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Punching shear failure of concrete-filled steel tubular CHS connections
Journal of Constructional Steel Research 124 (2016) 113–121
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Journal of Constructional Steel Research
Punching shear failure of concrete-filled steel tubular CHS connections Fei Xu, Ju Chen ⁎, Wei-liang Jin Institute of Structural Engineering, Zhejiang University, Hangzhou, Zhejiang 310058, People's Republic of China
a r t i c l e
i n f o
Article history: Received 29 October 2015 Received in revised form 30 March 2016 Accepted 15 May 2016 Available online xxxx Keywords: Axial tension Circular hollow section connections Concrete-filled steel tubes Finite element model Punching shear failure
a b s t r a c t Based on the experimental investigation and numerical simulation, the punching shear failure mode of concretefilled steel tubular CHS (circular hollow section) connections in axial tension was investigated. A finite element model was established using ABAQUS and verified against test results. It is shown that the developed model predicts the ultimate strengths and failure modes of test specimens well. Material properties, sizes of weld and contact interaction between concrete and steel were considered in the developed finite element model. The modified Mohr-Coulomb criterion for ductile fracture was used to define fracture criterion of the steel tube. Distribution of shear stress on the punching shear face was examined and a general equation describing stress distribution was proposed. An equation for equivalent thickness of punching shear failure face was also proposed. Parametric study was performed to determine the parameters in the proposed equations. Finally, design equations for ultimate strengths of concrete-filled steel tubular CHS connections failed in chord punching shear failure were proposed. It is shown that the design predictions agree with the finite element analysis results well. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction With the wide usage of concrete-filled steel tubular structures, concrete-filled steel tubular CHS (circular hollow section) connections are increasingly used in the engineering structures [1]. Previous research indicated that filling the hollow section chord member with concrete could effectively improve the strength of the connections [2–6]. Concrete inside chord could effectively hold the deformation of the steel tube so that chord plastification failure is prevented when the brace in axial tension load. Thus punching shear failure is the dominating failure mode for the chord of concrete-filled steel tubular CHS connections in this case. Test results indicated that the effect of concrete should be taken into consideration in the design and the connections should be designed based on punching shear failure mode [6]. Current AISC [7] standard has the design provisions for punching shear failure of circular section hollow steel tubular connections. However design strength predictions are very conservative for concretefilled steel tubular CHS connections, when shear yielding stress of the full punching shear failure face is assumed. Averagely design strength is only about 63% of the ultimate strength of test connections. If shear ultimate stress of the full shear failure face is assumed, the design predictions will be unconservative. Averagely design strength is about 121% of the ultimate strength of test specimens [6]. In this case, new design
method should be proposed for the punching shear failure of concrete-filled steel tubular CHS connections. 2. Summary of experimental investigation The test program presented in Xu et al. [6] provided experimental ultimate loads and failure modes of concrete-filled steel tubular CHS connections in tension. The test setup is shown in Fig. 1. The measured geometric sizes of the test specimens are presented in Table 1. The measured steel material properties obtained from the tensile coupon tests are summarized in Table 2. The compressive strength (fcu) and elastic modulus (Ec) obtained on 150-mm cubes at 28 days were 46.9 MPa and 37,420 MPa, respectively. The details of the experimental investigation are presented in Xu et al. [6]. The experimental ultimate loads (FExp) obtained from the test results are shown in Tables 3. The failure modes of all specimens are punching shear failure of the chord, except for KT type specimens. The test specimens are labeled such that the chord type, outer diameter of chord, thickness of chord, outer diameter of brace and thickness of brace could be identified from the label in this paper. 3. Finite element analysis 3.1. General
⁎ Corresponding author. E-mail address: [email protected] (J. Chen).
http://dx.doi.org/10.1016/j.jcsr.2016.05.010 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
The general purpose finite element program ABAQUS/Explicit was used for the numerical modeling of concrete-filled steel tubular CHS
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F. Xu et al. / Journal of Constructional Steel Research 124 (2016) 113–121
Fig. 1. Test setup [6]. (a) (b) (c) (d)
T type connection. Y type connection. K type connection. KT type connection.
connections. The finite element analysis (FEA) included various important factors, such as the modeling of materials and welds, contact interaction between the steel chord and the concrete core, fracture criterion of steel material, as well as loading and boundary conditions. The analysis time was reasonably reduced by introducing fixed mass scaling factor of 106 which is defined in ABAQUS [8]. Since there is bending stress in the chord wall, solid element rather than shell element is used to model the steel tube of connection [9,10]. In study, solid element C3D8R was used to model both steel and concrete. The element size near the braces to chord intersection (regions of high stresses) was kept small with aspect ratio as close to unity as possible. However, towards the ends of the braces and chord where the stresses
are more uniform, the element size and aspect ratio were increased, as shown in Fig. 2. The weld is simulated as steel material of chord since the failure is not occurred at weld. The measured stress–strain curves of steel tubes were used in the finite element models. Concrete constitutive model is the concrete-damaged plasticity model in ABAQUS [8] and the measured concrete material properties were used in the concrete material model. The interface model to simulate the interaction between steel and concrete in concrete-filled steel tubes is the contact interaction in ABAQUS. Following the testing procedure presented previously [6], the two ends of the chord were fixed against all degrees of freedom. Axial tension load (y direction) was applied on the top surface of the brace by applying a velocity (0.5 mm/min) which is the same as experiments. For K
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Table 1 Measured dimension of test specimens [6]. Specimens
T-300-4-133-6 Y-300-4-133-6 K-300-4-133-6 KT-300-4-133-6 T-300-4-133-6R Y-300-4-133-6R K-300-4-133-6R KT-300-4-133-6R T-300-5-133-6 Y-300-5-133-6 K-300-5-133-6 KT-300-5-133-6
Chord
Brace
d (mm)
t (mm)
db (mm)
tb (mm)
299.84 300.56 300.24 300.35 300.32 299.67 300.11 299.52 300.46 300.48 300.32 300.28
4.19 4.18 4.18 4.17 4.19 4.18 4.18 4.17 5.01 4.99 5.02 5.01
132.78 132.86 132.71 132.56 133.12 133.32 133.25 133.09 132.66 132.68 132.98 133.02
6.08 6.09 6.08 6.07 6.08 6.09 6.08 6.07 6.08 6.10 6.06 6.09
Note: d: outer diameter of chord; t: wall thickness of chord; db: outer diameter of brace; tb: wall thickness of brace.
Table 2 Tensile coupons test results [6]. Steel
Measured thickness (mm)
Measured E (GPa)
fy (MPa)
fu (MPa)
εf (%)
Q235 Q235 Q345
3.88 4.81 6.08
204.3 197.0 199.0
298 267 330
427 398 485
44.5 36.0 34.0
Table 3 Comparison of ultimate strength obtained from test results with FEA results. Specimens
T-300-4-133-6 Y-300-4-133-6 K-300-4-133-6 T-300-4-133-6R Y-300-4-133-6R K-300-4-133-6R T-300-5-133-6 Y-300-5-133-6 K-300-5-133-6
FExp
FFEA
(kN)
(kN)
534.8 620.3 785.0 549.1 699.9 698.9 662.4 836.1 814.0
509.2 679.3 730.2 509.2 679.3 679.3 630.3 824.2 824.2 Mean COV
FFEA / FExp
0.95 1.10 0.93 0.93 0.97 0.97 0.95 0.99 1.01 0.98 0.053
type connections, one web member is in tension while the other web member is fixed. 3.2. Fracture criterion of steel material The VUMAT in ABAQUS allows the user to define the fracture criterion of steel material. The Modified Mohr-Coulomb criterion proposed by Bai and Wierzbicki [11] was used to define the fracture criterion of steel material in the finite element model, as shown in Eq. (1). If a von Mises yielding function is used, the equation could be simplified as Eq. (2) by submitting cη = 0, csθ = ccθ = 1 [11]. The Modified Mohr-Coulomb criterion (MMC) predicts most of the shearing dominated fracture well [12].
εf ¼
f
" !!# pffiffiffi A θπ 3 s pffiffiffi cax 1−cη η−η0 csθ þ −c sec −1 θ θ c2 6 2− 3 2sffiffiffiffiffiffiffiffiffiffiffiffiffi ! !!3 −1n 1 þ c21 θπ 1 θπ 5 cos þ c1 η þ sin 4 ð1Þ 3 6 3 6
g
Fig. 2. Finite element model. (a) T type connection. (b) Y type connection. (c) K type connection.
where θ is normalized Lode angle, η is stress triaxiality, cax θ ¼ 1 for θ ≥ 0 ; ε is the equivalent strain at the point of fracture. ccθ for θ b 0 f
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F. Xu et al. / Journal of Constructional Steel Research 124 (2016) 113–121
8 2sffiffiffiffiffiffiffiffiffiffiffiffiffi ! !!39−1n =
Table 4 Coefficients of MMC criterion used in the finite element model. Steel
Measured thickness (mm)
Coefficients c1
c2
A
n
Q235 Q235 Q345
3.88 4.81 6.08
0.12 0.12 0.12
320.3 298.5 363.8
693.7 642.6 866.0
0.207 0.180 0.190
ð2Þ
There are a total of four parameters (A, n, c1, c2) that need to be found. The first two parameters, A and n, are parameters of material
Fig. 3. Comparison of failure modes. (a) T type connection. (b) Y type connection. (c) K type connection with overlapped part.
F. Xu et al. / Journal of Constructional Steel Research 124 (2016) 113–121
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strain hardening, which was calibrated from curve fitting of the measured stress-strain curve using power function. The two basic MohrCoulomb parameters, c1 and c2, are a “friction” coefficient and shear resistance respectively. In this study, c1 = 0.12 based on the test results of steel [12] and c2 = 0.75fu [13]. The parameters of MMC failure criterion adopted in this study are shown in Table 4. 3.3. Verification The ultimate loads and failure modes obtained from FEA are compared with test results presented by Xu et al. [6] in Table 3. The KT type connections are not simulated since the failure mode is brace yielding. The mean value of FFEA / FExp is 0.98 with the corresponding COV is 0.053, respectively. It is shown that the finite element model adequately predicted the ultimate strengths of the concrete-filled steel tubular CHS connections. The failure modes of connection obtained from FEA results are compared with the test results in Fig. 3. In addition, the K type connection with overlapped part could be simulated as well. The curves of the load against displacement obtained from the finite element analysis were plotted and compared with the test results, as shown in Fig. 4. The comparisons indicate that the finite element model is able to simulate the behavior concrete-filled steel tubular CHS connections in tension generally accurately. 4. Finite element analysis results
Fig. 4. Comparison of load-displacement curves of test specimens with FEA results. (a) Specimen T-300-4-133-6. (b) Specimen Y-300-4-133-6.
Typical shear stress distributions of connections T-300-4-150-6, T-300-5-140-6, T-300-6-140-6 and T-300-4-100-8 were plotted in Fig. 5. It is shown that the shear stress distribution on the punching shear failure face at the maximum load step was uneven and could be described by a sine curve. Eq. (3) was proposed to describe the
Fig. 5. Shear stress distribution on the punching shear failure face. (a) (b) (c) (d)
Specimen T-300-4-150-6. Specimen T-300-5-140-6. Specimen T-300-6-140-6. Specimen T-300-4-100-8.
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distribution of shear stress of the punching shear failure face at the maximum load step. f τ ¼ k f v; max þ ð1−kÞ f v; max
sinθ ð0≤θ ≤πÞ
ð3Þ
where f v,max is the maximum shear stress on the punching shear face, fv,min is the minimum shear stress on the punching shear face; k = fv,min / fv,max is the coefficient, θ is the angle as shown in Fig. 6. A parametric study was performed using the verified finite element model to study the coefficient k, as shown in Fig. 7. It is shown that the value of k ranged from 0.45 to 0.55 for common size connections. Therefore, k = 0.5 is recommended in this study. 5. Design methods 5.1. Equivalent thickness of punching shear failure face Since the thickness of the chord punching shear failure face varies along the chord-brace intersection curve, an equivalent thickness equation for T type connection is proposed for design simplicity.
Fig. 7. Parametric study of k value. (a) k value of connections with different β value (β = db/d). (b) k value of connections with different γ value (γ = d/2t). (c) k value of connections with different τ value (τ = tb/t).
The space intersection curve is also equivalent to a circle in plane, as shown in Fig. 8. The proposed equations are shown in Eqs. (4) and (5). T eq ¼
Apunch ¼ 1 þ μ eq t πdb
ð4Þ
μ eq ¼
Apunch −1 πdb t
ð5Þ
Fig. 6. Definition of punching shear failure face. (a) Top view. (b) Side view.
F. Xu et al. / Journal of Constructional Steel Research 124 (2016) 113–121
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Fig. 10. Ratios of maximum shear stress to ultimate shear strength.
5.2. Maximum shear stress Since the punching shear failure face is under triaxial stress state, the maximum shear stress (fv,max) is lower than the ultimate shear strength of steel material (fu,v) which is for pure shear stress state, as shown in Fig.5. The ratio of maximum shear stress to ultimate shear strength of steel material (fv,max / fu,v) is plotted against ultimate strengths of connections obtained from FEA results in Fig. 10. Generally, maximum shear stress is 90% of ultimate shear strength of steel material for 22 T type connections.
Fig. 8. Definition of equivalent thickness.
5.3. Design equation Where Teq is the equivalent thickness, Apunch is the total area of punching shear failure face, db is the outer diameter of brace, μeq is the coefficient. The coefficient μeq mainly varies with the diameter ratio of brace to chord (β = db/d). For common size T type connections, the value of β ranged between 0.2–0.8. The relationship between μeq and β is obtained by curve fitting of geometric calculation results, as shown in Fig. 9. The obtained equation is shown in Eq. (6).
3
μ eq ¼ 0:57β3 ¼ 0:57ðdb =dÞ ð0:2 ≤β ≤0:8Þ
ð6Þ
The ultimate strength corresponding to punching shear failure mode of concrete-filled steel tubular CHS connections in tension is considered as the summary of shear force on the punching shear face. Thus Eq. (7) is proposed to calculate the ultimate strength: Z F u ¼ 1 þ μ eq db t
0
π
f τ ðθÞdθ
ð7Þ
where Fu is the ultimate strength, fτ is the shear stress on the punching shear failure face. Since the shear stress distribution and area of punching shear failure face could be obtained with Eqs. (3) and (4), the ultimate strength of T type connection could be rewritten as Eq. (8). f u ¼ 1 þ μ eq ð2 þ kπ−2kÞdb t f v; max
ð8Þ
The maximum shear stress is taken as 90% of ultimate shear strength fv,max = 0.9 fu,v = 0.9 × 0.75fu [13] and the k value is taken as 0.5 as presented previously, Eq. (8) could be rewritten as Eq. (9). 3 f u ¼ 1:74 þ ðdb =dÞ db t f u
ð9Þ
Where fu is the ultimate tensile strength of chord material. For simplicity, ultimate strength of Y type connections is recommended be calculated using Eq. (10). 3 F u sinθY ¼ 1:74 þ ðdb =dÞ db t f u
Fig. 9. Relationship between μeq and β.
ð10Þ
Where θY is the angle between the brace and chord, 30° ≤ θY ≤ 60°. The ultimate strengths calculated using Eqs.(9) and (10) for T and Y type connections were compared with FEA results in Tables 5 and 6,
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Table 5 Comparison of design strengths with FEA results for T type connections. Specimens
T-300-4-60-6 T-300-4-100-6 T-300-4-100-6 T-300-4-100-6 T-300-4-100-4 T-300-4-100-8 T-300-4-133-6 T-300-4-133-6 T-300-4-133-6 T-300-3-140-6 T-300-4-140-6 T-300-5-140-6 T-300-6-140-6 T-300-4-150-6 T-300-4-180-6 T-300-4-240-6 T-240-4-60-6 T-240-4-110-6 T-240-4-133-6 T-240-4-168-6 T-400-4-140-6
fy
fu
FFEA
Fu-design
Fu-weld
(MPa)
(MPa)
(kN)
(kN)
(kN)
298 298 436 456 298 298 298 436 456 298 298 298 298 298 298 298 298 298 298 298 298
427 427 520 555 427 427 427 520 555 427 427 427 427 427 427 427 427 427 427 427 427
207.0 361.5 412.5 445.1 361.8 362.1 507.6 580.1 621.6 400.7 515.0 642.1 825.7 557.7 700.7 1014.0 231.0 441.6 529.4 720.6 494.6
179.1 303.5 369.6 394.5 303.5 303.5 415.0 505.4 539.4 330.3 440.4 550.5 660.6 477.8 601.4 923.1 179.9 345.0 433.9 597.7 426.3
215.7 349.5 425.6 454.2 349.5 349.5 474.0 577.2 616.1 375.8 501.1 626.4 751.6 541.4 675.9 1032.5 217.3 405.6 503.7 688.5 479.4 Mean COV
respectively. The mean value of Fu-design / FFEA and the corresponding COV for T type connections are 0.85 and 0.041, respectively. The mean value of Fu-design / FFEA and the corresponding COV for Y type connections are 0.88 and 0.032, respectively. The comparison indicates that the proposed equations are generally conservative. The reason of conservatism is that the width of weld is not considered in the design as mentioned in Xu, et al. [6]. If the width of weld is considered, the mean values of Fu-weld / FFEA are 0.97 and 1.00 for T and Y type connections, respectively. Since the width of weld is difficult to be considered in engineering design, Eqs. (9) and (10) are recommended for design. For K type connections having a branch with very little or no loading, the connection can be treated as a Y-connection [6]. Eq. (9) is also applicable to this kind of K type connections. It should be noted that the design equations are suitable for conventional connections with the limitations of 0.20 ≤ β ≤ 0.80, 25.0 ≤ γ ≤ 50.0, and 1.0 ≤ τ ≤ 2.0.
Fu-design / FFEA
Fu-weld / FFEA
0.87 0.84 0.90 0.89 0.84 0.84 0.82 0.87 0.87 0.82 0.86 0.86 0.80 0.86 0.86 0.91 0.78 0.78 0.82 0.83 0.86 0.85 0.041
1.04 0.97 1.03 1.02 0.97 0.97 0.93 1.00 0.99 0.94 0.97 0.98 0.91 0.97 0.96 1.02 0.94 0.92 0.95 0.96 0.97 0.97 0.036
6. Conclusions In this study, an accurate nonlinear finite element model for the analysis of concrete-filled steel tubular circular hollow section connections under axial tension has been developed. The Modified Mohr-Coulomb fracture criterion of steel material was adopted in the finite element model. The comparison between the finite element results and the experimental results showed a good agreement in predicating the behavior of the specimens. The shear stress distribution on the punching shear failure face was obtained from the finite element analysis results and is described by a proposed equation. Equations for equivalent thickness of the punching shear failure face were also proposed which enable the ultimate strength equation to be written in a simple form. Comparison between the design strengths and the finite element analysis results for T and Y type connections indicates the proposed equations are generally accurate.
Table 6 Comparison of design strengths with FEA results for Y type connections. Specimens
Y-300-4-60-6 Y-300-4-100-4 Y-300-4-100-6 Y-300-4-100-6 Y-300-4-100-6 Y-300-4-100-8 Y-300-3-140-6 Y-300-4-140-6 Y-300-4-140-6 Y-300-4-140-6 Y-300-5-140-6 Y-300-6-140-6 Y-300-4-150-6 Y-300-4-180-6
fy
fu
FFEA
Fu-design
Fu-weld
(MPa)
(MPa)
(kN)
(kN)
(kN)
298 298 298 436 456 298 298 298 436 456 298 298 298 298
427 427 427 520 555 427 427 427 520 555 427 427 427 427
294.4 513.4 508.5 579.7 623.5 510.2 524.8 719.6 815.0 916.6 876.0 1072.0 791.8 934.2
253.3 429.2 429.2 522.7 557.9 429.2 467.1 622.9 758.5 809.6 778.6 934.3 675.7 850.4
305.0 494.2 494.2 601.9 642.4 494.2 531.5 708.6 863.0 921.1 885.8 1063.0 765.6 955.8 Mean COV
Fu-design /FFEA
Fu-weld / FFEA
0.86 0.84 0.84 0.90 0.89 0.84 0.89 0.87 0.93 0.88 0.89 0.87 0.85 0.91 0.88 0.032
1.04 0.96 0.97 1.04 1.03 0.97 1.01 0.98 1.06 1.00 1.01 0.99 0.97 1.02 1.00 0.031
F. Xu et al. / Journal of Constructional Steel Research 124 (2016) 113–121
Notation The following symbols are used in this paper: A parameters of material strain hardening; the total area of the punching shear failure face; Apunch friction coefficient in the Mohr-Coulomb model; c1 shear resistance in the Mohr-Coulomb model; c2 s c parameters related to the pressure and Lode angle cax θ , cθ , cθ, cη dependence; d outer diameter of chord; outer diameter of brace; db E Young's modulus; Young's modulus of concrete; Ec concrete compressive strength, by 150-150-150 cubic fcu specimens; ultimate tensile stress of steel; fu ultimate shear strength of steel; fu,v the maximum shear stress on the punching shear face; fv,max the minimum shear stress on the punching shear face; fv,min yield stress of steel; fy shear stress on the punching shear face; fτ k fv,min / fv,max; n parameters of material strain hardening; ultimate strength of specimen obtained from tests; FExp ultimate strength of specimen obtained from FEA; FFEA ultimate strength of connections; Fu Fu-design ultimate strength of specimen predicted from proposed equations; ultimate strength of specimen predicted with the considerFu-weld ation of weld width; equivalent thickness; Teq t wall thickness of chord; wall thickness of brace; tb β ratio of brace outer diameter to chord outer diameter; γ ratio of chord outer radius to chord thickness; τ ratio of brace thickness to chord thickness; elongation (tensile strain) after fracture based on gauge εf length of 50 mm; εf the equivalent strain at the point of fracture;
θ θ θY μeq η η0
121
the angle defined in Fig. 6; Lode angle parameter (normalized Lode angle); the angle between the brace and chord; a coefficient related to Apunch, db and t; stress triaxiality; parameters related to the pressure and Lode angle dependence.
Acknowledgments The research work described in this paper was supported by National Key Technology R&D Program (2011BAJ09B03) and research project from Science and Technology Department of Zhejiang Province (2015C33005). References [1] L.H. Han, Concrete-Filled Steel Tube Structures-Theory and Design, second ed. Science Press, Beijing, 2007. [2] I.E. Tebbett, C.D. Beckett, J. Billington C, The punching shear strength of tubular joints reinforced with a grouted pile. Offshore technology conference, Offshore Technology Conference 1979, pp. 915–921. [3] J.A. Packer, Concrete-filled HSS connections, J. Struct. Eng. 121 (3) (1995) 458–467. [4] R. Feng, B. Young, Tests of concrete-filled stainless steel tubular T-joints, J. Constr. Steel Res. 64 (11) (2008) 1283–1293. [5] R. Feng, B. Young, Behaviour of concrete-filled stainless steel tubular X-joints subjected to compression, Thin-Walled Struct. 47 (4) (2009) 365–374. [6] F. Xu, J. Chen, W. Jin, Experimental investigation and design of concrete-filled steel tubular CHS connections, J. Struct. Eng. ASCE 141 (2) (2015) (04014106). [7] AISC, Specification for Structural Steel Buildings, American Institution of Steel Construction (AISC), ANSI/AISC, Chicago, Illinois, 2010 (360–10). [8] ABAQUS, Standard User's Manual, Version 6.10, Hibbitt HD, Karlsson BI and Sorensen P, USA, 2010. [9] S. Herion, F. Mang, R. Puthli, Parametric study on multiplanar K-joints with gap made of circular hollow sections by means of the finite element method, The Sixth International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, 1996. [10] M.M.K. Lee, D. Bowness, Prediction of stress intensity factors in semi-elliptical weld toe cracks in offshore tubular joints, Proceedings of the 9th International Symposium and Euroconference on Tubular Structures, 9 2001, pp. 299–310 (Dusseldorf, Germany). [11] Y. Bai, T. Wierzbicki, Application of extended Mohr–Coulomb criterion to ductile fracture, Int. J. Fract. 161 (1) (2010) 1–20. [12] Y. Bai, T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3D space, Eng. Fract. Mech. 135 (2015) 147–167. [13] J.M. Amiss, F.D. Jones, H.H. Ryffel, Machinery's Handbook Guide to the Use of Tables and Formulas, 28th ed. Industrial Press, New York, 2008.
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Punching shear failure of concrete-filled steel tubular CHS connections Fei Xu, Ju Chen ⁎, Wei-liang Jin Institute of Structural Engineering, Zhejiang University, Hangzhou, Zhejiang 310058, People's Republic of China
a r t i c l e
i n f o
Article history: Received 29 October 2015 Received in revised form 30 March 2016 Accepted 15 May 2016 Available online xxxx Keywords: Axial tension Circular hollow section connections Concrete-filled steel tubes Finite element model Punching shear failure
a b s t r a c t Based on the experimental investigation and numerical simulation, the punching shear failure mode of concretefilled steel tubular CHS (circular hollow section) connections in axial tension was investigated. A finite element model was established using ABAQUS and verified against test results. It is shown that the developed model predicts the ultimate strengths and failure modes of test specimens well. Material properties, sizes of weld and contact interaction between concrete and steel were considered in the developed finite element model. The modified Mohr-Coulomb criterion for ductile fracture was used to define fracture criterion of the steel tube. Distribution of shear stress on the punching shear face was examined and a general equation describing stress distribution was proposed. An equation for equivalent thickness of punching shear failure face was also proposed. Parametric study was performed to determine the parameters in the proposed equations. Finally, design equations for ultimate strengths of concrete-filled steel tubular CHS connections failed in chord punching shear failure were proposed. It is shown that the design predictions agree with the finite element analysis results well. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction With the wide usage of concrete-filled steel tubular structures, concrete-filled steel tubular CHS (circular hollow section) connections are increasingly used in the engineering structures [1]. Previous research indicated that filling the hollow section chord member with concrete could effectively improve the strength of the connections [2–6]. Concrete inside chord could effectively hold the deformation of the steel tube so that chord plastification failure is prevented when the brace in axial tension load. Thus punching shear failure is the dominating failure mode for the chord of concrete-filled steel tubular CHS connections in this case. Test results indicated that the effect of concrete should be taken into consideration in the design and the connections should be designed based on punching shear failure mode [6]. Current AISC [7] standard has the design provisions for punching shear failure of circular section hollow steel tubular connections. However design strength predictions are very conservative for concretefilled steel tubular CHS connections, when shear yielding stress of the full punching shear failure face is assumed. Averagely design strength is only about 63% of the ultimate strength of test connections. If shear ultimate stress of the full shear failure face is assumed, the design predictions will be unconservative. Averagely design strength is about 121% of the ultimate strength of test specimens [6]. In this case, new design
method should be proposed for the punching shear failure of concrete-filled steel tubular CHS connections. 2. Summary of experimental investigation The test program presented in Xu et al. [6] provided experimental ultimate loads and failure modes of concrete-filled steel tubular CHS connections in tension. The test setup is shown in Fig. 1. The measured geometric sizes of the test specimens are presented in Table 1. The measured steel material properties obtained from the tensile coupon tests are summarized in Table 2. The compressive strength (fcu) and elastic modulus (Ec) obtained on 150-mm cubes at 28 days were 46.9 MPa and 37,420 MPa, respectively. The details of the experimental investigation are presented in Xu et al. [6]. The experimental ultimate loads (FExp) obtained from the test results are shown in Tables 3. The failure modes of all specimens are punching shear failure of the chord, except for KT type specimens. The test specimens are labeled such that the chord type, outer diameter of chord, thickness of chord, outer diameter of brace and thickness of brace could be identified from the label in this paper. 3. Finite element analysis 3.1. General
⁎ Corresponding author. E-mail address: [email protected] (J. Chen).
http://dx.doi.org/10.1016/j.jcsr.2016.05.010 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
The general purpose finite element program ABAQUS/Explicit was used for the numerical modeling of concrete-filled steel tubular CHS
114
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Fig. 1. Test setup [6]. (a) (b) (c) (d)
T type connection. Y type connection. K type connection. KT type connection.
connections. The finite element analysis (FEA) included various important factors, such as the modeling of materials and welds, contact interaction between the steel chord and the concrete core, fracture criterion of steel material, as well as loading and boundary conditions. The analysis time was reasonably reduced by introducing fixed mass scaling factor of 106 which is defined in ABAQUS [8]. Since there is bending stress in the chord wall, solid element rather than shell element is used to model the steel tube of connection [9,10]. In study, solid element C3D8R was used to model both steel and concrete. The element size near the braces to chord intersection (regions of high stresses) was kept small with aspect ratio as close to unity as possible. However, towards the ends of the braces and chord where the stresses
are more uniform, the element size and aspect ratio were increased, as shown in Fig. 2. The weld is simulated as steel material of chord since the failure is not occurred at weld. The measured stress–strain curves of steel tubes were used in the finite element models. Concrete constitutive model is the concrete-damaged plasticity model in ABAQUS [8] and the measured concrete material properties were used in the concrete material model. The interface model to simulate the interaction between steel and concrete in concrete-filled steel tubes is the contact interaction in ABAQUS. Following the testing procedure presented previously [6], the two ends of the chord were fixed against all degrees of freedom. Axial tension load (y direction) was applied on the top surface of the brace by applying a velocity (0.5 mm/min) which is the same as experiments. For K
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Table 1 Measured dimension of test specimens [6]. Specimens
T-300-4-133-6 Y-300-4-133-6 K-300-4-133-6 KT-300-4-133-6 T-300-4-133-6R Y-300-4-133-6R K-300-4-133-6R KT-300-4-133-6R T-300-5-133-6 Y-300-5-133-6 K-300-5-133-6 KT-300-5-133-6
Chord
Brace
d (mm)
t (mm)
db (mm)
tb (mm)
299.84 300.56 300.24 300.35 300.32 299.67 300.11 299.52 300.46 300.48 300.32 300.28
4.19 4.18 4.18 4.17 4.19 4.18 4.18 4.17 5.01 4.99 5.02 5.01
132.78 132.86 132.71 132.56 133.12 133.32 133.25 133.09 132.66 132.68 132.98 133.02
6.08 6.09 6.08 6.07 6.08 6.09 6.08 6.07 6.08 6.10 6.06 6.09
Note: d: outer diameter of chord; t: wall thickness of chord; db: outer diameter of brace; tb: wall thickness of brace.
Table 2 Tensile coupons test results [6]. Steel
Measured thickness (mm)
Measured E (GPa)
fy (MPa)
fu (MPa)
εf (%)
Q235 Q235 Q345
3.88 4.81 6.08
204.3 197.0 199.0
298 267 330
427 398 485
44.5 36.0 34.0
Table 3 Comparison of ultimate strength obtained from test results with FEA results. Specimens
T-300-4-133-6 Y-300-4-133-6 K-300-4-133-6 T-300-4-133-6R Y-300-4-133-6R K-300-4-133-6R T-300-5-133-6 Y-300-5-133-6 K-300-5-133-6
FExp
FFEA
(kN)
(kN)
534.8 620.3 785.0 549.1 699.9 698.9 662.4 836.1 814.0
509.2 679.3 730.2 509.2 679.3 679.3 630.3 824.2 824.2 Mean COV
FFEA / FExp
0.95 1.10 0.93 0.93 0.97 0.97 0.95 0.99 1.01 0.98 0.053
type connections, one web member is in tension while the other web member is fixed. 3.2. Fracture criterion of steel material The VUMAT in ABAQUS allows the user to define the fracture criterion of steel material. The Modified Mohr-Coulomb criterion proposed by Bai and Wierzbicki [11] was used to define the fracture criterion of steel material in the finite element model, as shown in Eq. (1). If a von Mises yielding function is used, the equation could be simplified as Eq. (2) by submitting cη = 0, csθ = ccθ = 1 [11]. The Modified Mohr-Coulomb criterion (MMC) predicts most of the shearing dominated fracture well [12].
εf ¼
f
" !!# pffiffiffi A θπ 3 s pffiffiffi cax 1−cη η−η0 csθ þ −c sec −1 θ θ c2 6 2− 3 2sffiffiffiffiffiffiffiffiffiffiffiffiffi ! !!3 −1n 1 þ c21 θπ 1 θπ 5 cos þ c1 η þ sin 4 ð1Þ 3 6 3 6
g
Fig. 2. Finite element model. (a) T type connection. (b) Y type connection. (c) K type connection.
where θ is normalized Lode angle, η is stress triaxiality, cax θ ¼ 1 for θ ≥ 0 ; ε is the equivalent strain at the point of fracture. ccθ for θ b 0 f
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8 2sffiffiffiffiffiffiffiffiffiffiffiffiffi ! !!39−1n =
Table 4 Coefficients of MMC criterion used in the finite element model. Steel
Measured thickness (mm)
Coefficients c1
c2
A
n
Q235 Q235 Q345
3.88 4.81 6.08
0.12 0.12 0.12
320.3 298.5 363.8
693.7 642.6 866.0
0.207 0.180 0.190
ð2Þ
There are a total of four parameters (A, n, c1, c2) that need to be found. The first two parameters, A and n, are parameters of material
Fig. 3. Comparison of failure modes. (a) T type connection. (b) Y type connection. (c) K type connection with overlapped part.
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strain hardening, which was calibrated from curve fitting of the measured stress-strain curve using power function. The two basic MohrCoulomb parameters, c1 and c2, are a “friction” coefficient and shear resistance respectively. In this study, c1 = 0.12 based on the test results of steel [12] and c2 = 0.75fu [13]. The parameters of MMC failure criterion adopted in this study are shown in Table 4. 3.3. Verification The ultimate loads and failure modes obtained from FEA are compared with test results presented by Xu et al. [6] in Table 3. The KT type connections are not simulated since the failure mode is brace yielding. The mean value of FFEA / FExp is 0.98 with the corresponding COV is 0.053, respectively. It is shown that the finite element model adequately predicted the ultimate strengths of the concrete-filled steel tubular CHS connections. The failure modes of connection obtained from FEA results are compared with the test results in Fig. 3. In addition, the K type connection with overlapped part could be simulated as well. The curves of the load against displacement obtained from the finite element analysis were plotted and compared with the test results, as shown in Fig. 4. The comparisons indicate that the finite element model is able to simulate the behavior concrete-filled steel tubular CHS connections in tension generally accurately. 4. Finite element analysis results
Fig. 4. Comparison of load-displacement curves of test specimens with FEA results. (a) Specimen T-300-4-133-6. (b) Specimen Y-300-4-133-6.
Typical shear stress distributions of connections T-300-4-150-6, T-300-5-140-6, T-300-6-140-6 and T-300-4-100-8 were plotted in Fig. 5. It is shown that the shear stress distribution on the punching shear failure face at the maximum load step was uneven and could be described by a sine curve. Eq. (3) was proposed to describe the
Fig. 5. Shear stress distribution on the punching shear failure face. (a) (b) (c) (d)
Specimen T-300-4-150-6. Specimen T-300-5-140-6. Specimen T-300-6-140-6. Specimen T-300-4-100-8.
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distribution of shear stress of the punching shear failure face at the maximum load step. f τ ¼ k f v; max þ ð1−kÞ f v; max
sinθ ð0≤θ ≤πÞ
ð3Þ
where f v,max is the maximum shear stress on the punching shear face, fv,min is the minimum shear stress on the punching shear face; k = fv,min / fv,max is the coefficient, θ is the angle as shown in Fig. 6. A parametric study was performed using the verified finite element model to study the coefficient k, as shown in Fig. 7. It is shown that the value of k ranged from 0.45 to 0.55 for common size connections. Therefore, k = 0.5 is recommended in this study. 5. Design methods 5.1. Equivalent thickness of punching shear failure face Since the thickness of the chord punching shear failure face varies along the chord-brace intersection curve, an equivalent thickness equation for T type connection is proposed for design simplicity.
Fig. 7. Parametric study of k value. (a) k value of connections with different β value (β = db/d). (b) k value of connections with different γ value (γ = d/2t). (c) k value of connections with different τ value (τ = tb/t).
The space intersection curve is also equivalent to a circle in plane, as shown in Fig. 8. The proposed equations are shown in Eqs. (4) and (5). T eq ¼
Apunch ¼ 1 þ μ eq t πdb
ð4Þ
μ eq ¼
Apunch −1 πdb t
ð5Þ
Fig. 6. Definition of punching shear failure face. (a) Top view. (b) Side view.
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Fig. 10. Ratios of maximum shear stress to ultimate shear strength.
5.2. Maximum shear stress Since the punching shear failure face is under triaxial stress state, the maximum shear stress (fv,max) is lower than the ultimate shear strength of steel material (fu,v) which is for pure shear stress state, as shown in Fig.5. The ratio of maximum shear stress to ultimate shear strength of steel material (fv,max / fu,v) is plotted against ultimate strengths of connections obtained from FEA results in Fig. 10. Generally, maximum shear stress is 90% of ultimate shear strength of steel material for 22 T type connections.
Fig. 8. Definition of equivalent thickness.
5.3. Design equation Where Teq is the equivalent thickness, Apunch is the total area of punching shear failure face, db is the outer diameter of brace, μeq is the coefficient. The coefficient μeq mainly varies with the diameter ratio of brace to chord (β = db/d). For common size T type connections, the value of β ranged between 0.2–0.8. The relationship between μeq and β is obtained by curve fitting of geometric calculation results, as shown in Fig. 9. The obtained equation is shown in Eq. (6).
3
μ eq ¼ 0:57β3 ¼ 0:57ðdb =dÞ ð0:2 ≤β ≤0:8Þ
ð6Þ
The ultimate strength corresponding to punching shear failure mode of concrete-filled steel tubular CHS connections in tension is considered as the summary of shear force on the punching shear face. Thus Eq. (7) is proposed to calculate the ultimate strength: Z F u ¼ 1 þ μ eq db t
0
π
f τ ðθÞdθ
ð7Þ
where Fu is the ultimate strength, fτ is the shear stress on the punching shear failure face. Since the shear stress distribution and area of punching shear failure face could be obtained with Eqs. (3) and (4), the ultimate strength of T type connection could be rewritten as Eq. (8). f u ¼ 1 þ μ eq ð2 þ kπ−2kÞdb t f v; max
ð8Þ
The maximum shear stress is taken as 90% of ultimate shear strength fv,max = 0.9 fu,v = 0.9 × 0.75fu [13] and the k value is taken as 0.5 as presented previously, Eq. (8) could be rewritten as Eq. (9). 3 f u ¼ 1:74 þ ðdb =dÞ db t f u
ð9Þ
Where fu is the ultimate tensile strength of chord material. For simplicity, ultimate strength of Y type connections is recommended be calculated using Eq. (10). 3 F u sinθY ¼ 1:74 þ ðdb =dÞ db t f u
Fig. 9. Relationship between μeq and β.
ð10Þ
Where θY is the angle between the brace and chord, 30° ≤ θY ≤ 60°. The ultimate strengths calculated using Eqs.(9) and (10) for T and Y type connections were compared with FEA results in Tables 5 and 6,
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Table 5 Comparison of design strengths with FEA results for T type connections. Specimens
T-300-4-60-6 T-300-4-100-6 T-300-4-100-6 T-300-4-100-6 T-300-4-100-4 T-300-4-100-8 T-300-4-133-6 T-300-4-133-6 T-300-4-133-6 T-300-3-140-6 T-300-4-140-6 T-300-5-140-6 T-300-6-140-6 T-300-4-150-6 T-300-4-180-6 T-300-4-240-6 T-240-4-60-6 T-240-4-110-6 T-240-4-133-6 T-240-4-168-6 T-400-4-140-6
fy
fu
FFEA
Fu-design
Fu-weld
(MPa)
(MPa)
(kN)
(kN)
(kN)
298 298 436 456 298 298 298 436 456 298 298 298 298 298 298 298 298 298 298 298 298
427 427 520 555 427 427 427 520 555 427 427 427 427 427 427 427 427 427 427 427 427
207.0 361.5 412.5 445.1 361.8 362.1 507.6 580.1 621.6 400.7 515.0 642.1 825.7 557.7 700.7 1014.0 231.0 441.6 529.4 720.6 494.6
179.1 303.5 369.6 394.5 303.5 303.5 415.0 505.4 539.4 330.3 440.4 550.5 660.6 477.8 601.4 923.1 179.9 345.0 433.9 597.7 426.3
215.7 349.5 425.6 454.2 349.5 349.5 474.0 577.2 616.1 375.8 501.1 626.4 751.6 541.4 675.9 1032.5 217.3 405.6 503.7 688.5 479.4 Mean COV
respectively. The mean value of Fu-design / FFEA and the corresponding COV for T type connections are 0.85 and 0.041, respectively. The mean value of Fu-design / FFEA and the corresponding COV for Y type connections are 0.88 and 0.032, respectively. The comparison indicates that the proposed equations are generally conservative. The reason of conservatism is that the width of weld is not considered in the design as mentioned in Xu, et al. [6]. If the width of weld is considered, the mean values of Fu-weld / FFEA are 0.97 and 1.00 for T and Y type connections, respectively. Since the width of weld is difficult to be considered in engineering design, Eqs. (9) and (10) are recommended for design. For K type connections having a branch with very little or no loading, the connection can be treated as a Y-connection [6]. Eq. (9) is also applicable to this kind of K type connections. It should be noted that the design equations are suitable for conventional connections with the limitations of 0.20 ≤ β ≤ 0.80, 25.0 ≤ γ ≤ 50.0, and 1.0 ≤ τ ≤ 2.0.
Fu-design / FFEA
Fu-weld / FFEA
0.87 0.84 0.90 0.89 0.84 0.84 0.82 0.87 0.87 0.82 0.86 0.86 0.80 0.86 0.86 0.91 0.78 0.78 0.82 0.83 0.86 0.85 0.041
1.04 0.97 1.03 1.02 0.97 0.97 0.93 1.00 0.99 0.94 0.97 0.98 0.91 0.97 0.96 1.02 0.94 0.92 0.95 0.96 0.97 0.97 0.036
6. Conclusions In this study, an accurate nonlinear finite element model for the analysis of concrete-filled steel tubular circular hollow section connections under axial tension has been developed. The Modified Mohr-Coulomb fracture criterion of steel material was adopted in the finite element model. The comparison between the finite element results and the experimental results showed a good agreement in predicating the behavior of the specimens. The shear stress distribution on the punching shear failure face was obtained from the finite element analysis results and is described by a proposed equation. Equations for equivalent thickness of the punching shear failure face were also proposed which enable the ultimate strength equation to be written in a simple form. Comparison between the design strengths and the finite element analysis results for T and Y type connections indicates the proposed equations are generally accurate.
Table 6 Comparison of design strengths with FEA results for Y type connections. Specimens
Y-300-4-60-6 Y-300-4-100-4 Y-300-4-100-6 Y-300-4-100-6 Y-300-4-100-6 Y-300-4-100-8 Y-300-3-140-6 Y-300-4-140-6 Y-300-4-140-6 Y-300-4-140-6 Y-300-5-140-6 Y-300-6-140-6 Y-300-4-150-6 Y-300-4-180-6
fy
fu
FFEA
Fu-design
Fu-weld
(MPa)
(MPa)
(kN)
(kN)
(kN)
298 298 298 436 456 298 298 298 436 456 298 298 298 298
427 427 427 520 555 427 427 427 520 555 427 427 427 427
294.4 513.4 508.5 579.7 623.5 510.2 524.8 719.6 815.0 916.6 876.0 1072.0 791.8 934.2
253.3 429.2 429.2 522.7 557.9 429.2 467.1 622.9 758.5 809.6 778.6 934.3 675.7 850.4
305.0 494.2 494.2 601.9 642.4 494.2 531.5 708.6 863.0 921.1 885.8 1063.0 765.6 955.8 Mean COV
Fu-design /FFEA
Fu-weld / FFEA
0.86 0.84 0.84 0.90 0.89 0.84 0.89 0.87 0.93 0.88 0.89 0.87 0.85 0.91 0.88 0.032
1.04 0.96 0.97 1.04 1.03 0.97 1.01 0.98 1.06 1.00 1.01 0.99 0.97 1.02 1.00 0.031
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Notation The following symbols are used in this paper: A parameters of material strain hardening; the total area of the punching shear failure face; Apunch friction coefficient in the Mohr-Coulomb model; c1 shear resistance in the Mohr-Coulomb model; c2 s c parameters related to the pressure and Lode angle cax θ , cθ , cθ, cη dependence; d outer diameter of chord; outer diameter of brace; db E Young's modulus; Young's modulus of concrete; Ec concrete compressive strength, by 150-150-150 cubic fcu specimens; ultimate tensile stress of steel; fu ultimate shear strength of steel; fu,v the maximum shear stress on the punching shear face; fv,max the minimum shear stress on the punching shear face; fv,min yield stress of steel; fy shear stress on the punching shear face; fτ k fv,min / fv,max; n parameters of material strain hardening; ultimate strength of specimen obtained from tests; FExp ultimate strength of specimen obtained from FEA; FFEA ultimate strength of connections; Fu Fu-design ultimate strength of specimen predicted from proposed equations; ultimate strength of specimen predicted with the considerFu-weld ation of weld width; equivalent thickness; Teq t wall thickness of chord; wall thickness of brace; tb β ratio of brace outer diameter to chord outer diameter; γ ratio of chord outer radius to chord thickness; τ ratio of brace thickness to chord thickness; elongation (tensile strain) after fracture based on gauge εf length of 50 mm; εf the equivalent strain at the point of fracture;
θ θ θY μeq η η0
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the angle defined in Fig. 6; Lode angle parameter (normalized Lode angle); the angle between the brace and chord; a coefficient related to Apunch, db and t; stress triaxiality; parameters related to the pressure and Lode angle dependence.
Acknowledgments The research work described in this paper was supported by National Key Technology R&D Program (2011BAJ09B03) and research project from Science and Technology Department of Zhejiang Province (2015C33005). References [1] L.H. Han, Concrete-Filled Steel Tube Structures-Theory and Design, second ed. Science Press, Beijing, 2007. [2] I.E. Tebbett, C.D. Beckett, J. Billington C, The punching shear strength of tubular joints reinforced with a grouted pile. Offshore technology conference, Offshore Technology Conference 1979, pp. 915–921. [3] J.A. Packer, Concrete-filled HSS connections, J. Struct. Eng. 121 (3) (1995) 458–467. [4] R. Feng, B. Young, Tests of concrete-filled stainless steel tubular T-joints, J. Constr. Steel Res. 64 (11) (2008) 1283–1293. [5] R. Feng, B. Young, Behaviour of concrete-filled stainless steel tubular X-joints subjected to compression, Thin-Walled Struct. 47 (4) (2009) 365–374. [6] F. Xu, J. Chen, W. Jin, Experimental investigation and design of concrete-filled steel tubular CHS connections, J. Struct. Eng. ASCE 141 (2) (2015) (04014106). [7] AISC, Specification for Structural Steel Buildings, American Institution of Steel Construction (AISC), ANSI/AISC, Chicago, Illinois, 2010 (360–10). [8] ABAQUS, Standard User's Manual, Version 6.10, Hibbitt HD, Karlsson BI and Sorensen P, USA, 2010. [9] S. Herion, F. Mang, R. Puthli, Parametric study on multiplanar K-joints with gap made of circular hollow sections by means of the finite element method, The Sixth International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, 1996. [10] M.M.K. Lee, D. Bowness, Prediction of stress intensity factors in semi-elliptical weld toe cracks in offshore tubular joints, Proceedings of the 9th International Symposium and Euroconference on Tubular Structures, 9 2001, pp. 299–310 (Dusseldorf, Germany). [11] Y. Bai, T. Wierzbicki, Application of extended Mohr–Coulomb criterion to ductile fracture, Int. J. Fract. 161 (1) (2010) 1–20. [12] Y. Bai, T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3D space, Eng. Fract. Mech. 135 (2015) 147–167. [13] J.M. Amiss, F.D. Jones, H.H. Ryffel, Machinery's Handbook Guide to the Use of Tables and Formulas, 28th ed. Industrial Press, New York, 2008.