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Experimental investigation of thin-walled centrifugal concrete-filled steel tubes under torsion
ARTICLE IN PRESS
Thin-Walled Structures 46 (2008) 1087–1093 www.elsevier.com/locate/tws
Experimental investigation of thin-walled centrifugal concrete-filled steel tubes under torsion Ju Chen, Wei Liang Jin, Jun Fu Department of Civil Engineering, Zhejiang University, Hang Zhou 310027, China Received 10 December 2007; received in revised form 21 January 2008; accepted 24 January 2008 Available online 14 March 2008
Abstract The main objective of this paper is to study the behavior and design of thin-walled centrifugal concrete-filled steel tubes under torsion. The thin-walled centrifugal concrete-filled steel tubes were a steel tube with a centrifugal concrete tube inside. A test program has been carried out to study the behavior of thin-walled centrifugal concrete-filled steel tube under torsion. Material properties of the concrete and steel used in the test specimens were measured. In addition, torsion tests were also carried out on the steel tubes. Current design standards are used to predict the specimen strengths under torsion. It is shown that design strengths predicted by standards are conservative. Design method proposed by other researchers for concreted-filled steel tubes under torsion are also used to predict the strengths of centrifugal concrete-filled steel tubes. It is shown that design strengths predicted by other researchers are unconservative. r 2008 Elsevier Ltd. All rights reserved. Keywords: Centrifugal concrete-filled steel tube; Composite structure; Design; Experimental investigation; Torsion
1. Introduction Concrete-filled steel tubes have been widely used in structural members in factories, power stations, bridges, high-rise buildings, etc. for decades, due to their excellent structural performance characteristics, which include high strength and high ductility. Recently, concrete-filled steel tubes have undergone increased usage, which has been influenced by the development of building material and fabricating technique, enabling these columns to be considerably economized. A new kind of concrete-filled steel tubes, namely thin-walled centrifugal concrete-filled steel tubes has been used increasingly, especially in power station structures. The thin-walled centrifugal concretefilled steel tubes were a thin-walled steel tube with a centrifugal concrete tube inside. Due to the effect of centrifugalization, the concrete tube inside the steel tube is relatively thin. With the thin concrete tube, the weight of thin-walled centrifugal concrete-filled steel tubes was small. Previous studies have focused on a better understanding of the behavior of concrete-filled tubes under axial load and Corresponding author. Tel./fax: +86 571 87951817.
E-mail address: [email protected] (J. Chen). 0263-8231/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2008.01.015
bending [1–3]. There is little research towards the concretefilled tubes under torsion [4,5]. There is no provision for concrete-filled tubes under torsion in current AISC specification [6]. However, the torsion effect could not be neglected in some cases, such as in power station structures. Therefore, it is important to know the behavior of concrete-filled tubes under torsion. In this study, experimental investigation was carried out to study the behavior and design of thin-walled centrifugal concretefilled steel tube under torsion.
2. Test program 2.1. Test specimen A total of 21 centrifugal concrete-filled steel tube specimens, with different specimen lengths, cross-section dimensions were tested. The measured cross-section dimensions and specimen length for each test specimen are shown in Table 1, using the nomenclature defined in Fig. 1. The test specimens are labeled such that the thickness of steel tube and thickness of concrete tube as well as the specimen length could be identified from the
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fscy
Nomenclature Ac Ao
concrete tube cross-section area concrete tube cross-section area specified in ACI code As steel tube cross-section area a, b, B, C, a, x, g coefficients C steel tube torsional constant D outer diameter of steel tube d inner diameter of concrete tube Ec elastic modulus of concrete Ect elastic modulus of concrete tubes Es elastic modulus of steel Fcr buckling stress of steel tubes under torsion fct compressive stress of concrete tubes fcu compressive stress of concrete obtained from standard cubic test
label. For example, the labels ‘‘S3.0C30L600A’’ and ‘‘S4.5C25L2000C’’ define the specimens as follows:
compressive yield stress of the concrete-filled steel tube fy yield stress of steel L specimen length tc thickness of concrete tube ts thickness of steel tube T torsional strength TC-ACI torsional strength of concrete tubes calculated using ACI code TS-AISC torsional strength of steel tubes calculated using AISC standard Tu torsional strength Tu-design torsional strength calculated using design standard Tu-test torsional strength obtained from test results Wsct torsional modulus ex, ey, exy measured strains l slenderness ratio
The first three letters indicate that the thickness of the steel tube, where the prefix letter ‘‘S’’ refers to steel tubes, ‘‘3.0’’ and ‘‘4.5’’ refer to the nominal plate thickness of the steel tube in mm. The following three letters indicate the thickness of the concrete tube, where the letter ‘‘C’’ refers to concrete tube, ‘‘30’’ and ‘‘25’’ refer to the nominal plate thickness of the concrete tube in mm.
Table 1 Measured dimensions of test specimens Specimen
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S4.5C25L600A S4.5C25L600B S4.5C25L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D S4.5C25L3000A S4.5C25L3000B
Diameter D (mm) 201.1 200.9 201.0 199.8 200.9 201.3 198.6 198.8 200.4 201.0 202.0 200.8 198.9 199.3 199.1 202.3 200.4 200.1 200.6 200.0 199.8
Length L (mm) 598 597 596 599 601 603 598 596 602 1997 1995 1998 1996 1998 1997 3000 2995 2996 2998 2994 2998
The following three or four digits are the nominal length of the specimen in mm (600 and 3000 mm). The last letter ‘‘A’’ (‘‘B’’, ‘‘C’’, ‘‘D’’) indicates the repeated test.
The steel tubes were all manufactured from mild steel sheet, with the plate being cut from the sheet, tack welded into a circular shape and then welded with a single-bevel butt weld. The strips of the steel tubes were tested in tension. Three coupons were taken from the steel tube were tested in tension. From these tests, the average yield strength (fy) of the tubes having nominal plate thicknesses of 3.0 and 4.5 mm was found to be 272 and 302 MPa. The ultimate strength was found to be 360 and 450 MPa,
Thickness ts (mm)
tc (mm)
2.92 2.96 2.93 2.94 2.97 2.95 4.46 4.47 4.44 2.98 2.97 2.96 4.49 4.46 4.47 2.95 2.93 2.96 2.96 4.43 4.48
29.8 29.4 30.6 19.5 19.2 19.1 25.5 26.0 24.6 19.0 19.2 19.1 25.7 26.0 25.6 19.3 20.5 20.8 20.9 24.3 24.8
ts
tc
d
D Fig. 1. Definition of symbols.
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Fig. 2. Compressive test of stub concrete tube.
and the modulus of elasticity (Es) was 214,000 and 211,000 MPa, respectively. The concrete mix was designed for compressive cube strength (fcu) at 28 days of approximately 40 MPa. The modulus of elasticity (Ec) of concrete was measured, the average value being 32,500 MPa. The mix proportions were (cement:sand:coarse aggregate:cement ¼ 1:1.8:2.2:0.5). Both compressive strength and split strength tests were carried out on concrete cubic specimens (150 150 mm) at 28 days. The average cubic compressive strength and split strength were 43.4 and 2.037 MPa, respectively. The concrete inside the steel tubes were centrifugal and was considered to be different from the standard cubic concrete specimen. However, due to the thin thickness of the concrete tubes (20–30 mm), standard cubic compressive strength tests are not applicable. Therefore, eight plain centrifugal concrete stub tubes using the same batch of concrete were tested in compression, as shown in Fig. 2. The average compressive strengths (fct) and elastic modulus of the concrete tubes (Ect) was found to be 36.8 and 42,000 MPa, respectively. The compressive strengths obtained from concrete tube tests were lower than those obtained from the standard cubic tests while the elastic modulus obtained from concrete tube tests was higher. The lower compressive strengths may be due to the tube test specimens. Therefore, the cubic compressive strength test results were used in the design.
Fig. 3. Test setup.
calculated as the product of pull force and radius of fan shape plate. It should be noted that both end plates could be rotated or fixed. A theodolites was used to keep the horizontal level of the specimens during setup. A scale plate with angle measurement was used to measure the rotation of the specimens. In addition, 24 linear strain gauges were used to measure the strain. Twelve strain gauges were attached around the specimen at the mid-length. Six strain gauges were attached around the specimens at the 1/4 and 3/4 length of the specimen, respectively. Three strain gauges were attached at each point to measure the two normal strains (ex, ey) and the shear strain (exy). A data acquisition system was used to record the readings of strain at regular intervals during the tests. A load interval of approximately one-tenth of the estimated load capacity was used. Each load interval was maintained for about 2–3 min. At each load increment the strain readings and the rotation measurements were recorded. A load interval of approximately 5% of the estimate load capacity was used near failure. All specimens were loaded to failure. Each test took approximately 2 h to complete. 3. Test results 3.1. Steel tubes
2.2. Test setup A special torsion test setup was used in this test program, as shown in Fig. 3. The two ends of the specimen were fixed on two thick high strength steel end plates using flange, respectively. Fan shape plates with the radius of approximate 1000 mm were welded on the end plates. The torsion torque was applied to the specimen by rotating the fan shape plates. A steel cable around the circuit of the fan shape plate was used to pull the fan shape. A sensor was used to measure the pull force applied on the steel cable by loading the machine so that the torsion torque could be
Because of its closed cross section, a round steel tube is far more efficient in resisting torsion than an open cross section. While normal and shear stresses due to restrained warping are usually significant in shapes of open cross section, they are insignificant in closed cross sections. The total torsional moment could be assumed to be resisted by pure torsional shear stresses. [7] In this study, local buckling was observed for steel tubes with nominal plate thickness of 3.0 mm. No obvious local buckling was observed for steel tubes with nominal plate thickness of 4.5 mm during tests. Current AISC specification [6] has
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Table 2 Comparison of ultimate strengths of steel tubes obtained from test results with AISC predictions Specimen D (mm) ts (mm) L (mm) Tu (kN m) TS-AISC Tu/TS-AISC S1 S2
201.2 200.6
2.94 4.48
598 597
25.0 49.8
30.5 48.8
0.82 1.02
provisions considering local buckling in round steel tubes subjected to torsion. However, the design equations in AISC specification for elastic local buckling strength are either for long cylinders unaffected by end conditions (Eq. (1)) [8] or for round steel tubes of moderate length where the edges are not fixed at the ends against rotation (Eq. (2)) [8,9]. In this study, the specimens are relatively short (L=600 mm) and fixed at the both two ends. The ultimate strengths of steel tubes under torsion obtained from the test rustles are compared with the design strengths calculated using Eq. (1) in Table 2. In this study, the local buckling stress calculated using Eqs. (2) and (3) are larger than shear yield strength 0.6fy, therefore, shear yield strength 0.6fy is used to calculate the ultimate strengths according to AISC specification [6]. It is shown that design strengths are unconservative for steel tubes having nominal plate thickness of 3.0 mm but conservative for steel tubes having nominal plate thickness of 4.5 mm. This may be due to the relative short length of the test specimens: T n ¼ F cr C,
(1)
1:23E , F cr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi ðL=DÞðD=tÞ5=4
(2)
F cr ¼
0:60E ðD=tÞ3=2
.
(3)
3.2. Centrifugal concrete-filled steel tubes Based on the observation during the tests processor and analysis of test data, the specimens are considered to experience three stages under loading until failure. In the first stage, the concrete and steel tubes work together initially; minor crack occurs in the tension zone of concrete tube with the load increases. With the growth of the crack, the concrete under tension gradually lost its strength. In the second stage, the concrete in the tension zone completely lost its strength while the concrete in compression continue to resist the load. At the end of the second stage, the steel tubes reach yielding. In the third stage, the concrete in compression completely lost its strength and large deformation occurs in the compression zone of steel tubes. The concrete inside the steel tubes was taken out from those failure specimens. There are lots of crack distributed on the concrete tubes. The angel between the crack and axis along the length of specimens is approximately 451, as
Fig. 4. Concrete tube taken from the failure specimen.
shown in Fig. 4. The concrete in the compression zone was crushed. The coherence between the concrete and steel tubes remains well except in the concrete crushed zone. The ultimate strengths of centrifugal concrete-filled steel tubes obtained from the tests are presented in Tables 3 and 4. The load versus angle curves are plotted in Fig. 5. The y-axis is plotted against load while the x-axis is plotted against relative angle rotated of the two end sections. It is shown that the ultimate strengths of the repeated specimens are similar. Strain gauges are used to measure the strain of specimens during tests, as described above. Based on the measure strains (ex, ey, exy), the principal tensile stress (s1) and compressive stress (s2) could be calculated using the following equations within the elastic range: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E x þ y 1 2ðxy x Þ2 þ 2ðxy y Þ2 , (4) þ s1 ¼ 2 1þm 1þm s2 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E x þ y 1 2ðxy x Þ2 þ 2ðxy y Þ2 . 2 1þm 1þm
(5)
The test results indicate that the principal tensile stress s1 is larger than the principal compressive stress s1 on the steel tube surface. This may be explained that the tensile stress is mainly resisted by the steel tube while the compressive stress is resisted by the steel tube and concrete together. Based on the test results of specimen series S3.0C20 and S4.5C25, the effect of slenderness ratio (l ¼ L/D) on specimens ultimate strength under torsion was also investigated, as shown in Fig. 6. It is shown that
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Table 3 Comparison of ultimate strengths obtained from test results with standard predictions for specimen series S3.0 Specimen
Test
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D
Design
Comparison Tu-test/Tu-design
Tu-test (kN m)
TC-ACI (kN m)
TS-AISC (kN m)
Tu-design (kN m)
44.5 44.5 44.1 39.1 39.1 38.6 38.9 39.7 42.7 39.6 35.6 37.3 40.1
3.4 3.3 3.4 2.5 2.5 2.5 2.4 2.5 2.4 2.5 2.6 2.6 2.6
29.8 30.2 29.9 29.6 30.3 30.2 30.4 30.6 30.1 30.5 29.7 29.9 30.1
33.2 33.5 33.3 32.1 32.7 32.6 32.8 33.1 32.6 33.0 32.3 32.5 32.7 Mean COV
1.34 1.33 1.32 1.22 1.20 1.18 1.19 1.20 1.31 1.20 1.10 1.15 1.23 1.23 0.061
Table 4 Comparison of ultimate strengths obtained from test results with standard predictions for specimen series S4.5 Specimen
Test
S4.5C25L600A S4.5C25L600B S4.5C25L600C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S4.5C25L3000A S4.5C25L3000B
Design
Comparison Tu-test/Tu-design
Tu-test (kN m)
TC-ACI (kN m)
TS-AISC (kN m)
Tu-design (kN m)
60.5 60.2 59.4 54.5 57.1 55.0 53.3 55.0
2.8 2.9 2.8 2.8 2.9 2.8 2.8 2.8
52.9 53.1 53.7 53.4 53.3 53.3 53.4 53.8
55.7 56.0 56.5 56.2 56.2 56.1 56.2 56.6 Mean COV
1.09 1.08 1.05 0.97 1.02 0.98 0.95 0.97 1.01 0.051
4. Design methods
50.0
4.1. Current design standard
40.0
Fig. 5. Torsion moment versus angle curves obtained from test results.
The ultimate strengths of centrifugal concrete-filled steel tubes (Tu-test) are compared with the design strengths (Tu-design). The design strengths are taken as the summary of the design strengths of concrete plain tube (TC-ACI) and design strengths of steel tubes (TS-ASCE), as shown in Tables 3 and 4. The design strengths of steel tubes are calculated according to AISC specification [6] using Eq. (1). The design strengths of concrete tubes are calculated according to ACI code [10] used below: qffiffiffiffiffi T ¼ 8Ao t f 0c . (6)
for both series generally the slenderness ratio has no significant effect on the ultimate strength of centrifugal concrete-filled steel tubes under torsion.
It is also shown that the design strengths enhancement is very conservative for specimen series S3.0. The design strengths for specimen series S4.5 generally agree with the test results well. Taken into account the unconservative
Tu (kN.m)
60.0
30.0 S3.0C20L200A 20.0
S3.0C30L600A S4.5C25L2000A
10.0
S4.5C25L3000A
0.0 0
2
4
6 (degree)
8
10
12
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8 > < 1; a ¼ 450 > : f ; y
70 60
Tu (kN)
50
f y p450 MPa;
2
40
6 6 6 6 6 6 b¼6 6 6 6 0:1 6 fc 4 41
30 20
Series S3.0C20
10
Series S4.5C25
0 20
10
0
30
40
50
(13)
f y 4450 MPa; !1:1 0:1 f ck 450 41 fy
f y 4450 MPa; f c p41 MPa;
1
450 fy
f y p450 MPa;
!0:4 fc441 MPa
60
(14)
Fig. 6. Effect of slenderness ratio on ultimate strengths.
predictions of steel tubes strength under torsion as shown in Table 2, the concrete inside the steel tubes greatly enhance the specimen strengths. This may be explained by the restraining effect of filled concrete on the steel tube wall. 4.2. Han’s method Based on experimental and numerical investigation, Han [11] proposed a design method for concrete-filled steel tubes under torsion. It should be noted that the proposed design method is based on the study of full section concrete-filled steel tubes. The design equations are shown in Eqs. (7)–(14). The design torsion strength, Tu is T u ¼ gt W sct tscy ,
(7)
where Wsct is the torsional modulus, gt is the coefficient: gt ¼ 1:294 þ 0:267 lnðxÞ.
(8)
The torsion yielding stress tscy of the concrete-filled steel tube is tscy ¼ ð0:422 þ 0:313a2:33 Þx0:134 f scy .
fy B ¼ 0:1759 235
(10)
a
f C ¼ 0:1038 c 20
þ 0:974,
(11)
b þ 0:0309,
5. Conclusions An experimental investigation on centrifugal concretefilled steel tubes under torsion has been carried out in this study. Material properties of the concrete and steel used in the test specimens were measured. In addition, torsion tests were also carried out on the steel tubes. Local buckling was Table 5 Comparison of ultimate strengths obtained from test results with Han’s predictions for specimen series S3.0 Specimen
Test Tu-test (kN m)
Design Tu-design (kN m)
Comparison Tu-test/Tu-design
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D
44.5 44.5 44.1 39.1 39.1 38.6 38.9 39.7 42.7 39.6 35.6 37.3 40.1
46.1 46.5 46.2 45.3 46.2 46.1 46.3 46.7 46.0 46.6 45.5 45.8 46.0 Mean COV
0.97 0.96 0.96 0.86 0.85 0.84 0.84 0.85 0.93 0.85 0.78 0.81 0.87 0.87 0.069
(9)
The torsion yielding stress tscy is considered to be relating to compressive yield stress of the concrete-filled steel tube. The compressive yield stress of the concretefilled steel tube fscy could be calculated using the equations given below: f scy ¼ ð1:212 þ Bx þ Cx2 Þf c ,
where a=As/Ac; x=Asfy/Acfc; fy is the steel yield strength; fc is the concrete compressive strength; As is the section area of steel tube and Ac is the section area of concrete tube. The suitability of these equations for centrifugal concrete-filled steel tubes is evaluated by using test results in Tables 5 and 6. The mean values of Tu-test/Tu-design for S3.0 and S4.5 series are 0.87 and 0.77, with the corresponding coefficients of variation (COV) of 0.069 and 0.051, respectively. It is shown that the predictions from Eqs. (7)–(14) are unconservative for all specimens. This may due to the design method proposed by Han [11] was based on the study of full section concrete-filled steel tubes.
(12)
ARTICLE IN PRESS J. Chen et al. / Thin-Walled Structures 46 (2008) 1087–1093 Table 6 Comparison of ultimate strengths obtained from test results with Han’s predictions for specimen series S4.5 Specimen
Test Tu-test (kN m)
Design Tu-design (kN m)
Comparison Tu-test/Tu-design
S4.5C25L600A S4.5C25L600B S4.5C25L600C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S4.5C25L3000A S4.5C25L3000B
60.5 60.2 59.4 54.5 57.1 55.0 53.3 55.0
73.5 73.7 74.8 74.0 74.0 74.0 74.4 74.8 Mean COV
0.82 0.82 0.79 0.74 0.77 0.74 0.72 0.74 0.77 0.051
observed from the test of specimen series S3.0. It is shown that AISC specification unconservatively predicted the ultimate strengths of steel tubes having nominal plate thickness of 3.0 mm but conservatively predicted the ultimate strengths of steel tubes having nominal plate thickness of 4.5 mm. The ultimate strengths of centrifugal concrete-filled steel tubes obtained from the test results were compared with the design strengths. It is also shown that the design strengths predicted using current standards are very conservative for specimen series S3.0 but generally agree with the test results of specimen series S4.5 well. The suitability of the equations proposed by Han for centrifugal concrete-filled steel tubes is evaluated in this study. It is
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shown that the proposed equations are unconservative. Based on the test results, the effect of slenderness ratio on ultimate strength under torsion was investigated. It is shown that generally the slenderness ratio has no significant effect on the ultimate strength of centrifugal concrete-filled steel tubes under torsion. References [1] Shams M, Saadeghvaziri MA. State of the art of concrete-filled steel tubular columns. ACI Struct J 1997;94(5):558–71. [2] Han LH. Test on stub columns of concrete-filled RHS sections. J Construct Steel Res 2002;58(3):363–75. [3] Elchalakani M, Zhao XL, Grzebieta R. Concrete-filled circular steel tubes subjected to pure bending. J Construct Steel Res 2001;57(11): 1141–68. [4] Han L, Zhong S. The studies of pure torsion problem for concrete filled steel tube. Ind Construct 1995;23:7–13. [5] Beck J, Kiyomiya O. Fundamental pure torsional properties of concrete filled circular steel tubes. J Mater Conc Struct Pavements JSCE 2003;60:285–96. [6] Specification for structural steel buildings. ANSI/AISC 360-05. Chicago, IL: American Institution of Steel Construction (AISC); 2005. [7] Yu WW. Cold-formed steel design. 3rd ed. New York: Wiley; 2000. [8] Galambos TV, editor. Guide to stability design criteria for metal structures, structural stability research council. 5th ed. New York, NY: Wiley; 1998. [9] Schilling CG. Buckling strength of circular tubes. J Struct Div ASCE 1965;91(ST5):4520. [10] ACI Committee 318 (ACI 318). Building code requirements for structural concrete and commentary. Detroit, USA: American Concrete Institute; 2005. [11] Han LH. Concrete-filled steel tube structures—theory and design. 2nd ed. Beijing: Science Press; 2007.
Thin-Walled Structures 46 (2008) 1087–1093 www.elsevier.com/locate/tws
Experimental investigation of thin-walled centrifugal concrete-filled steel tubes under torsion Ju Chen, Wei Liang Jin, Jun Fu Department of Civil Engineering, Zhejiang University, Hang Zhou 310027, China Received 10 December 2007; received in revised form 21 January 2008; accepted 24 January 2008 Available online 14 March 2008
Abstract The main objective of this paper is to study the behavior and design of thin-walled centrifugal concrete-filled steel tubes under torsion. The thin-walled centrifugal concrete-filled steel tubes were a steel tube with a centrifugal concrete tube inside. A test program has been carried out to study the behavior of thin-walled centrifugal concrete-filled steel tube under torsion. Material properties of the concrete and steel used in the test specimens were measured. In addition, torsion tests were also carried out on the steel tubes. Current design standards are used to predict the specimen strengths under torsion. It is shown that design strengths predicted by standards are conservative. Design method proposed by other researchers for concreted-filled steel tubes under torsion are also used to predict the strengths of centrifugal concrete-filled steel tubes. It is shown that design strengths predicted by other researchers are unconservative. r 2008 Elsevier Ltd. All rights reserved. Keywords: Centrifugal concrete-filled steel tube; Composite structure; Design; Experimental investigation; Torsion
1. Introduction Concrete-filled steel tubes have been widely used in structural members in factories, power stations, bridges, high-rise buildings, etc. for decades, due to their excellent structural performance characteristics, which include high strength and high ductility. Recently, concrete-filled steel tubes have undergone increased usage, which has been influenced by the development of building material and fabricating technique, enabling these columns to be considerably economized. A new kind of concrete-filled steel tubes, namely thin-walled centrifugal concrete-filled steel tubes has been used increasingly, especially in power station structures. The thin-walled centrifugal concretefilled steel tubes were a thin-walled steel tube with a centrifugal concrete tube inside. Due to the effect of centrifugalization, the concrete tube inside the steel tube is relatively thin. With the thin concrete tube, the weight of thin-walled centrifugal concrete-filled steel tubes was small. Previous studies have focused on a better understanding of the behavior of concrete-filled tubes under axial load and Corresponding author. Tel./fax: +86 571 87951817.
E-mail address: [email protected] (J. Chen). 0263-8231/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2008.01.015
bending [1–3]. There is little research towards the concretefilled tubes under torsion [4,5]. There is no provision for concrete-filled tubes under torsion in current AISC specification [6]. However, the torsion effect could not be neglected in some cases, such as in power station structures. Therefore, it is important to know the behavior of concrete-filled tubes under torsion. In this study, experimental investigation was carried out to study the behavior and design of thin-walled centrifugal concretefilled steel tube under torsion.
2. Test program 2.1. Test specimen A total of 21 centrifugal concrete-filled steel tube specimens, with different specimen lengths, cross-section dimensions were tested. The measured cross-section dimensions and specimen length for each test specimen are shown in Table 1, using the nomenclature defined in Fig. 1. The test specimens are labeled such that the thickness of steel tube and thickness of concrete tube as well as the specimen length could be identified from the
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fscy
Nomenclature Ac Ao
concrete tube cross-section area concrete tube cross-section area specified in ACI code As steel tube cross-section area a, b, B, C, a, x, g coefficients C steel tube torsional constant D outer diameter of steel tube d inner diameter of concrete tube Ec elastic modulus of concrete Ect elastic modulus of concrete tubes Es elastic modulus of steel Fcr buckling stress of steel tubes under torsion fct compressive stress of concrete tubes fcu compressive stress of concrete obtained from standard cubic test
label. For example, the labels ‘‘S3.0C30L600A’’ and ‘‘S4.5C25L2000C’’ define the specimens as follows:
compressive yield stress of the concrete-filled steel tube fy yield stress of steel L specimen length tc thickness of concrete tube ts thickness of steel tube T torsional strength TC-ACI torsional strength of concrete tubes calculated using ACI code TS-AISC torsional strength of steel tubes calculated using AISC standard Tu torsional strength Tu-design torsional strength calculated using design standard Tu-test torsional strength obtained from test results Wsct torsional modulus ex, ey, exy measured strains l slenderness ratio
The first three letters indicate that the thickness of the steel tube, where the prefix letter ‘‘S’’ refers to steel tubes, ‘‘3.0’’ and ‘‘4.5’’ refer to the nominal plate thickness of the steel tube in mm. The following three letters indicate the thickness of the concrete tube, where the letter ‘‘C’’ refers to concrete tube, ‘‘30’’ and ‘‘25’’ refer to the nominal plate thickness of the concrete tube in mm.
Table 1 Measured dimensions of test specimens Specimen
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S4.5C25L600A S4.5C25L600B S4.5C25L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D S4.5C25L3000A S4.5C25L3000B
Diameter D (mm) 201.1 200.9 201.0 199.8 200.9 201.3 198.6 198.8 200.4 201.0 202.0 200.8 198.9 199.3 199.1 202.3 200.4 200.1 200.6 200.0 199.8
Length L (mm) 598 597 596 599 601 603 598 596 602 1997 1995 1998 1996 1998 1997 3000 2995 2996 2998 2994 2998
The following three or four digits are the nominal length of the specimen in mm (600 and 3000 mm). The last letter ‘‘A’’ (‘‘B’’, ‘‘C’’, ‘‘D’’) indicates the repeated test.
The steel tubes were all manufactured from mild steel sheet, with the plate being cut from the sheet, tack welded into a circular shape and then welded with a single-bevel butt weld. The strips of the steel tubes were tested in tension. Three coupons were taken from the steel tube were tested in tension. From these tests, the average yield strength (fy) of the tubes having nominal plate thicknesses of 3.0 and 4.5 mm was found to be 272 and 302 MPa. The ultimate strength was found to be 360 and 450 MPa,
Thickness ts (mm)
tc (mm)
2.92 2.96 2.93 2.94 2.97 2.95 4.46 4.47 4.44 2.98 2.97 2.96 4.49 4.46 4.47 2.95 2.93 2.96 2.96 4.43 4.48
29.8 29.4 30.6 19.5 19.2 19.1 25.5 26.0 24.6 19.0 19.2 19.1 25.7 26.0 25.6 19.3 20.5 20.8 20.9 24.3 24.8
ts
tc
d
D Fig. 1. Definition of symbols.
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Fig. 2. Compressive test of stub concrete tube.
and the modulus of elasticity (Es) was 214,000 and 211,000 MPa, respectively. The concrete mix was designed for compressive cube strength (fcu) at 28 days of approximately 40 MPa. The modulus of elasticity (Ec) of concrete was measured, the average value being 32,500 MPa. The mix proportions were (cement:sand:coarse aggregate:cement ¼ 1:1.8:2.2:0.5). Both compressive strength and split strength tests were carried out on concrete cubic specimens (150 150 mm) at 28 days. The average cubic compressive strength and split strength were 43.4 and 2.037 MPa, respectively. The concrete inside the steel tubes were centrifugal and was considered to be different from the standard cubic concrete specimen. However, due to the thin thickness of the concrete tubes (20–30 mm), standard cubic compressive strength tests are not applicable. Therefore, eight plain centrifugal concrete stub tubes using the same batch of concrete were tested in compression, as shown in Fig. 2. The average compressive strengths (fct) and elastic modulus of the concrete tubes (Ect) was found to be 36.8 and 42,000 MPa, respectively. The compressive strengths obtained from concrete tube tests were lower than those obtained from the standard cubic tests while the elastic modulus obtained from concrete tube tests was higher. The lower compressive strengths may be due to the tube test specimens. Therefore, the cubic compressive strength test results were used in the design.
Fig. 3. Test setup.
calculated as the product of pull force and radius of fan shape plate. It should be noted that both end plates could be rotated or fixed. A theodolites was used to keep the horizontal level of the specimens during setup. A scale plate with angle measurement was used to measure the rotation of the specimens. In addition, 24 linear strain gauges were used to measure the strain. Twelve strain gauges were attached around the specimen at the mid-length. Six strain gauges were attached around the specimens at the 1/4 and 3/4 length of the specimen, respectively. Three strain gauges were attached at each point to measure the two normal strains (ex, ey) and the shear strain (exy). A data acquisition system was used to record the readings of strain at regular intervals during the tests. A load interval of approximately one-tenth of the estimated load capacity was used. Each load interval was maintained for about 2–3 min. At each load increment the strain readings and the rotation measurements were recorded. A load interval of approximately 5% of the estimate load capacity was used near failure. All specimens were loaded to failure. Each test took approximately 2 h to complete. 3. Test results 3.1. Steel tubes
2.2. Test setup A special torsion test setup was used in this test program, as shown in Fig. 3. The two ends of the specimen were fixed on two thick high strength steel end plates using flange, respectively. Fan shape plates with the radius of approximate 1000 mm were welded on the end plates. The torsion torque was applied to the specimen by rotating the fan shape plates. A steel cable around the circuit of the fan shape plate was used to pull the fan shape. A sensor was used to measure the pull force applied on the steel cable by loading the machine so that the torsion torque could be
Because of its closed cross section, a round steel tube is far more efficient in resisting torsion than an open cross section. While normal and shear stresses due to restrained warping are usually significant in shapes of open cross section, they are insignificant in closed cross sections. The total torsional moment could be assumed to be resisted by pure torsional shear stresses. [7] In this study, local buckling was observed for steel tubes with nominal plate thickness of 3.0 mm. No obvious local buckling was observed for steel tubes with nominal plate thickness of 4.5 mm during tests. Current AISC specification [6] has
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Table 2 Comparison of ultimate strengths of steel tubes obtained from test results with AISC predictions Specimen D (mm) ts (mm) L (mm) Tu (kN m) TS-AISC Tu/TS-AISC S1 S2
201.2 200.6
2.94 4.48
598 597
25.0 49.8
30.5 48.8
0.82 1.02
provisions considering local buckling in round steel tubes subjected to torsion. However, the design equations in AISC specification for elastic local buckling strength are either for long cylinders unaffected by end conditions (Eq. (1)) [8] or for round steel tubes of moderate length where the edges are not fixed at the ends against rotation (Eq. (2)) [8,9]. In this study, the specimens are relatively short (L=600 mm) and fixed at the both two ends. The ultimate strengths of steel tubes under torsion obtained from the test rustles are compared with the design strengths calculated using Eq. (1) in Table 2. In this study, the local buckling stress calculated using Eqs. (2) and (3) are larger than shear yield strength 0.6fy, therefore, shear yield strength 0.6fy is used to calculate the ultimate strengths according to AISC specification [6]. It is shown that design strengths are unconservative for steel tubes having nominal plate thickness of 3.0 mm but conservative for steel tubes having nominal plate thickness of 4.5 mm. This may be due to the relative short length of the test specimens: T n ¼ F cr C,
(1)
1:23E , F cr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi ðL=DÞðD=tÞ5=4
(2)
F cr ¼
0:60E ðD=tÞ3=2
.
(3)
3.2. Centrifugal concrete-filled steel tubes Based on the observation during the tests processor and analysis of test data, the specimens are considered to experience three stages under loading until failure. In the first stage, the concrete and steel tubes work together initially; minor crack occurs in the tension zone of concrete tube with the load increases. With the growth of the crack, the concrete under tension gradually lost its strength. In the second stage, the concrete in the tension zone completely lost its strength while the concrete in compression continue to resist the load. At the end of the second stage, the steel tubes reach yielding. In the third stage, the concrete in compression completely lost its strength and large deformation occurs in the compression zone of steel tubes. The concrete inside the steel tubes was taken out from those failure specimens. There are lots of crack distributed on the concrete tubes. The angel between the crack and axis along the length of specimens is approximately 451, as
Fig. 4. Concrete tube taken from the failure specimen.
shown in Fig. 4. The concrete in the compression zone was crushed. The coherence between the concrete and steel tubes remains well except in the concrete crushed zone. The ultimate strengths of centrifugal concrete-filled steel tubes obtained from the tests are presented in Tables 3 and 4. The load versus angle curves are plotted in Fig. 5. The y-axis is plotted against load while the x-axis is plotted against relative angle rotated of the two end sections. It is shown that the ultimate strengths of the repeated specimens are similar. Strain gauges are used to measure the strain of specimens during tests, as described above. Based on the measure strains (ex, ey, exy), the principal tensile stress (s1) and compressive stress (s2) could be calculated using the following equations within the elastic range: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E x þ y 1 2ðxy x Þ2 þ 2ðxy y Þ2 , (4) þ s1 ¼ 2 1þm 1þm s2 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E x þ y 1 2ðxy x Þ2 þ 2ðxy y Þ2 . 2 1þm 1þm
(5)
The test results indicate that the principal tensile stress s1 is larger than the principal compressive stress s1 on the steel tube surface. This may be explained that the tensile stress is mainly resisted by the steel tube while the compressive stress is resisted by the steel tube and concrete together. Based on the test results of specimen series S3.0C20 and S4.5C25, the effect of slenderness ratio (l ¼ L/D) on specimens ultimate strength under torsion was also investigated, as shown in Fig. 6. It is shown that
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Table 3 Comparison of ultimate strengths obtained from test results with standard predictions for specimen series S3.0 Specimen
Test
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D
Design
Comparison Tu-test/Tu-design
Tu-test (kN m)
TC-ACI (kN m)
TS-AISC (kN m)
Tu-design (kN m)
44.5 44.5 44.1 39.1 39.1 38.6 38.9 39.7 42.7 39.6 35.6 37.3 40.1
3.4 3.3 3.4 2.5 2.5 2.5 2.4 2.5 2.4 2.5 2.6 2.6 2.6
29.8 30.2 29.9 29.6 30.3 30.2 30.4 30.6 30.1 30.5 29.7 29.9 30.1
33.2 33.5 33.3 32.1 32.7 32.6 32.8 33.1 32.6 33.0 32.3 32.5 32.7 Mean COV
1.34 1.33 1.32 1.22 1.20 1.18 1.19 1.20 1.31 1.20 1.10 1.15 1.23 1.23 0.061
Table 4 Comparison of ultimate strengths obtained from test results with standard predictions for specimen series S4.5 Specimen
Test
S4.5C25L600A S4.5C25L600B S4.5C25L600C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S4.5C25L3000A S4.5C25L3000B
Design
Comparison Tu-test/Tu-design
Tu-test (kN m)
TC-ACI (kN m)
TS-AISC (kN m)
Tu-design (kN m)
60.5 60.2 59.4 54.5 57.1 55.0 53.3 55.0
2.8 2.9 2.8 2.8 2.9 2.8 2.8 2.8
52.9 53.1 53.7 53.4 53.3 53.3 53.4 53.8
55.7 56.0 56.5 56.2 56.2 56.1 56.2 56.6 Mean COV
1.09 1.08 1.05 0.97 1.02 0.98 0.95 0.97 1.01 0.051
4. Design methods
50.0
4.1. Current design standard
40.0
Fig. 5. Torsion moment versus angle curves obtained from test results.
The ultimate strengths of centrifugal concrete-filled steel tubes (Tu-test) are compared with the design strengths (Tu-design). The design strengths are taken as the summary of the design strengths of concrete plain tube (TC-ACI) and design strengths of steel tubes (TS-ASCE), as shown in Tables 3 and 4. The design strengths of steel tubes are calculated according to AISC specification [6] using Eq. (1). The design strengths of concrete tubes are calculated according to ACI code [10] used below: qffiffiffiffiffi T ¼ 8Ao t f 0c . (6)
for both series generally the slenderness ratio has no significant effect on the ultimate strength of centrifugal concrete-filled steel tubes under torsion.
It is also shown that the design strengths enhancement is very conservative for specimen series S3.0. The design strengths for specimen series S4.5 generally agree with the test results well. Taken into account the unconservative
Tu (kN.m)
60.0
30.0 S3.0C20L200A 20.0
S3.0C30L600A S4.5C25L2000A
10.0
S4.5C25L3000A
0.0 0
2
4
6 (degree)
8
10
12
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8 > < 1; a ¼ 450 > : f ; y
70 60
Tu (kN)
50
f y p450 MPa;
2
40
6 6 6 6 6 6 b¼6 6 6 6 0:1 6 fc 4 41
30 20
Series S3.0C20
10
Series S4.5C25
0 20
10
0
30
40
50
(13)
f y 4450 MPa; !1:1 0:1 f ck 450 41 fy
f y 4450 MPa; f c p41 MPa;
1
450 fy
f y p450 MPa;
!0:4 fc441 MPa
60
(14)
Fig. 6. Effect of slenderness ratio on ultimate strengths.
predictions of steel tubes strength under torsion as shown in Table 2, the concrete inside the steel tubes greatly enhance the specimen strengths. This may be explained by the restraining effect of filled concrete on the steel tube wall. 4.2. Han’s method Based on experimental and numerical investigation, Han [11] proposed a design method for concrete-filled steel tubes under torsion. It should be noted that the proposed design method is based on the study of full section concrete-filled steel tubes. The design equations are shown in Eqs. (7)–(14). The design torsion strength, Tu is T u ¼ gt W sct tscy ,
(7)
where Wsct is the torsional modulus, gt is the coefficient: gt ¼ 1:294 þ 0:267 lnðxÞ.
(8)
The torsion yielding stress tscy of the concrete-filled steel tube is tscy ¼ ð0:422 þ 0:313a2:33 Þx0:134 f scy .
fy B ¼ 0:1759 235
(10)
a
f C ¼ 0:1038 c 20
þ 0:974,
(11)
b þ 0:0309,
5. Conclusions An experimental investigation on centrifugal concretefilled steel tubes under torsion has been carried out in this study. Material properties of the concrete and steel used in the test specimens were measured. In addition, torsion tests were also carried out on the steel tubes. Local buckling was Table 5 Comparison of ultimate strengths obtained from test results with Han’s predictions for specimen series S3.0 Specimen
Test Tu-test (kN m)
Design Tu-design (kN m)
Comparison Tu-test/Tu-design
S3.0C30L600A S3.0C30L600B S3.0C30L600C S3.0C20L600A S3.0C20L600B S3.0C20L600C S3.0C20L2000A S3.0C20L2000B S3.0C20L2000C S3.0C20L3000A S3.0C20L3000B S3.0C20L3000C S3.0C20L3000D
44.5 44.5 44.1 39.1 39.1 38.6 38.9 39.7 42.7 39.6 35.6 37.3 40.1
46.1 46.5 46.2 45.3 46.2 46.1 46.3 46.7 46.0 46.6 45.5 45.8 46.0 Mean COV
0.97 0.96 0.96 0.86 0.85 0.84 0.84 0.85 0.93 0.85 0.78 0.81 0.87 0.87 0.069
(9)
The torsion yielding stress tscy is considered to be relating to compressive yield stress of the concrete-filled steel tube. The compressive yield stress of the concretefilled steel tube fscy could be calculated using the equations given below: f scy ¼ ð1:212 þ Bx þ Cx2 Þf c ,
where a=As/Ac; x=Asfy/Acfc; fy is the steel yield strength; fc is the concrete compressive strength; As is the section area of steel tube and Ac is the section area of concrete tube. The suitability of these equations for centrifugal concrete-filled steel tubes is evaluated by using test results in Tables 5 and 6. The mean values of Tu-test/Tu-design for S3.0 and S4.5 series are 0.87 and 0.77, with the corresponding coefficients of variation (COV) of 0.069 and 0.051, respectively. It is shown that the predictions from Eqs. (7)–(14) are unconservative for all specimens. This may due to the design method proposed by Han [11] was based on the study of full section concrete-filled steel tubes.
(12)
ARTICLE IN PRESS J. Chen et al. / Thin-Walled Structures 46 (2008) 1087–1093 Table 6 Comparison of ultimate strengths obtained from test results with Han’s predictions for specimen series S4.5 Specimen
Test Tu-test (kN m)
Design Tu-design (kN m)
Comparison Tu-test/Tu-design
S4.5C25L600A S4.5C25L600B S4.5C25L600C S4.5C25L2000A S4.5C25L2000B S4.5C25L2000C S4.5C25L3000A S4.5C25L3000B
60.5 60.2 59.4 54.5 57.1 55.0 53.3 55.0
73.5 73.7 74.8 74.0 74.0 74.0 74.4 74.8 Mean COV
0.82 0.82 0.79 0.74 0.77 0.74 0.72 0.74 0.77 0.051
observed from the test of specimen series S3.0. It is shown that AISC specification unconservatively predicted the ultimate strengths of steel tubes having nominal plate thickness of 3.0 mm but conservatively predicted the ultimate strengths of steel tubes having nominal plate thickness of 4.5 mm. The ultimate strengths of centrifugal concrete-filled steel tubes obtained from the test results were compared with the design strengths. It is also shown that the design strengths predicted using current standards are very conservative for specimen series S3.0 but generally agree with the test results of specimen series S4.5 well. The suitability of the equations proposed by Han for centrifugal concrete-filled steel tubes is evaluated in this study. It is
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shown that the proposed equations are unconservative. Based on the test results, the effect of slenderness ratio on ultimate strength under torsion was investigated. It is shown that generally the slenderness ratio has no significant effect on the ultimate strength of centrifugal concrete-filled steel tubes under torsion. References [1] Shams M, Saadeghvaziri MA. State of the art of concrete-filled steel tubular columns. ACI Struct J 1997;94(5):558–71. [2] Han LH. Test on stub columns of concrete-filled RHS sections. J Construct Steel Res 2002;58(3):363–75. [3] Elchalakani M, Zhao XL, Grzebieta R. Concrete-filled circular steel tubes subjected to pure bending. J Construct Steel Res 2001;57(11): 1141–68. [4] Han L, Zhong S. The studies of pure torsion problem for concrete filled steel tube. Ind Construct 1995;23:7–13. [5] Beck J, Kiyomiya O. Fundamental pure torsional properties of concrete filled circular steel tubes. J Mater Conc Struct Pavements JSCE 2003;60:285–96. [6] Specification for structural steel buildings. ANSI/AISC 360-05. Chicago, IL: American Institution of Steel Construction (AISC); 2005. [7] Yu WW. Cold-formed steel design. 3rd ed. New York: Wiley; 2000. [8] Galambos TV, editor. Guide to stability design criteria for metal structures, structural stability research council. 5th ed. New York, NY: Wiley; 1998. [9] Schilling CG. Buckling strength of circular tubes. J Struct Div ASCE 1965;91(ST5):4520. [10] ACI Committee 318 (ACI 318). Building code requirements for structural concrete and commentary. Detroit, USA: American Concrete Institute; 2005. [11] Han LH. Concrete-filled steel tube structures—theory and design. 2nd ed. Beijing: Science Press; 2007.