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Design of thin-walled centrifugal concrete-filled steel tubes under torsion
ARTICLE IN PRESS Thin-Walled Structures 47 (2009) 271–276
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Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Design of thin-walled centrifugal concrete-filled steel tubes under torsion Juan Chen, Ju Chen , Wei Liang Jin Department of Civil Engineering, Zhejiang University, Hang Zhou, Zhe Jiang 310027, China
a r t i c l e in fo
abstract
Article history: Received 8 April 2008 Accepted 1 August 2008 Available online 7 September 2008
The paper addresses the design of thin-walled centrifugal concrete-filled steel tubes under torsion. An experimental research project was conducted to study the behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion. To further study the structural behaviour of the tubes thoroughly, finite element analyses were performed using ANSYS. The nonlinear finite element model was developed and verified against experimental results. Parametric study was conducted to investigate the effects of different concrete strengths, steel strengths and cross-section geometries on the strength and behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion. The use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion was also investigated. The specimen strengths predicted from the finite element analysis were compared with the design strengths calculated using the AISC and ACI standards. It is also shown design strengths predicted by standards are very conservative. Design method is also proposed based on current standards. It is also shown that design strengths predicted using the proposed method agree with the numerical results well. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Centrifugal concrete-filled steel tube Composite structure Finite element model Structural design Torsion
1. Introduction This paper concerns design of thin-walled centrifugal concretefilled steel tubes under torsion. Normally concrete-filled steel tubes are used as structural members in compression and bending and there is no provision for concrete-filled steel tubes under torsion in current AISC standards [1]. However, in design a thinwalled centrifugal concrete-filled steel tube used in power station structures, it is required to calculate the torsion capacity. The torsion load is mainly caused by the pulling force of the cable. Therefore, it is important to develop a design method for thinwalled centrifugal concrete-filled steel tubes under torsion. An experimental research project to study the behaviour of thinwalled centrifugal concrete-filled steel tubes under torsion has been reported previously [2]. Although the experimental results provided us much useful knowledge, there is still not enough data to propose a design method. Therefore, finite element method was used to further study the structural behaviour of the tubes thoroughly, and provided more data. Finite element method has been used to study the behaviour of concrete-filled steel tubes by many researchers [3–6]. In this study, finite element program ANSYS [7] was used to study the behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion.
Corresponding author. Tel./fax: +86 57187951817.
E-mail address: [email protected] (J. Chen). 0263-8231/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2008.08.001
The main objective of this paper is firstly to develop an accurate finite element model to simulate the behaviour of thinwalled centrifugal concrete-filled steel tubes. The finite element program ANSYS [7] was used in the analysis. The effects of concrete strength and concrete confinement were considered in the analysis. A multi-linear stress–strain curve for the steel tube was used. The interface between concrete and the steel tube was also modeled. The results obtained from the finite element analysis were verified against the test results. Parametric studies were performed to investigate the effect of concrete strength, steel strength and cross-section geometries on the behaviour of thinwalled centrifugal concrete-filled steel tubes under torsion. The results obtained from the parametric study were compared with design strengths calculated using AISC [1] and ACI Standards [8]. In addition, design equations are proposed based on current standards.
2. Finite element model 2.1. General The finite element program ANSYS [7] was used in the simulation. In order to accurately simulate the actual behaviour of thin-walled centrifugal concrete-filled steel tubes, the main three components, namely the confined concrete, the circular steel tube and the interface between the concrete and the steel tube have to be modeled properly. In addition, careful attention
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Nomenclature Ac Ao As
x C D d Fcr fcu
concrete tube cross-section area concrete tube cross-section area specified in ACI code steel tube cross-section area coefficients steel tube torsional constant outer diameter of steel tube inner diameter of concrete tube buckling stress of steel tubes under torsion compressive stress of concrete obtained from standard cubic test
fy L tc ts TC-ACI
yield stress of steel specimen length thickness of concrete tube thickness of steel tube torsional strength of concrete tubes calculated using ACI code torsional strength of steel tubes calculated using AISC standard torsional strength specimen design strength torsional strength obtained from FEA analysis torsional strength obtained from test results
TS-AISC Tu Tu-design Tu-FEA Tu-test
was given to the choice of the element type and mesh size to combining a high level of numerical accuracy and stability with optimum computational efficiency. The load–displacement nonlinear analysis was performed in the analysis.
load was applied in the polar coordinate system so that the applied displacement is tangent to the circle of the steel tube.
2.2. Finite element type and mesh
2.4.1. Steel tubes In the finite element model, the measured stress–strain curves of steel tubes presented by Chen et al. [2] were used. The experimental measured yield stresses (fy) were 272 and 306 MPa for steel tubes with nominal plate thickness of 3.0 and 4.5 mm, respectively. The material behaviour provided by ANSYS [7] allows a multi-linear stress–strain curve to be used. The first part of the multi-linear curve represents the elastic part up to the proportional limit stress with measured Young’s modulus (214,000 and 211,000 MPa for steel tubes with nominal plate thickness of 3.0 and 4.5 mm, respectively) and Poisson’s ratio equal to 0.30.
Different element types have been tried and solid elements were found to be more efficient in modeling the steel tube and the concrete tube as well as the clear defined boundaries of their elements. An eight-node brick element (SOLID45) is used to simulate the steel tube. The SOLID45 element is used for the 3-D modeling of solid structures. A reduced integration option with hourglass control is available for the SOLID45 element [7]. A 3-D structural solid element (SOLID65) is used to simulate the concrete tube. The SOLID65 element is similar to the SOLID45 element with the addition of special cracking and crushing capabilities [7]. Different mesh sizes were tried in order to find a reasonable mesh that provides both accurate results and less computational time. It is found a mesh size of 1 (depth):2 (width):2 (length), for both steel and concrete elements, could achieve accurate results with optimum computational efficiency. Fig. 1 shows the finite element mesh of a thin-walled concretefilled steel tube of 5 mm plate thickness having an outer diameter of 200 mm with a column length of 600 mm.
2.3. Boundary conditions and load application
2.4.2. Concrete tubes Confined concrete model has used to simulate concrete-filled steel tube circular columns with a small value of the D/t ratio [5]. However, in this case, the concrete is not in triaxial compression statue, therefore unconfined concrete model proposed by Hognestad et al. [9] is used in this study, as shown in Fig. 2. The concrete compressive stress–strain curve can be determined from Eqs. (1) and (2) as below: " 2 # 2 s ¼ fc (1) for 0pp0
0
Right surface
0
s ¼ f c 1 0:15
0 for 0 ppu u 0
σ
(2)
0.15f c
Following the testing procedure presented previously [2], the left and right surfaces of the specimen were fixed against all degrees of freedom except for the displacement at the loaded end in the direction of applied load. The load was applied using the displacement control at nodes of the steel tube in the loaded left surface, which is identical to the experimental investigation. The
Steel tube
2.4. Material modeling
fc
Concrete tube
Left surface
Fig. 1. Finite element mesh of thin-walled centrifugal concrete-filled steel tubes.
0
0
u
0.002
0.0038
Fig. 2. Stress–strain curve of concrete in compression proposed by Hognestad et al. [9].
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2.5. Concrete–steel tube interface The contact between the steel tube and the concrete is modeled by CONTA174 element. The CONTA174 element is used to represent contact and sliding between 3-D ‘‘target’’ surface (TARGE170) and a deformable surface, defined by this element. TARGE170 is used to model the inner surface of the steel tube and CONTA173 is used to model the outer surface of the concrete tube [7]. The friction between the two faces is maintained as long as the surfaces remain in contact. The coefficient of friction between the two faces is taken as 0.6 in the analysis as recommended by Han et al. [6]. The interface element allows the surfaces to separate under the influence of a tensile force. However, the two contact elements are not allowed to penetrate each other.
3. Verification of finite element model The experimental investigations on thin-walled centrifugal concrete-filled steel tubes under torsion presented previously [2] were used to verify the FE model developed in this study. The experimental investigation of thin-walled centrifugal concretefilled steel tubes performed previously provided the experimental ultimate loads of specimens between fixed ends under torsion. The steel tubes were all manufactured from mild steel sheet having nominal plate thicknesses (ts) of 3.0 and 4.5 mm. The thickness of the inside concrete tubes (tc) were 20, 25 and 30 mm. The specimen labeling system used in this paper follows that specified in the experimental investigation paper. 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 label. The label ‘‘S3.0C30L600’’ defines the specimen that has steel tube of 3.0 mm thickness (S3.0), concrete tube of 30 mm thickness (C30) and specimen length of 600 mm (L600). The ultimate strengths of the specimens obtained from the finite element analysis and test results are compared in Table 1. The mean values of the ultimate strength ratio (Tu-test/Tu-FEA) are 0.99 with the corresponding coefficients of variation (COV) of 0.031. It is shown that the finite element model adequately predicted the ultimate strengths of the thin-walled centrifugal
Table 1 Comparison between test and finite element analysis of thin-walled centrifugal concrete-filled steel tube strengths under torsion Specimen
Test Tu-test
FEA Tu-FEA
Comparison Tu-test/Tu-FEA
S3.0C20L600A S3.0C30L600A S4.5C25L600A S3.0C20L2000B S4.5C25L2000B S3.0C20L3000A S4.5C25L3000B
39.1 44.5 60.5 39.7 57.1 39.6 55.0
40.1 42.7 59.3 40.3 58.9 40.5 57.9
0.98 1.04 1.02 0.98 0.97 0.98 0.95
Mean COV
0.99 0.031
60 50 Load (kN.m)
where fc is concrete cube compressive strength; s is the stress; e is the strain; e0 ¼ 0.002 is the strain corresponding to the maximum strength; eu ¼ 0.0038 is the ultimate strain. The concrete cube compressive strength fc is chosen from the material test results and was 43.4 MPa. The concrete tensile was assumed to be 10% of the concrete compression strength. Poisson’s ratio of concrete is taken as 0.2.
273
40 30 20 10
TEST FEA
0 0
2
4 6 Rotation (degree)
8
10
Fig. 3. Torsion moment versus angle curves for specimen S4.5C25L2000B.
concrete-filled steel tubes under torsion. The curve of the load against end rotation angle of specimen S4.5C25L2000A obtained from the finite element analysis is plotted and compared with the test results, as shown in Fig. 3. The comparison indicates that the finite element model is able to predict the load–rotation curves of the specimens closely.
4. Parametric study The verification showed that the finite element model of thinwalled centrifugal concrete-filled tubes was reasonably accurate. Hence, parametric study was carried out to investigate the behaviour of tubes having cross-sectional dimensions and material properties. In addition, specimens having high strength steel tubes (fy ¼ 789 MPa) were also investigated. A total of 48 specimens were analyzed in the parametric study and the dimensions and material properties of the specimens are summarized in Tables 2 and 3. The symbols of cross-section are defined in Fig. 4. The experimental investigation conducted by Chen et al. [2] indicates that the specimen lengths have small effect on the ultimate strengths. Therefore, the specimens in the parametric study had the same overall length of 600 mm. The specimens were divided into four series with different thickness and yield strength of steel tubes. Each series of specimens was divided into three groups with different thickness of concrete tubes. The four specimens investigated in each group had concrete cube strengths of 30, 40, 50 and 60 MPa, respectively. The measured stress–strain curves of steel tubes investigated in the torsion tests [2] were used in finite element analysis of Series 1 and 2. Previous research has been conducted on the use of high strength steel in composite columns [10]. In this study, the use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion is investigated. Therefore, the measured stress–strain curves reported by Chen et al. [11] of mild steel (XLERPLATE Grade 350) and high strength steel (BISALLOY80) at normal room temperature were used in finite element analysis of Series 3 and 4. The torsion strengths (Tu-FEA) obtained from the parametric study using finite element model of all specimens are given in Table 4. For all series of specimens, it could be seen that the specimen strengths increases with the increase of steel plate thickness and yield strengths. The specimen strengths of Series 3 are compared with the specimen strengths of Series 4 in Table 5. The mean value of the specimen strength ratio (Tu-Series 3/Tu-Series 4 ¼ 1.953) is approximately the same as the ratio of yield strength
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Table 2 Specimen dimensions and material properties for the parametric study for Series 1 (group 1–3) and Series 2 (group 4–6) Series
1
Group
G1
G2
G3
2
G4
G5
G6
Specimen
Dimensions
Material properties
L (mm)
D (mm)
ts (mm)
tc (mm)
Concrete fcu (MPa)
Steel fy (MPa)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
272 272 272 272 272 272 272 272 272 272 272 272
S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
306 306 306 306 306 306 306 306 306 306 306 306
Table 3 Specimen dimensions and material properties for the parametric study for Series 3 (group 7–9) and Series 4 (group 10–12) Series
3
Group
G7
G8
G9
4
G10
G11
G12
Specimen
Dimensions
Material properties
L (mm)
D (mm)
ts (mm)
tc (mm)
Concrete fcu (MPa)
Steel fy (MPa)
S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
401 401 401 401 401 401 401 401 401 401 401 401
S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
789 789 789 789 789 789 789 789 789 789 789 789
of high strength steel to mild steel (789/401 ¼ 1.968). The comparison indicates that the high strength steel could be effectively utilized in the investigated specimens. The relationship between the specimen torsion strengths and the concrete cube strengths are plotted in Figs. 5 and 6. The x-axis is the concrete cube strengths, while the y-axis plotted against the specimen
torsion strengths. It is shown that the relationship between specimen strengths and concrete strengths increase approximately linearly as the concrete strength increases. It is also shown that the effect of concrete strength enhancement on specimen torsion strengths decreases with the plate thickness and yield strength of steel tubes increases.
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275
Table 5 Comparison of specimen strengths between Series 3 (mild steel) and Series 4 (high strength steel)
ts
tc
d D Fig. 4. Definition of symbols.
Specimen Series 3
Strength Tu (kN m)
Specimen Series 4
Strength Tu (kN m)
Comparison Tu-Sereis4/Tu-Series3
S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36
78.5 80.8 83.1 85.9 80.7 84.5 87.4 90.6 84.4 87.8 91.6 96.1
S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
163.9 164.3 165.0 166.1 164.3 167.4 167.4 168.4 166.8 169.0 172.7 175.5
2.087 2.033 1.985 1.935 2.036 1.980 1.915 1.858 1.976 1.924 1.885 1.826
Mean
1.953
Table 4 Comparison of specimen strengths obtained from finite element analysis with design strength Comparison
Tu-FEA (kN m)
Tu-Standard (kN m)
Tu-Proposed (kN m)
Tu-FEA/ Tu-standard
Tu-FEA/ Tu-proposed
37.9 40.1 42.5 44.7 39.5 42.7 46.5 49.8 40.4 46.1 50.0 53.5 51.2 54.1 56.4 59.0 54.1 57.6 59.8 63.4 55.5 59.8 63.2 66.9 78.5 80.8 83.1 85.9 80.7 84.5 87.4 90.6 84.4 87.8 91.6 96.1 163.9 164.3 165.0 166.1 164.3 167.4 167.4 168.4 166.8 169.0 172.7 175.5
31.8 32.0 32.2 32.4 32.3 32.6 32.9 33.1 32.7 33.0 33.3 33.6 45.8 46.1 46.2 46.4 46.3 46.6 46.9 47.1 46.7 47.0 47.3 47.6 73.6 73.8 74.0 74.2 74.1 74.4 74.6 74.8 74.4 74.8 75.0 75.3 143.6 143.8 144.0 144.1 144.1 144.4 144.6 144.8 144.4 144.8 145.0 145.3
38.1 40.7 42.4 44.0 41.5 44.1 45.7 47.0 43.6 46.1 47.6 48.8 51.2 54.0 56.4 58.7 55.0 58.7 61.3 63.5 58.0 61.9 64.3 66.4 82.9 81.2 82.4 84.8 81.6 84.8 88.2 91.7 83.9 88.9 92.9 96.6 167.1 178.7 170.5 163.4 176.8 164.3 159.8 159.4 166.8 159.6 160.0 163.2
1.19 1.25 1.32 1.38 1.22 1.31 1.42 1.51 1.24 1.40 1.50 1.59 1.12 1.17 1.22 1.27 1.17 1.23 1.28 1.35 1.19 1.27 1.34 1.41 1.07 1.09 1.12 1.16 1.09 1.14 1.17 1.21 1.13 1.17 1.22 1.28 1.14 1.14 1.15 1.15 1.14 1.16 1.16 1.16 1.16 1.17 1.19 1.21
0.99 0.98 1.00 1.02 0.95 0.97 1.02 1.06 0.92 1.00 1.05 1.10 1.00 1.00 1.00 1.01 0.98 0.98 0.98 1.00 0.96 0.97 0.98 1.01 0.95 1.00 1.01 1.01 0.99 1.00 0.99 0.99 1.01 0.99 0.99 1.00 0.98 0.92 0.97 1.02 0.93 1.02 1.05 1.06 1.00 1.06 1.08 1.08
Mean COV
1.23 0.095
1.00 0.039
80
Torsion strength (kN.m)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
Design
60
40
20 G2 G5
G1 G4
G3 G6
0 20
30
40 50 Concrete cube strength (MPa)
60
70
Fig. 5. Specimen strength and concrete cube strength relationships obtained from the parametric study for group 1–6.
200
Torsion strength (kN.m)
Specimen FEA
150
100
50 G7
G8
G9
G10
G11
G12
0 20
30
40 50 Concrete cube strength (MPa)
60
70
Fig. 6. Specimen strength and concrete cube strength relationships obtained from the parametric study for group 7–12.
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5. Comparison with design rules
6. Conclusions
5.1. Current standards
T u ¼ T S-AISC þ T C -ACI
(3)
T S-AISC ¼ F cr C
(4)
In this study, an accurate nonlinear finite element model for the analysis of thin-walled centrifugal concrete-filled steel tubes under torsion has been developed. The comparison between the finite element results and the experimental results showed good agreement in predicating the behaviour of the specimens. The torsion strengths and load–displacement curves of the specimens obtained from the finite element analysis compared well with the experimental results. A parametric study of 48 thin-walled centrifugal concrete-filled steel tubes with different cross-section and material properties was performed using the verified finite element model. In addition, the use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion was also investigated. It is shown that the high strength steel could be effectively utilized. The results of the parametric study showed that the design strengths predicted using current standards are very conservative. Therefore, a new design method was proposed based on current design standards. It is shown that the design strengths predicted using the proposed method agrees with the FEA results well.
(5)
References
The ultimate axial strengths of concrete-filled steel tube circular columns obtained from the parametric study were compared with the design strengths predicted by the AISC and ACI standards in Table 4. The design strengths (Tu) are taken as the summary of the design strengths of concrete plain tube (TC-ACI) and design strengths of steel tubes (TS-AISC), as shown in Eq. (3). The design strengths of steel tubes are calculated according to AISC specification [1] using Eq. (4). The design strengths of concrete tubes are calculated according to ACI code [8] using Eq. (5). It can be seen that the predictions from the AISC and ACI standards are very conservative in calculating the design strengths for all specimens. The mean value of the Tu-FEA/Tu-design ratio is 1.23 with the COV of 0.095
T C -ACI
qffiffiffiffiffi 0 ¼ 8Ao t f c
5.2. Proposed method The comparison indicates that the design strengths predicted by the AISC and ACI standards are very conservative. It may due to the restraining effect of filled concrete on the steel tube wall is not taken into consideration. In this study, new design equation is proposed based on the current AISC and ACI standards, as shown in Eq. (6). A parameter x is used to express the effect of restraining effect of filled concrete on the steel tube. The parameter x is defined as in Eq. (7). The design strengths predicted by the proposed equation are compared with the numerical results in Table 4. It is shown that the design strengths predicted by the proposed equation agree with the numerical results well. The mean value of the Tu-FEA/Tu-design ratio is 1.00 with the COV of 0.039 3
2
T u ¼ ð0:0026x þ 0:0537x 0:322x þ 1:7ÞT S-AISC þ T C -ACI
(6)
x ¼ As f s =Ac f c
(7)
[1] Specification for structural steel buildings. American Institution of Steel Construction (AISC), ANSI/AISC 360-05, Chicago, IL, 2005. [2] Chen J, Jin WL, Fu J. Experimental investigation of thin-walled centrifugal concrete-filled steel tubes under torsion. Thin-Walled Structures 2008;46(10):1087–93. [3] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear analysis of axially loaded concrete-filled tube columns with confinement effect. J Struct Eng ASCE 2003;129(10):1322–9. [4] Gupta PK, Sarda SM, Kumar MS. Experimental and computational study of concrete filled steel tubular columns under axial loads. J Constr Steel Res 2007;63(1):182–93. [5] Ellobody E, Young B, Lam D. Behaviour of normal and high strength concretefilled compact steel tube circular stub columns. J Constr Steel Res 2006;62(8):706–15. [6] Han LH, Yao GH, Tao Z. Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Struct 2007;45(1):24–36. [7] ANSYS. ANSYS release 9.0 documentation. SAS IP Inc., 2004. [8] ACI Committee 318 (ACI 318). Building code requirements for structural concrete and commentary. Detroit, USA: American Concrete Institute; 2005. [9] Hognestad E, Hanson NW, McHenry D. Concrete stress distribution in ultimate strength design. ACI J 1955;52(4):455–79. [10] Uy B. Strength of short concrete filled high strength steel box columns. J Constr Steel Res 2001;57(2):113–34. [11] Chen J, Young B, Uy B. Behavior of high strength structural steel at elevated temperatures. J Struct Eng ASCE 2006;132(12):1948–54.
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Design of thin-walled centrifugal concrete-filled steel tubes under torsion Juan Chen, Ju Chen , Wei Liang Jin Department of Civil Engineering, Zhejiang University, Hang Zhou, Zhe Jiang 310027, China
a r t i c l e in fo
abstract
Article history: Received 8 April 2008 Accepted 1 August 2008 Available online 7 September 2008
The paper addresses the design of thin-walled centrifugal concrete-filled steel tubes under torsion. An experimental research project was conducted to study the behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion. To further study the structural behaviour of the tubes thoroughly, finite element analyses were performed using ANSYS. The nonlinear finite element model was developed and verified against experimental results. Parametric study was conducted to investigate the effects of different concrete strengths, steel strengths and cross-section geometries on the strength and behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion. The use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion was also investigated. The specimen strengths predicted from the finite element analysis were compared with the design strengths calculated using the AISC and ACI standards. It is also shown design strengths predicted by standards are very conservative. Design method is also proposed based on current standards. It is also shown that design strengths predicted using the proposed method agree with the numerical results well. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Centrifugal concrete-filled steel tube Composite structure Finite element model Structural design Torsion
1. Introduction This paper concerns design of thin-walled centrifugal concretefilled steel tubes under torsion. Normally concrete-filled steel tubes are used as structural members in compression and bending and there is no provision for concrete-filled steel tubes under torsion in current AISC standards [1]. However, in design a thinwalled centrifugal concrete-filled steel tube used in power station structures, it is required to calculate the torsion capacity. The torsion load is mainly caused by the pulling force of the cable. Therefore, it is important to develop a design method for thinwalled centrifugal concrete-filled steel tubes under torsion. An experimental research project to study the behaviour of thinwalled centrifugal concrete-filled steel tubes under torsion has been reported previously [2]. Although the experimental results provided us much useful knowledge, there is still not enough data to propose a design method. Therefore, finite element method was used to further study the structural behaviour of the tubes thoroughly, and provided more data. Finite element method has been used to study the behaviour of concrete-filled steel tubes by many researchers [3–6]. In this study, finite element program ANSYS [7] was used to study the behaviour of thin-walled centrifugal concrete-filled steel tubes under torsion.
Corresponding author. Tel./fax: +86 57187951817.
E-mail address: [email protected] (J. Chen). 0263-8231/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2008.08.001
The main objective of this paper is firstly to develop an accurate finite element model to simulate the behaviour of thinwalled centrifugal concrete-filled steel tubes. The finite element program ANSYS [7] was used in the analysis. The effects of concrete strength and concrete confinement were considered in the analysis. A multi-linear stress–strain curve for the steel tube was used. The interface between concrete and the steel tube was also modeled. The results obtained from the finite element analysis were verified against the test results. Parametric studies were performed to investigate the effect of concrete strength, steel strength and cross-section geometries on the behaviour of thinwalled centrifugal concrete-filled steel tubes under torsion. The results obtained from the parametric study were compared with design strengths calculated using AISC [1] and ACI Standards [8]. In addition, design equations are proposed based on current standards.
2. Finite element model 2.1. General The finite element program ANSYS [7] was used in the simulation. In order to accurately simulate the actual behaviour of thin-walled centrifugal concrete-filled steel tubes, the main three components, namely the confined concrete, the circular steel tube and the interface between the concrete and the steel tube have to be modeled properly. In addition, careful attention
ARTICLE IN PRESS 272
J. Chen et al. / Thin-Walled Structures 47 (2009) 271–276
Nomenclature Ac Ao As
x C D d Fcr fcu
concrete tube cross-section area concrete tube cross-section area specified in ACI code steel tube cross-section area coefficients steel tube torsional constant outer diameter of steel tube inner diameter of concrete tube buckling stress of steel tubes under torsion compressive stress of concrete obtained from standard cubic test
fy L tc ts TC-ACI
yield stress of steel specimen length thickness of concrete tube thickness of steel tube torsional strength of concrete tubes calculated using ACI code torsional strength of steel tubes calculated using AISC standard torsional strength specimen design strength torsional strength obtained from FEA analysis torsional strength obtained from test results
TS-AISC Tu Tu-design Tu-FEA Tu-test
was given to the choice of the element type and mesh size to combining a high level of numerical accuracy and stability with optimum computational efficiency. The load–displacement nonlinear analysis was performed in the analysis.
load was applied in the polar coordinate system so that the applied displacement is tangent to the circle of the steel tube.
2.2. Finite element type and mesh
2.4.1. Steel tubes In the finite element model, the measured stress–strain curves of steel tubes presented by Chen et al. [2] were used. The experimental measured yield stresses (fy) were 272 and 306 MPa for steel tubes with nominal plate thickness of 3.0 and 4.5 mm, respectively. The material behaviour provided by ANSYS [7] allows a multi-linear stress–strain curve to be used. The first part of the multi-linear curve represents the elastic part up to the proportional limit stress with measured Young’s modulus (214,000 and 211,000 MPa for steel tubes with nominal plate thickness of 3.0 and 4.5 mm, respectively) and Poisson’s ratio equal to 0.30.
Different element types have been tried and solid elements were found to be more efficient in modeling the steel tube and the concrete tube as well as the clear defined boundaries of their elements. An eight-node brick element (SOLID45) is used to simulate the steel tube. The SOLID45 element is used for the 3-D modeling of solid structures. A reduced integration option with hourglass control is available for the SOLID45 element [7]. A 3-D structural solid element (SOLID65) is used to simulate the concrete tube. The SOLID65 element is similar to the SOLID45 element with the addition of special cracking and crushing capabilities [7]. Different mesh sizes were tried in order to find a reasonable mesh that provides both accurate results and less computational time. It is found a mesh size of 1 (depth):2 (width):2 (length), for both steel and concrete elements, could achieve accurate results with optimum computational efficiency. Fig. 1 shows the finite element mesh of a thin-walled concretefilled steel tube of 5 mm plate thickness having an outer diameter of 200 mm with a column length of 600 mm.
2.3. Boundary conditions and load application
2.4.2. Concrete tubes Confined concrete model has used to simulate concrete-filled steel tube circular columns with a small value of the D/t ratio [5]. However, in this case, the concrete is not in triaxial compression statue, therefore unconfined concrete model proposed by Hognestad et al. [9] is used in this study, as shown in Fig. 2. The concrete compressive stress–strain curve can be determined from Eqs. (1) and (2) as below: " 2 # 2 s ¼ fc (1) for 0pp0
0
Right surface
0
s ¼ f c 1 0:15
0 for 0 ppu u 0
σ
(2)
0.15f c
Following the testing procedure presented previously [2], the left and right surfaces of the specimen were fixed against all degrees of freedom except for the displacement at the loaded end in the direction of applied load. The load was applied using the displacement control at nodes of the steel tube in the loaded left surface, which is identical to the experimental investigation. The
Steel tube
2.4. Material modeling
fc
Concrete tube
Left surface
Fig. 1. Finite element mesh of thin-walled centrifugal concrete-filled steel tubes.
0
0
u
0.002
0.0038
Fig. 2. Stress–strain curve of concrete in compression proposed by Hognestad et al. [9].
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2.5. Concrete–steel tube interface The contact between the steel tube and the concrete is modeled by CONTA174 element. The CONTA174 element is used to represent contact and sliding between 3-D ‘‘target’’ surface (TARGE170) and a deformable surface, defined by this element. TARGE170 is used to model the inner surface of the steel tube and CONTA173 is used to model the outer surface of the concrete tube [7]. The friction between the two faces is maintained as long as the surfaces remain in contact. The coefficient of friction between the two faces is taken as 0.6 in the analysis as recommended by Han et al. [6]. The interface element allows the surfaces to separate under the influence of a tensile force. However, the two contact elements are not allowed to penetrate each other.
3. Verification of finite element model The experimental investigations on thin-walled centrifugal concrete-filled steel tubes under torsion presented previously [2] were used to verify the FE model developed in this study. The experimental investigation of thin-walled centrifugal concretefilled steel tubes performed previously provided the experimental ultimate loads of specimens between fixed ends under torsion. The steel tubes were all manufactured from mild steel sheet having nominal plate thicknesses (ts) of 3.0 and 4.5 mm. The thickness of the inside concrete tubes (tc) were 20, 25 and 30 mm. The specimen labeling system used in this paper follows that specified in the experimental investigation paper. 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 label. The label ‘‘S3.0C30L600’’ defines the specimen that has steel tube of 3.0 mm thickness (S3.0), concrete tube of 30 mm thickness (C30) and specimen length of 600 mm (L600). The ultimate strengths of the specimens obtained from the finite element analysis and test results are compared in Table 1. The mean values of the ultimate strength ratio (Tu-test/Tu-FEA) are 0.99 with the corresponding coefficients of variation (COV) of 0.031. It is shown that the finite element model adequately predicted the ultimate strengths of the thin-walled centrifugal
Table 1 Comparison between test and finite element analysis of thin-walled centrifugal concrete-filled steel tube strengths under torsion Specimen
Test Tu-test
FEA Tu-FEA
Comparison Tu-test/Tu-FEA
S3.0C20L600A S3.0C30L600A S4.5C25L600A S3.0C20L2000B S4.5C25L2000B S3.0C20L3000A S4.5C25L3000B
39.1 44.5 60.5 39.7 57.1 39.6 55.0
40.1 42.7 59.3 40.3 58.9 40.5 57.9
0.98 1.04 1.02 0.98 0.97 0.98 0.95
Mean COV
0.99 0.031
60 50 Load (kN.m)
where fc is concrete cube compressive strength; s is the stress; e is the strain; e0 ¼ 0.002 is the strain corresponding to the maximum strength; eu ¼ 0.0038 is the ultimate strain. The concrete cube compressive strength fc is chosen from the material test results and was 43.4 MPa. The concrete tensile was assumed to be 10% of the concrete compression strength. Poisson’s ratio of concrete is taken as 0.2.
273
40 30 20 10
TEST FEA
0 0
2
4 6 Rotation (degree)
8
10
Fig. 3. Torsion moment versus angle curves for specimen S4.5C25L2000B.
concrete-filled steel tubes under torsion. The curve of the load against end rotation angle of specimen S4.5C25L2000A obtained from the finite element analysis is plotted and compared with the test results, as shown in Fig. 3. The comparison indicates that the finite element model is able to predict the load–rotation curves of the specimens closely.
4. Parametric study The verification showed that the finite element model of thinwalled centrifugal concrete-filled tubes was reasonably accurate. Hence, parametric study was carried out to investigate the behaviour of tubes having cross-sectional dimensions and material properties. In addition, specimens having high strength steel tubes (fy ¼ 789 MPa) were also investigated. A total of 48 specimens were analyzed in the parametric study and the dimensions and material properties of the specimens are summarized in Tables 2 and 3. The symbols of cross-section are defined in Fig. 4. The experimental investigation conducted by Chen et al. [2] indicates that the specimen lengths have small effect on the ultimate strengths. Therefore, the specimens in the parametric study had the same overall length of 600 mm. The specimens were divided into four series with different thickness and yield strength of steel tubes. Each series of specimens was divided into three groups with different thickness of concrete tubes. The four specimens investigated in each group had concrete cube strengths of 30, 40, 50 and 60 MPa, respectively. The measured stress–strain curves of steel tubes investigated in the torsion tests [2] were used in finite element analysis of Series 1 and 2. Previous research has been conducted on the use of high strength steel in composite columns [10]. In this study, the use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion is investigated. Therefore, the measured stress–strain curves reported by Chen et al. [11] of mild steel (XLERPLATE Grade 350) and high strength steel (BISALLOY80) at normal room temperature were used in finite element analysis of Series 3 and 4. The torsion strengths (Tu-FEA) obtained from the parametric study using finite element model of all specimens are given in Table 4. For all series of specimens, it could be seen that the specimen strengths increases with the increase of steel plate thickness and yield strengths. The specimen strengths of Series 3 are compared with the specimen strengths of Series 4 in Table 5. The mean value of the specimen strength ratio (Tu-Series 3/Tu-Series 4 ¼ 1.953) is approximately the same as the ratio of yield strength
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Table 2 Specimen dimensions and material properties for the parametric study for Series 1 (group 1–3) and Series 2 (group 4–6) Series
1
Group
G1
G2
G3
2
G4
G5
G6
Specimen
Dimensions
Material properties
L (mm)
D (mm)
ts (mm)
tc (mm)
Concrete fcu (MPa)
Steel fy (MPa)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
272 272 272 272 272 272 272 272 272 272 272 272
S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
306 306 306 306 306 306 306 306 306 306 306 306
Table 3 Specimen dimensions and material properties for the parametric study for Series 3 (group 7–9) and Series 4 (group 10–12) Series
3
Group
G7
G8
G9
4
G10
G11
G12
Specimen
Dimensions
Material properties
L (mm)
D (mm)
ts (mm)
tc (mm)
Concrete fcu (MPa)
Steel fy (MPa)
S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
401 401 401 401 401 401 401 401 401 401 401 401
S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
600 600 600 600 600 600 600 600 600 600 600 600
200 200 200 200 200 200 200 200 200 200 200 200
5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
20.00 20.00 20.00 20.00 30.00 30.00 30.00 30.00 40.00 40.00 40.00 40.00
30 40 50 60 30 40 50 60 30 40 50 60
789 789 789 789 789 789 789 789 789 789 789 789
of high strength steel to mild steel (789/401 ¼ 1.968). The comparison indicates that the high strength steel could be effectively utilized in the investigated specimens. The relationship between the specimen torsion strengths and the concrete cube strengths are plotted in Figs. 5 and 6. The x-axis is the concrete cube strengths, while the y-axis plotted against the specimen
torsion strengths. It is shown that the relationship between specimen strengths and concrete strengths increase approximately linearly as the concrete strength increases. It is also shown that the effect of concrete strength enhancement on specimen torsion strengths decreases with the plate thickness and yield strength of steel tubes increases.
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275
Table 5 Comparison of specimen strengths between Series 3 (mild steel) and Series 4 (high strength steel)
ts
tc
d D Fig. 4. Definition of symbols.
Specimen Series 3
Strength Tu (kN m)
Specimen Series 4
Strength Tu (kN m)
Comparison Tu-Sereis4/Tu-Series3
S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36
78.5 80.8 83.1 85.9 80.7 84.5 87.4 90.6 84.4 87.8 91.6 96.1
S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
163.9 164.3 165.0 166.1 164.3 167.4 167.4 168.4 166.8 169.0 172.7 175.5
2.087 2.033 1.985 1.935 2.036 1.980 1.915 1.858 1.976 1.924 1.885 1.826
Mean
1.953
Table 4 Comparison of specimen strengths obtained from finite element analysis with design strength Comparison
Tu-FEA (kN m)
Tu-Standard (kN m)
Tu-Proposed (kN m)
Tu-FEA/ Tu-standard
Tu-FEA/ Tu-proposed
37.9 40.1 42.5 44.7 39.5 42.7 46.5 49.8 40.4 46.1 50.0 53.5 51.2 54.1 56.4 59.0 54.1 57.6 59.8 63.4 55.5 59.8 63.2 66.9 78.5 80.8 83.1 85.9 80.7 84.5 87.4 90.6 84.4 87.8 91.6 96.1 163.9 164.3 165.0 166.1 164.3 167.4 167.4 168.4 166.8 169.0 172.7 175.5
31.8 32.0 32.2 32.4 32.3 32.6 32.9 33.1 32.7 33.0 33.3 33.6 45.8 46.1 46.2 46.4 46.3 46.6 46.9 47.1 46.7 47.0 47.3 47.6 73.6 73.8 74.0 74.2 74.1 74.4 74.6 74.8 74.4 74.8 75.0 75.3 143.6 143.8 144.0 144.1 144.1 144.4 144.6 144.8 144.4 144.8 145.0 145.3
38.1 40.7 42.4 44.0 41.5 44.1 45.7 47.0 43.6 46.1 47.6 48.8 51.2 54.0 56.4 58.7 55.0 58.7 61.3 63.5 58.0 61.9 64.3 66.4 82.9 81.2 82.4 84.8 81.6 84.8 88.2 91.7 83.9 88.9 92.9 96.6 167.1 178.7 170.5 163.4 176.8 164.3 159.8 159.4 166.8 159.6 160.0 163.2
1.19 1.25 1.32 1.38 1.22 1.31 1.42 1.51 1.24 1.40 1.50 1.59 1.12 1.17 1.22 1.27 1.17 1.23 1.28 1.35 1.19 1.27 1.34 1.41 1.07 1.09 1.12 1.16 1.09 1.14 1.17 1.21 1.13 1.17 1.22 1.28 1.14 1.14 1.15 1.15 1.14 1.16 1.16 1.16 1.16 1.17 1.19 1.21
0.99 0.98 1.00 1.02 0.95 0.97 1.02 1.06 0.92 1.00 1.05 1.10 1.00 1.00 1.00 1.01 0.98 0.98 0.98 1.00 0.96 0.97 0.98 1.01 0.95 1.00 1.01 1.01 0.99 1.00 0.99 0.99 1.01 0.99 0.99 1.00 0.98 0.92 0.97 1.02 0.93 1.02 1.05 1.06 1.00 1.06 1.08 1.08
Mean COV
1.23 0.095
1.00 0.039
80
Torsion strength (kN.m)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48
Design
60
40
20 G2 G5
G1 G4
G3 G6
0 20
30
40 50 Concrete cube strength (MPa)
60
70
Fig. 5. Specimen strength and concrete cube strength relationships obtained from the parametric study for group 1–6.
200
Torsion strength (kN.m)
Specimen FEA
150
100
50 G7
G8
G9
G10
G11
G12
0 20
30
40 50 Concrete cube strength (MPa)
60
70
Fig. 6. Specimen strength and concrete cube strength relationships obtained from the parametric study for group 7–12.
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5. Comparison with design rules
6. Conclusions
5.1. Current standards
T u ¼ T S-AISC þ T C -ACI
(3)
T S-AISC ¼ F cr C
(4)
In this study, an accurate nonlinear finite element model for the analysis of thin-walled centrifugal concrete-filled steel tubes under torsion has been developed. The comparison between the finite element results and the experimental results showed good agreement in predicating the behaviour of the specimens. The torsion strengths and load–displacement curves of the specimens obtained from the finite element analysis compared well with the experimental results. A parametric study of 48 thin-walled centrifugal concrete-filled steel tubes with different cross-section and material properties was performed using the verified finite element model. In addition, the use of high strength steel in thin-walled centrifugal concrete-filled steel tubes under torsion was also investigated. It is shown that the high strength steel could be effectively utilized. The results of the parametric study showed that the design strengths predicted using current standards are very conservative. Therefore, a new design method was proposed based on current design standards. It is shown that the design strengths predicted using the proposed method agrees with the FEA results well.
(5)
References
The ultimate axial strengths of concrete-filled steel tube circular columns obtained from the parametric study were compared with the design strengths predicted by the AISC and ACI standards in Table 4. The design strengths (Tu) are taken as the summary of the design strengths of concrete plain tube (TC-ACI) and design strengths of steel tubes (TS-AISC), as shown in Eq. (3). The design strengths of steel tubes are calculated according to AISC specification [1] using Eq. (4). The design strengths of concrete tubes are calculated according to ACI code [8] using Eq. (5). It can be seen that the predictions from the AISC and ACI standards are very conservative in calculating the design strengths for all specimens. The mean value of the Tu-FEA/Tu-design ratio is 1.23 with the COV of 0.095
T C -ACI
qffiffiffiffiffi 0 ¼ 8Ao t f c
5.2. Proposed method The comparison indicates that the design strengths predicted by the AISC and ACI standards are very conservative. It may due to the restraining effect of filled concrete on the steel tube wall is not taken into consideration. In this study, new design equation is proposed based on the current AISC and ACI standards, as shown in Eq. (6). A parameter x is used to express the effect of restraining effect of filled concrete on the steel tube. The parameter x is defined as in Eq. (7). The design strengths predicted by the proposed equation are compared with the numerical results in Table 4. It is shown that the design strengths predicted by the proposed equation agree with the numerical results well. The mean value of the Tu-FEA/Tu-design ratio is 1.00 with the COV of 0.039 3
2
T u ¼ ð0:0026x þ 0:0537x 0:322x þ 1:7ÞT S-AISC þ T C -ACI
(6)
x ¼ As f s =Ac f c
(7)
[1] Specification for structural steel buildings. American Institution of Steel Construction (AISC), ANSI/AISC 360-05, Chicago, IL, 2005. [2] Chen J, Jin WL, Fu J. Experimental investigation of thin-walled centrifugal concrete-filled steel tubes under torsion. Thin-Walled Structures 2008;46(10):1087–93. [3] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear analysis of axially loaded concrete-filled tube columns with confinement effect. J Struct Eng ASCE 2003;129(10):1322–9. [4] Gupta PK, Sarda SM, Kumar MS. Experimental and computational study of concrete filled steel tubular columns under axial loads. J Constr Steel Res 2007;63(1):182–93. [5] Ellobody E, Young B, Lam D. Behaviour of normal and high strength concretefilled compact steel tube circular stub columns. J Constr Steel Res 2006;62(8):706–15. [6] Han LH, Yao GH, Tao Z. Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Struct 2007;45(1):24–36. [7] ANSYS. ANSYS release 9.0 documentation. SAS IP Inc., 2004. [8] ACI Committee 318 (ACI 318). Building code requirements for structural concrete and commentary. Detroit, USA: American Concrete Institute; 2005. [9] Hognestad E, Hanson NW, McHenry D. Concrete stress distribution in ultimate strength design. ACI J 1955;52(4):455–79. [10] Uy B. Strength of short concrete filled high strength steel box columns. J Constr Steel Res 2001;57(2):113–34. [11] Chen J, Young B, Uy B. Behavior of high strength structural steel at elevated temperatures. J Struct Eng ASCE 2006;132(12):1948–54.