzolanic materials and the prediction of the model parameters is restricted to Portland cement concrete with the parameter ranges as 17 MPar f c r 70 MPa, 0:35 rw=c r 0:85,
ð1Þ
where f c ¼mean 28-day standard cylinder compression strength of concrete (MPa); w/c¼ water–cement ratio, by weight. It has been demonstrated that the higher compressive strength, lower water–cement ratio and the presence of silica fume can make the creep of HSC quite different from that of normal strength concrete [20,22,24,26]. In order to predict the creep of HSC, it is vital to modify the Model B3 directed against these factors. Therefore, the model developed in this paper for the creep of HSCFT columns is based on the creep model for HSC proposed by Ma and Wang [28]. The concrete core of CFT columns subjected to constant axial loads is under the state of triaxial variable stress, whose confining stress and axial stress both vary with time since the variation of the transverse strain and the internal force redistribution between the two components, respectively. Therefore, the creep of the concrete core concerns the concepts of the effective creep Poisson’s ratio of concrete [35,36] and the principle of superposition [37]. According to the principle of superposition, the creep strain in one direction of the concrete under the state of triaxial stress is the algebraic sum of the creep strain in this direction caused by each stress component acting separately, and the total creep of the concrete subjected to a uniaxial variable stress can be obtained by adding the creep strains caused by small stress increments applied at small time intervals.
Fig. 2. Instrumentation for axial creep tests.
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In addition, the microstructure of the HSC determines an obvious difference in the long-term deformation between the NSCFT columns and HSCFT columns. It is feasible to only consider the basic creep of the concrete core for the former case, because the sealing action provided by the steel tube protects the concrete core from migration and loss of moisture, and considerably reduces its shrinkage and drying creep [17]. However, for the latter case, the autogenous shrinkage of the HSC unrelated to migration and loss of moisture accounts for a considerable proportion of the total shrinkage [21,23]. Therefore, the basic creep and autogenous shrinkage of the HSC core should be both considered in the long-term deformation of HSCFT columns. The creep model for HSCFT developed in this paper is based on the autogeneous shrinkage model given by Mazloom et al. [26] and Mazloom [27], which can consider the effect of the silica fume content as
esh ðtÞ ¼
t 516y106 0:3SF þ12:6 þ t
y ¼ 0:014SF þ 0:39
ð2Þ ð3Þ
where SF¼percentage of silica fume to binder materials; t ¼concrete age (d). 3.2. Creep model for HSCFT The creep model for HSCFT is developed by incorporating the creep model for the concrete core into the composite section analysis based on the mechanical equilibrium and strain compatibility, with considering the confinement effect. The creep analysis in this paper is based on the linear creep assumption, given the fact that the levels of the concrete stress for the four specimens are all within 40% of the cylindrical compressive strength. Detailedly, it is performed through two steps: initial static analysis and creep analysis. Being given a proper initial value, the initial axial stress in the HSC core sc1 ðt 0 Þ due to the applied constant axial stress s can be determined by an iterative calculation based on the short-time stress–strain relationship of the concrete core in CFT columns [38] and the following conditions as
principle of superposition, can therefore be written as
ec1 ðtn Þ ¼ Jðtn ,t0 Þsc1 ðt 0 Þ þ "
n X 1 i¼1
2
2mc Jðt n ,t 0 Þsc3 ðt 0 Þ þ
½Jðt n ,t i Þ þ Jðt n ,t i1 ÞDsc1 ðt i Þ þ esh ðt n Þ n X 1 i¼1
2
# ½Jðt n ,t i Þ þJðt n ,t i1 ÞDsc3 ðt i Þ ð8Þ
where ec1 ðt n Þ¼axial strain of the concrete core at the age of tn; Jðt n ,t 0 Þ¼creep compliance function of concrete under uniaxial constant stress, which is taken as elastic plus creep strain caused by a unit uniaxial constant stress; tn ¼target time, representing the age of concrete; t0 ¼age at loading; Dsc1 ðt i Þ ¼small axial stress increment in concrete applied at small time interval t i t i1 ; esh ðt n Þ ¼autogenous shrinkage of concrete at time tn; mc ¼effective creep Poisson’s ratio of concrete; sc3 ðt 0 Þ¼initial confining (hoop) stress in concrete; Dsc3 ðt i Þ ¼small confining (hoop) stress increment in concrete applied at small time interval t i t i1 . In accordance to the geometric compatibility, the axial strains of the concrete core and the steel tube are equal for every time step. Apparently, the axial strain of the steel tube es1 ðt n Þ, further the axial stress increment of the steel tube Dss1 ðt n Þ, can be drawn from the present ec1 ðt n Þ. Here the steel tube is assumed to remain linear-elastic. Consequently, the axial stress increment of the concrete core Dsc1 ðt n Þ can be obtained by satisfying another essential requirement, the static equilibrium, for each time step as
Dsc1 ðtn ÞAc þ Dss1 ðtn ÞAs ¼ 0
ð9Þ
where Ac and As ¼cross-sectional areas of the steel tube and the concrete core, respectively. On the other hand, the hoop strain of the concrete core for this step ec3 ðt n Þ can also be obtained from the present level of ec1 ðt n Þ as
ec3 ðtn Þ ¼ mc ec1 ðtn Þ
ð10Þ
es1 ðt0 Þ ¼ ec1 ðt0 Þ
ð4Þ
In sequence, the condition of geometric compatibility es3 ðtn Þ ¼ ec3 ðtn Þ gives the present hoop strain of the steel tube es3 ðtn Þ and then the hoop stress increment of the steel tube Dss3 ðt n Þ. Finally from the condition of static equilibrium, the hoop (confining) stress increment in the concrete core Dsc3 ðt n Þ can be calculated as
es3 ðt0 Þ ¼ ec3 ðt0 Þ ¼ m0 ec1 ðt0 Þ
ð5Þ
Dsc3 ðtn Þ ¼
ss1 ðt0 Þ ¼
Es es1 ðt0 Þ þ ms es3 ðt0 Þ 1m2s
sc1 ðt0 Þ ¼ sss1 ðt0 Þ
ð6Þ ð7Þ
where sc1 ðt 0 Þ and ss1 ðt 0 Þ¼initial axial stresses in the concrete core and the steel tube, respectively; ec1 ðt 0 Þ and es1 ðt 0 Þ ¼initial axial strains in the concrete core and the steel tube, respectively; ec3 ðt0 Þ and es3 ðt0 Þ ¼initial hoop strains in the concrete core and the steel tube, respectively; m0 and ms ¼Poisson’s ratio of concrete and steel, respectively; Es ¼ elastic modulus of the steel tube. By giving the new value to the variable sc1 ðt 0 Þ, the iterative procedure can be realized, until the equivalence of the present and new values of sc1 ðt0 Þ is achieved. Once the initial stresses in the HSC core and the steel tube both have been determined, the creep analysis can then be performed by dispersing the long-term process into small time intervals, because the axial stresses in the concrete core and steel tube and the confining stress all vary with time constantly. The creep analysis needs an iterative procedure as well. For one aimed age tn, by giving proper initial values to the axial and confining stress increments of the concrete core corresponding to the present time step t n t n1 , the axial strain of the concrete core, according to the
a 2
Dss3 ðtn Þ
ð11Þ
where a ¼steel ratio, a ¼ As =Ac ¼ 2t=r; t¼ thickness of the steel tube; r ¼radius of the concrete core. It is clear that new values of the axial and confining stress increments of the concrete core can be acquired from the present values of these two variables by this procedure. If the differences between the new values and the present values are greater than the allowable tolerances, these two variables should be given the new values to repeat the procedure. And the differences being within the allowable tolerances means the proper values of these two variables have been obtained for this time step. For the following time steps the procedure should be repeated. It is notable that the state of multiaxial stress of the steel tube should also be taken into account when calculating the Dss1 ðt n Þ and Dss3 ðt n Þ. The procedure to calculate the axial strain of HSCFT under the sustained axial load is elaborated in Fig. 3.
4. Experimental results and theoretical predictions The measured axial elastic plus creep strains of the cylindrical specimens HSCFT-A and HSCFT-B under the sustained axial load for 380 day are plotted in Figs. 4 and 5, where shrinkage strains
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Fig. 3. Calculation procedure for the creep of HSCFT.
have been excluded. It can be observed that the strain of the specimens kept increasing during the whole test. However, especially for the two specimens of HSCFT-B, the creep strain grows with a relatively rapid rate for the early ages; and it maintains a slow growing tendency during the later ages. The axial strains of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 at the age of 50 day account for 86.0%, 90.3%, 98.1% and 91.9% of the corresponding axial strains measured at the end of the test. And the percentages reach 91.0%, 93.5%, 98.9% and 93.8% at the age of 100 day. The tested creep coefficients at the age of 126 day, defined as the ratio of the net creep strains to the initial elastic strains, of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 are 0.72, 0.75, 0.53 and 0.57, respectively. These tested results are fairly lower than that presented by Uy [7], whose HSCFT column specimens subjected to a sustained low-level axial stress for 126 day have the maximum creep coefficient of 1.0. It can be concluded that the compressive strength of the HSC core, being 52 MPa for Uy’s
Fig. 4. Test data and prediction for the creep of HSCFT-A.
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Fig. 5. Test data and prediction for the creep of HSCFT-B.
specimens and 70.5 MPa and 85.5 MPa for the specimens investigated in this paper as mentioned above, contributes a lot to this diversity. The comparisons in the creep coefficient are further made between HSCFT columns and NSCFT columns. The creep coefficients given by Nakai et al. [14] and Terrey et al. [15] are 1.5 and 1.25, respectively, both of which are markedly greater than the results measured from HSCFT columns. The comparisons between the test data and the predictions by the proposed creep model for HSCFT using the modified B3 Model for HSC are also given in Figs. 4 and 5. It can be seen that the theoretical predictions are basically in accordance with the test results, although for the early age the creep model under-predicts the axial strain a little. According to Neville et al. [37], the error coefficient of a creep model can be calculated as M¼
1 C ðt,t 0 Þ
X
" 2 #0:5 Cðt,t 0 ÞC 0 ðt,t 0 Þ n
ð12Þ
Fig. 6. Error coefficient of the creep model. (a) Specimens HSCFT-A. (b) Specimens HSCFT-B.
where M ¼error coefficient; Cðt,t 0 Þ ¼ observed strain at time t; C 0 ðt,t 0 Þ¼ predicted strain at time t; C ðt,t 0 Þ ¼mean observed strain for a number of observations n. The error coefficients of the proposed model for the creep of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 are shown in Fig. 6. As expected, the magnitude of the error coefficients tends to decrease with time for both HSCFTA and HSCFT-B. For most of the loading process, the error coefficients are within the 0–5% band. Especially, for the later period, the error coefficients are comparative low, which proves the effectiveness of the creep model.
5. Parametric analysis The long-term behavior of HSCFT columns is influenced by many parameters, particularly the diameter-to-thickness ratio and concrete mix composition and compressive strength. It is highly expensive and time consuming to experimentally investigate the effects of every parameter. Therefore, theoretical analysis based on a reliable model is a feasible alternative in observing the influences of extensive parameters. In view that the effect of the diameter-to-thickness ratio has been investigated thoroughly [17], parametric analysis was performed to gain insight into the possible influences of the concrete mix composition and compressive strength in this paper. Figs. 7–9 illustrate the influences of the water-binder ratio (w/b), the aggregate-binder ratio (a/b) and the silica fume-binder ratio (s/b) on the creep of HSCFT columns. The dimension and the concrete mix of the calculated columns are same to the test
Fig. 7. Effect of water-binder ratio on the creep of HSCFT.
specimens HSCFT-A, except for the factors being studied for their effects. The object for comparison is the creep compliance of each column, which gets rid of the effect of stress and can reveal the essential creep property of HSCFT columns with different parameters. As shown in Figs. 7 and 8, it is clear that the general effect of increasing w/b or decreasing a/b is to increase the creep of HSCFT columns. As the w/b are 0.4 and 0.5, the corresponding creep compliances at the age of 380 day are 1.05 and 1.11 times greater
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97
remains comparatively stable during the later period. Therefore, it is important to account for the significant reducing effect of silica fume on the creep of HSCFT columns. Fig. 10 displays the influence of concrete compressive strength on the creep of CFT columns. This influence is interrelated with the concrete composition actually. The NSCFT column with the compressive strength of the concrete core of 40 MPa is set for highlighting the difference in creep between HSCFT and NSCFT columns. Its concrete composition is totally different from that of the HSCFT column, and is representative of common concrete mix for NSCFT columns, with the contents of cement, water, aggregate and silica fume being 370 kg/m3, 163 kg/m3, 1913 kg/m3 and 0 kg/m3, respectively. As it can be seen, the final creep compliance of the NSCFT column is about 15% higher than that of the HSCFT column. Fig. 8. Effect of aggregate-binder ratio on the creep of HSCFT.
6. Conclusions This paper focuses on the creep behavior of HSCFT columns. Creep and companion shrinkage tests have been conducted on eight HSCFT specimens with different concrete mix composition. It has been found that the creep of HSCFT columns develops mostly in the early ages, and it grows comparatively slowly during the later period of loading. Comparison with the creep of NSCFT columns manifests that the creep coefficient of HSCFT columns is generally lower than that of NSCFT columns. Analytical model for the creep of HSCFT columns, based on the modified B3 Model, has been developed to support the investigation and has been demonstrated to be accordance with the test results. Parametric analysis shows that there exists an important influence of the concrete composition and compressive strength on the creep of HSCFT columns.
Fig. 9. Effect of silica-binder ratio on the creep of HSCFT.
Acknowledgments The authors would like to gratefully acknowledge the financial support of National Science Foundation of China (grant no.: 50778020). References
Fig. 10. Effect of concrete compressive strength on the creep of HSCFT.
than that with the w/b of 0.3, respectively. As the a/b are 4.5 and 5.5, the corresponding creep compliances at the age of 380 day are 97% and 95% of that with the a/b of 3.5, respectively. As it can be seen in Fig. 9, there is an obvious decrease in the creep compliance at high levels of silica fume content. When the s/b are 5% and 10%, the corresponding creep compliances are 86% and 78%, respectively, of that without the silica fume at the age of 380 day. Additionally, the creep compliance of the specimen without silica fume tends to ascent obviously even in the later ages; while that of the other two specimens with silica fume
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[25] Townsend BD. Creep and shrinkage of a high strength concrete mixture. MS thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA; 2003. [26] Mazloom M, Ramezanianpour AA, Brooks JJ. Effect of silica fume on mechanical properties of high-strength concrete. Cement and Concrete Composites 2004;26(4):347–57. [27] Mazloom M. Estimating long-term creep and shrinkage of high-strength concrete. Cement and Concrete Composites 2008;30(4):316–26. [28] Ma YS, Wang YF Creep of AFRP confined high-strength concrete columns under low-level stress. Advances in Structural Engineering, in press. [29] China Association for Engineering Construction Standardization. Technical specification for high-strength concrete structure (CECS 104: 99). Beijing, China; 1999 [in Chinese]. [30] ACI Committee 209. Prediction of creep, shrinkage and temperature effects in concrete structures (209R-92). Manual of Concrete Practice, Part 1; 1992. [31] CEB-FIP Model Code. Evaluation of the time dependent behavior of concrete; 1990. [32] Gardner NJ, Lockman MJ. Design provisions for drying shrinkage and creep of normal-strength concrete. ACI Materials Journal 2001;98:159–67. [33] Bazˇant ZP, Baweja S. Creep and shrinkage prediction model for analysis and design of concrete structures: Model B3. In: Proceedings of the Adam Neville symposium: creep and shrinkage—structural design effects, Michigan; 2000. p. 1–83. [34] Goel R, Kumar R, Paul DK. Comparative study of various creep and shrinkage prediction models for concrete. Journal of Materials in Civil Engineering 2007;19(3):249–60. [35] Gopalakrishnan KS, Neville AM, Ghali A. A hypothesis on mechanism creep of concrete with reference to multiaxial compression. ACI Journal 1970;67(3):29–35. [36] Jordaan IJ, Illston JM. Time-dependent strains in sealed concrete under multiaxial compressive stress. Magazine of Concrete Research 1971;23(75– 76):79–88. [37] Neville AM, Dilger WH, Brooks JJ. Creep of plain and structural concrete. London and New York: Construction Press; 1983. [38] Zhong ST. Concrete-filled steel tube structures. Beijing: Tsinghua University Press; 2003. [in Chinese].
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Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Creep of high strength concrete filled steel tube columns Yi Shuo Ma, Yuan Feng Wang n School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
a r t i c l e i n f o
abstract
Article history: Received 19 May 2011 Accepted 2 December 2011 Available online 31 January 2012
High strength concrete filled steel tube (HSCFT) members have found wide applications. However, there are few reports on the test and model of their creep. This paper investigates the creep of axially loaded HSCFT columns by testing eight specimens for 380 day. A creep model, considering the state of triaxial stress and autogenous shrinkage of the high strength concrete core, has been proposed and validated against the test data. Parametric analysis demonstrates that there exists an obvious difference in the creep between HSCFT columns and normal strength concrete filled steel tube columns, additionally, concrete composition influences the creep of HSCFT columns considerably. & 2011 Elsevier Ltd. All rights reserved.
Keywords: High strength concretes Concrete filled steel tube Columns Creep Model studies Tests
1. Introduction Mechanical characteristics superior to conventional reinforced concrete columns in terms of stiffness, strength, ductility and energy absorption capacity promote the use of concrete filled steel tube (CFT) columns as a competitive composite system [1,2]. In modern CFT structures, mineral and supplementary cementitious materials, such as silica fume, are commonly added into the concrete core to enable the concrete to have higher strength and better performances. CFT columns prepared in this way can be referred to as high strength concrete filled steel tube (HSCFT) columns. For HSCFT columns, the composite action between the two constituent elements, which means that the concrete prevents the wall of the steel tube from buckling inwards and the steel tube acts as reinforcements as well as provides confining pressure to the concrete, effectively reduces the brittleness of the high strength concrete (HSC) core and provokes the enhancement of the mechanical properties [3,4]. Nevertheless, as to the long-term performances of CFT columns, the creep and shrinkage of the concrete core would weaken the interface bond between the steel tube and concrete, affect the composite interaction [5], cause a decrease in the ultimate strength [6,7] and consequently induce serviceability problems. These highlight the need for a thorough observation on the creep and shrinkage behaviors of CFT columns, along with the development of an effective model. In this context, the extensive use in practice and the particularity of HSCFT
n
Corresponding author. Tel.: þ86 10 51685552; fax: þ86 10 62221591. E-mail address: [email protected] (Y.F. Wang).
0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.12.012
columns especially necessitate a comprehensive understanding on their time-dependent behavior. However, most experimental as well as theoretical research performed to date on the creep behavior of CFT columns is to deal principally with normal strength concrete, with various affecting parameters being investigated, including cross-sectional shape [6], level of sustained loading [8], concrete strength [8,9], loading age [8–10], eccentricity [10,11], loading case [12,13], specimen dimension [13], steel ratio (the ratio of the cross-sectional areas of the steel tube to the concrete core) [8,9,12,14] and interface bond condition [15]. On the theoretical plane, the creep behaviors of circular or square normal strength concrete filled steel tube (NSCFT) columns subjected to axial or eccentric compressive loads were analyzed by means of regression on the experimental creep data of NSCFT members [10,12] or combining the creep model for normal strength concrete either into the section analysis based on the conditions of the mechanical equilibrium and geometric compatibility [7,16–18] or into the finite element model of NSCFT columns [13,19]. The available test data concerning the creep behavior of HSCFT columns are too limited so far to provide a solid research basis. To be specific, only Uy [7] conducted experiments to ascertain the creep and shrinkage characteristics of 6 HSCFT column specimens with the 28-day compressive strength of the HSC core being 52 MPa, presenting the conclusion that the final creep coefficient for HSCFT columns was significantly lower than that for HSC cylinders, however, no comparison on the creep between HSCFT columns and NSCFT columns. The insufficiency of the research on the creep behavior of HSCFT columns lies in not only the weak experimental support but also the incomplete theoretical analysis, which is limited to utilizing the creep model calibrated for normal strength concrete directly to consider the creep of HSCFT
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columns at present [7]. Instead, this issue demands a deep insight into the special long-term property of HSC, which is considerably different from that of normal strength concrete because of the significant influence of various admixtures and pozzolanic materials on the creep [20–27]. Therefore, a rational creep model for HSC is the primary concern in the framework of analyzing the creep of HSCFT columns theoretically. As to this point, regression equations based on test data [20,22,26,27] and a modified B3 Model based on solidification theory [28] have been proposed, which are of much significance for the creep of HSCFT columns. This paper investigates the creep behavior of HSCFT columns under axial loads by experimental and theoretical analysis. Four specimens were tested for 380 day to measure their creep behavior under sustained axial compression, and other four companion specimens were tested for shrinkage at the same time. In addition, on the basis of modified B3 Model [28], which is suitable for predicting the creep of HSC, considering the autogenous shrinkage, the state of triaxial stress, and the composite action between the steel tube and the HSC core, an analytical model is presented to predict the creep of axially loaded HSCFT columns.
2. Materials and experiments
steel ratio a, the sustained axial load N, the ultimate capacity Nu calculated according to CECS 104:99 [29], the initial axial stress in the concrete sc1 ðt 0 Þ calculated based on the measured initial axial strain, and the ratio ac of sc1 ðt 0 Þ to the 28-day cylindrical compressive strength of concrete fc, 28. 2.2. Materials and mix proportions The cementitious materials of the concrete core used in the test were ordinary Portland cement and an amount of silica fume corresponding to 5% of the weight of the total cementitious materials. The minimum compressive strengths of the cement at the ages of 3 d and 28 d are 17.0 MPa and 42.5 MPa, respectively, and its minimum folding strengths at the ages of 3 d and 28 d are 3.5 MPa and 6.5 MPa, respectively. River sand and crushed granite stone were used as the fine and coarse aggregates, respectively. The densities of the fine and coarse aggregates were 2.65 103 kg/m3 and 2.74 103 kg/m3, respectively. The composition and properties of the HSC adopted in the test are outlined in Table 2, where fcu,28 represents the measured 28-day cube compressive strength. Cold-formed, mild steel tubes were used in the present investigation, with the elastic modulus and yielding strength of 2.06 105 MPa and 235 MPa, respectively.
2.1. Specimen design 2.3. Specimen preparation A total of eight HSCFT columns with circular cross-section were tested in the laboratory for the research of the long-term deformation. The primary variables in this investigation are the composition and compressive strength of HSC. Two series of concrete which were mixed from two batches with the designed cube compressive strengths of 60 MPa and 80 MPa were used, designated as concrete A and B. Correspondingly, HSCFT columns are also divided into two groups, labeled as HSCFT-A and HSCFT-B, respectively. Two specimens in each group were used to perform the creep study. The parallel shrinkage tests were carried out on the other two specimens, which were kept unloaded for the whole duration of the long-term tests and had the same materials, age, dimensions and environmental conditions as the loaded ones. The actual creep strains were calculated by subtracting the shrinkage values from the total timedependent strains of the corresponding specimens under loading. Three cube specimens with the side length of 150 mm for each concrete series were prepared to measure the compressive strength of the HSC. The summary of the specimen test matrix is given in Table 1. The following give the tabulated variables: the outer diameter D and thickness t of the steel tube, the length of the specimen L, the Table 1 Specimen test matrix. Specimen
D L t (mm)
a
N (kN)
Nu (kN)
sc1 ðt0 Þ (MPa)
ac
HSCFT-A1 HSCFT-A2 HSCFT-B1 HSCFT-B2
150 450 5 150 450 5 150 450 5 150 450 5
0.148 0.148 0.148 0.148
503 549 598 644
1372.5 1372.5 1418.2 1418.2
17.69 23.08 29.28 27.27
0.26 0.34 0.35 0.32
The steel tubes used in this test, being manufactured from mild steel sheet, were wire brushed to remove rust and loose debris in the insides, and were kept ungreased on the outer surfaces to reflect the common site practice. The bottom end of each steel tube was welded to a circular steel base plate with the thickness of 10 mm. The well-mixed HSC for filling in the steel tubes was poured from the top and vibrated to ensure the compactness, with the steel tubes being kept in an upright position. Meanwhile, the corresponding HSC cube specimens, with the side length of 150 mm, were cast for concrete strength tests. The specimens were then cured for 28 day, under the controlled temperature of 20 72 1C and the relative humidity of 95% above. Prior to testing, the top surface of each HSCFT specimen, being trimmed off by a trowel, was welded with another circular steel cover plate with the thickness of 10 mm, in order that the load could be applied evenly across the cross-section. 2.4. Instrumentation and test setup For measuring the deformations of the specimens, creep and shrinkage specimens were all instrumented at their mid-height with an embedded vibrating wire strain gage (DI-25) in the axial direction. At the age of 28 day, the creep specimens were subjected to sustained axial stresses, with the stress level in the concrete core varying from 0.26fc,28 to 0.35fc,28, for a load duration of 380 day. And shrinkage specimens were maintained unloaded for the whole duration of the long-term tests. The centering of the loaded specimens was necessary to avoid eccentric loading before the test. The loaded specimen is illustrated in Fig. 1.
Table 2 Composition and properties of HSC. Concrete
A B
fcu,28 (MPa)
70.5 85.5
Slump (mm)
37 37
Composition (kg/m3) Cement
Silica fume
Water
Fine aggregate
Coarse aggregate
478.2 478.2
25.17 25.17
151 151
881.43 672.58
881.43 1097.37
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The stress-relaxation coefficient instrument, a specialized laboratory apparatus for testing creep and temperature stress of concrete, which consists of computer, hydraulic servo system, strain-measuring system and loading system, was used for the axial creep test, as shown in Fig. 2. Companion specimens corresponding to the creep ones were tested for their free shrinkage strains. All creep and shrinkage specimens were kept in a controlled temperature of 20 1C throughout the test duration, so that the influence of temperature gradient could be kept to minimum values. 3. Creep model for axially loaded HSCFT 3.1. Creep and shrinkage model for HSC The most useful prediction models for concrete creep at present include ACI 209 Model [30], CEB 90 Model [31], GL
Fig. 1. Loaded specimen for creep test.
93
2000 Model [32] and B3 Model [33], which are all developed based on normal strength concrete. Among these four creep models, B3 Model takes account of the most comprehensive parameters including the concrete composition, concrete compressive strength, relative humidity of environment, member dimension and so on, and is calibrated by a computerized data bank comprising practically all the relevant test data obtained in various laboratories throughout the world [33]. The coefficients of variation of the deviations of the Model B3 from those data have been evaluated to be distinctly smaller than those for CEB 90 Model and ACI 209 model [25,33,34]. But the model cannot consider the effects of admixtures and pozzolanic materials and the prediction of the model parameters is restricted to Portland cement concrete with the parameter ranges as 17 MPar f c r 70 MPa, 0:35 rw=c r 0:85,
ð1Þ
where f c ¼mean 28-day standard cylinder compression strength of concrete (MPa); w/c¼ water–cement ratio, by weight. It has been demonstrated that the higher compressive strength, lower water–cement ratio and the presence of silica fume can make the creep of HSC quite different from that of normal strength concrete [20,22,24,26]. In order to predict the creep of HSC, it is vital to modify the Model B3 directed against these factors. Therefore, the model developed in this paper for the creep of HSCFT columns is based on the creep model for HSC proposed by Ma and Wang [28]. The concrete core of CFT columns subjected to constant axial loads is under the state of triaxial variable stress, whose confining stress and axial stress both vary with time since the variation of the transverse strain and the internal force redistribution between the two components, respectively. Therefore, the creep of the concrete core concerns the concepts of the effective creep Poisson’s ratio of concrete [35,36] and the principle of superposition [37]. According to the principle of superposition, the creep strain in one direction of the concrete under the state of triaxial stress is the algebraic sum of the creep strain in this direction caused by each stress component acting separately, and the total creep of the concrete subjected to a uniaxial variable stress can be obtained by adding the creep strains caused by small stress increments applied at small time intervals.
Fig. 2. Instrumentation for axial creep tests.
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In addition, the microstructure of the HSC determines an obvious difference in the long-term deformation between the NSCFT columns and HSCFT columns. It is feasible to only consider the basic creep of the concrete core for the former case, because the sealing action provided by the steel tube protects the concrete core from migration and loss of moisture, and considerably reduces its shrinkage and drying creep [17]. However, for the latter case, the autogenous shrinkage of the HSC unrelated to migration and loss of moisture accounts for a considerable proportion of the total shrinkage [21,23]. Therefore, the basic creep and autogenous shrinkage of the HSC core should be both considered in the long-term deformation of HSCFT columns. The creep model for HSCFT developed in this paper is based on the autogeneous shrinkage model given by Mazloom et al. [26] and Mazloom [27], which can consider the effect of the silica fume content as
esh ðtÞ ¼
t 516y106 0:3SF þ12:6 þ t
y ¼ 0:014SF þ 0:39
ð2Þ ð3Þ
where SF¼percentage of silica fume to binder materials; t ¼concrete age (d). 3.2. Creep model for HSCFT The creep model for HSCFT is developed by incorporating the creep model for the concrete core into the composite section analysis based on the mechanical equilibrium and strain compatibility, with considering the confinement effect. The creep analysis in this paper is based on the linear creep assumption, given the fact that the levels of the concrete stress for the four specimens are all within 40% of the cylindrical compressive strength. Detailedly, it is performed through two steps: initial static analysis and creep analysis. Being given a proper initial value, the initial axial stress in the HSC core sc1 ðt 0 Þ due to the applied constant axial stress s can be determined by an iterative calculation based on the short-time stress–strain relationship of the concrete core in CFT columns [38] and the following conditions as
principle of superposition, can therefore be written as
ec1 ðtn Þ ¼ Jðtn ,t0 Þsc1 ðt 0 Þ þ "
n X 1 i¼1
2
2mc Jðt n ,t 0 Þsc3 ðt 0 Þ þ
½Jðt n ,t i Þ þ Jðt n ,t i1 ÞDsc1 ðt i Þ þ esh ðt n Þ n X 1 i¼1
2
# ½Jðt n ,t i Þ þJðt n ,t i1 ÞDsc3 ðt i Þ ð8Þ
where ec1 ðt n Þ¼axial strain of the concrete core at the age of tn; Jðt n ,t 0 Þ¼creep compliance function of concrete under uniaxial constant stress, which is taken as elastic plus creep strain caused by a unit uniaxial constant stress; tn ¼target time, representing the age of concrete; t0 ¼age at loading; Dsc1 ðt i Þ ¼small axial stress increment in concrete applied at small time interval t i t i1 ; esh ðt n Þ ¼autogenous shrinkage of concrete at time tn; mc ¼effective creep Poisson’s ratio of concrete; sc3 ðt 0 Þ¼initial confining (hoop) stress in concrete; Dsc3 ðt i Þ ¼small confining (hoop) stress increment in concrete applied at small time interval t i t i1 . In accordance to the geometric compatibility, the axial strains of the concrete core and the steel tube are equal for every time step. Apparently, the axial strain of the steel tube es1 ðt n Þ, further the axial stress increment of the steel tube Dss1 ðt n Þ, can be drawn from the present ec1 ðt n Þ. Here the steel tube is assumed to remain linear-elastic. Consequently, the axial stress increment of the concrete core Dsc1 ðt n Þ can be obtained by satisfying another essential requirement, the static equilibrium, for each time step as
Dsc1 ðtn ÞAc þ Dss1 ðtn ÞAs ¼ 0
ð9Þ
where Ac and As ¼cross-sectional areas of the steel tube and the concrete core, respectively. On the other hand, the hoop strain of the concrete core for this step ec3 ðt n Þ can also be obtained from the present level of ec1 ðt n Þ as
ec3 ðtn Þ ¼ mc ec1 ðtn Þ
ð10Þ
es1 ðt0 Þ ¼ ec1 ðt0 Þ
ð4Þ
In sequence, the condition of geometric compatibility es3 ðtn Þ ¼ ec3 ðtn Þ gives the present hoop strain of the steel tube es3 ðtn Þ and then the hoop stress increment of the steel tube Dss3 ðt n Þ. Finally from the condition of static equilibrium, the hoop (confining) stress increment in the concrete core Dsc3 ðt n Þ can be calculated as
es3 ðt0 Þ ¼ ec3 ðt0 Þ ¼ m0 ec1 ðt0 Þ
ð5Þ
Dsc3 ðtn Þ ¼
ss1 ðt0 Þ ¼
Es es1 ðt0 Þ þ ms es3 ðt0 Þ 1m2s
sc1 ðt0 Þ ¼ sss1 ðt0 Þ
ð6Þ ð7Þ
where sc1 ðt 0 Þ and ss1 ðt 0 Þ¼initial axial stresses in the concrete core and the steel tube, respectively; ec1 ðt 0 Þ and es1 ðt 0 Þ ¼initial axial strains in the concrete core and the steel tube, respectively; ec3 ðt0 Þ and es3 ðt0 Þ ¼initial hoop strains in the concrete core and the steel tube, respectively; m0 and ms ¼Poisson’s ratio of concrete and steel, respectively; Es ¼ elastic modulus of the steel tube. By giving the new value to the variable sc1 ðt 0 Þ, the iterative procedure can be realized, until the equivalence of the present and new values of sc1 ðt0 Þ is achieved. Once the initial stresses in the HSC core and the steel tube both have been determined, the creep analysis can then be performed by dispersing the long-term process into small time intervals, because the axial stresses in the concrete core and steel tube and the confining stress all vary with time constantly. The creep analysis needs an iterative procedure as well. For one aimed age tn, by giving proper initial values to the axial and confining stress increments of the concrete core corresponding to the present time step t n t n1 , the axial strain of the concrete core, according to the
a 2
Dss3 ðtn Þ
ð11Þ
where a ¼steel ratio, a ¼ As =Ac ¼ 2t=r; t¼ thickness of the steel tube; r ¼radius of the concrete core. It is clear that new values of the axial and confining stress increments of the concrete core can be acquired from the present values of these two variables by this procedure. If the differences between the new values and the present values are greater than the allowable tolerances, these two variables should be given the new values to repeat the procedure. And the differences being within the allowable tolerances means the proper values of these two variables have been obtained for this time step. For the following time steps the procedure should be repeated. It is notable that the state of multiaxial stress of the steel tube should also be taken into account when calculating the Dss1 ðt n Þ and Dss3 ðt n Þ. The procedure to calculate the axial strain of HSCFT under the sustained axial load is elaborated in Fig. 3.
4. Experimental results and theoretical predictions The measured axial elastic plus creep strains of the cylindrical specimens HSCFT-A and HSCFT-B under the sustained axial load for 380 day are plotted in Figs. 4 and 5, where shrinkage strains
Y.S. Ma, Y.F. Wang / Thin-Walled Structures 53 (2012) 91–98
Fig. 3. Calculation procedure for the creep of HSCFT.
have been excluded. It can be observed that the strain of the specimens kept increasing during the whole test. However, especially for the two specimens of HSCFT-B, the creep strain grows with a relatively rapid rate for the early ages; and it maintains a slow growing tendency during the later ages. The axial strains of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 at the age of 50 day account for 86.0%, 90.3%, 98.1% and 91.9% of the corresponding axial strains measured at the end of the test. And the percentages reach 91.0%, 93.5%, 98.9% and 93.8% at the age of 100 day. The tested creep coefficients at the age of 126 day, defined as the ratio of the net creep strains to the initial elastic strains, of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 are 0.72, 0.75, 0.53 and 0.57, respectively. These tested results are fairly lower than that presented by Uy [7], whose HSCFT column specimens subjected to a sustained low-level axial stress for 126 day have the maximum creep coefficient of 1.0. It can be concluded that the compressive strength of the HSC core, being 52 MPa for Uy’s
Fig. 4. Test data and prediction for the creep of HSCFT-A.
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Fig. 5. Test data and prediction for the creep of HSCFT-B.
specimens and 70.5 MPa and 85.5 MPa for the specimens investigated in this paper as mentioned above, contributes a lot to this diversity. The comparisons in the creep coefficient are further made between HSCFT columns and NSCFT columns. The creep coefficients given by Nakai et al. [14] and Terrey et al. [15] are 1.5 and 1.25, respectively, both of which are markedly greater than the results measured from HSCFT columns. The comparisons between the test data and the predictions by the proposed creep model for HSCFT using the modified B3 Model for HSC are also given in Figs. 4 and 5. It can be seen that the theoretical predictions are basically in accordance with the test results, although for the early age the creep model under-predicts the axial strain a little. According to Neville et al. [37], the error coefficient of a creep model can be calculated as M¼
1 C ðt,t 0 Þ
X
" 2 #0:5 Cðt,t 0 ÞC 0 ðt,t 0 Þ n
ð12Þ
Fig. 6. Error coefficient of the creep model. (a) Specimens HSCFT-A. (b) Specimens HSCFT-B.
where M ¼error coefficient; Cðt,t 0 Þ ¼ observed strain at time t; C 0 ðt,t 0 Þ¼ predicted strain at time t; C ðt,t 0 Þ ¼mean observed strain for a number of observations n. The error coefficients of the proposed model for the creep of HSCFT-A1, HSCFT-A2, HSCFT-B1 and HSCFT-B2 are shown in Fig. 6. As expected, the magnitude of the error coefficients tends to decrease with time for both HSCFTA and HSCFT-B. For most of the loading process, the error coefficients are within the 0–5% band. Especially, for the later period, the error coefficients are comparative low, which proves the effectiveness of the creep model.
5. Parametric analysis The long-term behavior of HSCFT columns is influenced by many parameters, particularly the diameter-to-thickness ratio and concrete mix composition and compressive strength. It is highly expensive and time consuming to experimentally investigate the effects of every parameter. Therefore, theoretical analysis based on a reliable model is a feasible alternative in observing the influences of extensive parameters. In view that the effect of the diameter-to-thickness ratio has been investigated thoroughly [17], parametric analysis was performed to gain insight into the possible influences of the concrete mix composition and compressive strength in this paper. Figs. 7–9 illustrate the influences of the water-binder ratio (w/b), the aggregate-binder ratio (a/b) and the silica fume-binder ratio (s/b) on the creep of HSCFT columns. The dimension and the concrete mix of the calculated columns are same to the test
Fig. 7. Effect of water-binder ratio on the creep of HSCFT.
specimens HSCFT-A, except for the factors being studied for their effects. The object for comparison is the creep compliance of each column, which gets rid of the effect of stress and can reveal the essential creep property of HSCFT columns with different parameters. As shown in Figs. 7 and 8, it is clear that the general effect of increasing w/b or decreasing a/b is to increase the creep of HSCFT columns. As the w/b are 0.4 and 0.5, the corresponding creep compliances at the age of 380 day are 1.05 and 1.11 times greater
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remains comparatively stable during the later period. Therefore, it is important to account for the significant reducing effect of silica fume on the creep of HSCFT columns. Fig. 10 displays the influence of concrete compressive strength on the creep of CFT columns. This influence is interrelated with the concrete composition actually. The NSCFT column with the compressive strength of the concrete core of 40 MPa is set for highlighting the difference in creep between HSCFT and NSCFT columns. Its concrete composition is totally different from that of the HSCFT column, and is representative of common concrete mix for NSCFT columns, with the contents of cement, water, aggregate and silica fume being 370 kg/m3, 163 kg/m3, 1913 kg/m3 and 0 kg/m3, respectively. As it can be seen, the final creep compliance of the NSCFT column is about 15% higher than that of the HSCFT column. Fig. 8. Effect of aggregate-binder ratio on the creep of HSCFT.
6. Conclusions This paper focuses on the creep behavior of HSCFT columns. Creep and companion shrinkage tests have been conducted on eight HSCFT specimens with different concrete mix composition. It has been found that the creep of HSCFT columns develops mostly in the early ages, and it grows comparatively slowly during the later period of loading. Comparison with the creep of NSCFT columns manifests that the creep coefficient of HSCFT columns is generally lower than that of NSCFT columns. Analytical model for the creep of HSCFT columns, based on the modified B3 Model, has been developed to support the investigation and has been demonstrated to be accordance with the test results. Parametric analysis shows that there exists an important influence of the concrete composition and compressive strength on the creep of HSCFT columns.
Fig. 9. Effect of silica-binder ratio on the creep of HSCFT.
Acknowledgments The authors would like to gratefully acknowledge the financial support of National Science Foundation of China (grant no.: 50778020). References
Fig. 10. Effect of concrete compressive strength on the creep of HSCFT.
than that with the w/b of 0.3, respectively. As the a/b are 4.5 and 5.5, the corresponding creep compliances at the age of 380 day are 97% and 95% of that with the a/b of 3.5, respectively. As it can be seen in Fig. 9, there is an obvious decrease in the creep compliance at high levels of silica fume content. When the s/b are 5% and 10%, the corresponding creep compliances are 86% and 78%, respectively, of that without the silica fume at the age of 380 day. Additionally, the creep compliance of the specimen without silica fume tends to ascent obviously even in the later ages; while that of the other two specimens with silica fume
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