Abstract
Tension stress in steel-concrete composite is widely observed in engineering design. Based on an experimental program on tension performance of three square concrete-filled tubes (SCFT), the tension theory of SCFT is proposed using a mechanics-based approach. The tension stiffening effect, the confining strengthening effect and the confining stiffening effect, observed in tests of SCFTs are included in the developed tension theory model. Subsequently, simplified constitutive models of steel and concrete are proposed for the axial tension performance of SCFT. Based on the MSC.MARC software, a special fiber beam-column element is proposed to include the confining effect of SCFTs under tension and verified. The proposed analytical theory, effective formulas, and equivalent constitutive laws are extensively verified against three available tests reported in the literature on both global level (e.g., load-displacement curves) and strain level. The experimental verification proves the accuracy of the proposed theory and formulations in simulating the performance of SCFT members under tension with the capability to accurately predict the tensile strength and stiffness enhancements and realistically simulate the fractal cracking phenomenon.
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Abbreviations
- α strength :
-
strength enhancement ratio of SCFT compared to steel tube
- α stiffness :
-
stiffness enhancement ratio of SCFT compared to steel tube
- α, C :
-
two coefficients introduced for solving ordinary differential equations
- ε*p,initial :
-
initial plastic strain of steel
- ε*t,f t*:
-
cracking strain and cracking stress of concrete in SCFT
- ε* y,f*y :
-
modified yield strain and stress of steel tube in SCFT
- ε*resi :
-
residual strain of cocnrete (defined as the strain corresponding to the time when the primary concrete crack is fully open, i.e., ω =ωu)
- f*resi :
-
residual stress of cocnrete
- ε s,l, ε s,t :
-
longitudinal strain and hoop strain of steel tube εc,l, εc,t, εc,r longitudinal strain, hoop strain, and radial strain of concrete
- \({{\bar \varepsilon}_{\rm{l}}}\) :
-
average longitudinal strain of steel
- \({{\bar \varepsilon}_{\rm{t}}},{{\bar \varepsilon}_{\rm{r}}}\) :
-
average hoop strain of concrete and average radial strain of concrete
- σ s,l, σ s,t :
-
longitudinal stress and hoop stress of steel tube
- σ c,l, σ c,t, σrc,r :
-
longitudinal stress, hoop stress, and radial stress of concrete
- \({{\bar \sigma}_{{\rm{c,l}}}},{{\bar \sigma}_{{\rm{c,r}}}}\) :
-
average longitudinal stress and average radial stress of concrete
- \({{\bar \sigma}_{{\rm{s,l}}}},{{\bar \sigma}_{{\rm{s,t}}}}\) :
-
average longitudinal stress and average hoop stress of steel
- λ :
-
a coefficient between hoop stress and longitudinal stress of steel tube at crack section
- γ :
-
the ratio between transverse strain increment and longitudinal stress increments of steel tube
- \({\bar \tau}\) :
-
average interface friction stress between steel tube and concrete
- k :
-
friction coefficient for Coulomb’s law
- τ 0 :
-
initial shear strength of interface between steel and concrete for Coulomb’s law
- ν c, ν s :
-
poisson ratio of concrete and steel
- ω, ω u :
-
crack width and ultimate crack width (when concrete fully lost tensile stress).
- χ :
-
a factor for SCFT (which is calibrated as 1.9 based on tests)
- D :
-
section length of SCFT
- E c, E s :
-
elastic modulus of concrete and steel
- E h :
-
modified hardening modulus of steel
- f t :
-
tensile strength of concrete
- L min, L max, L m :
-
minimum crack spacing, maximum crack spacing, and aveerage crack spacing
- M :
-
a coefficient for steel constitutive model (M = 400 is recommended for SCFT based on regression results using test data)
- N :
-
a fractal coefficient (N = 2, 3, or 4 for SCFT based on test results)
- n :
-
ratio of elastic modulus of steel divided by that of concrete
- R 0 :
-
initial value of R (before concrete cracking)
- R :
-
average transverse strain to average longitudinal strain ratio of steel tube
- t :
-
steel tube thickness
References
Nie J G, Wang J J, Gou S K, Zhu Y Y, Fan J S. Technological development and engineering applications of novel steel-concrete composite structures. Frontiers of Structural and Civil Engineering, 2019, 13(1): 1–14
Shao X D, Deng L, Cao J H. Innovative steel-UHPC composite bridge girders for long-span bridges. Frontiers of Structural and Civil Engineering, 2019, 13(4): 981–989
EN 1994-1-1: 2004. Eurocode 4: Design of Composite Steel and Concrete Structures. Part1-1: General Rules and Rules for Buildings. Brussels: European Committee for Standardization (CEN), 2004
Leon R T, Gao Y. Resiliency of steel and composite structures. Frontiers of Structural and Civil Engineering, 2016, 10(3): 239–253
Deng S W, Shao X D, Zhao X D, Wang Y, Wang Y. Precast steel-UHPC lightweight composite bridge foraccelerated bridge construction. Frontiers of Structural and Civl Engieering, 2021, 15(2): 364–377
Zhou M, Fan J S, Tao M X, Nie J G. Experimental study on the tensile behaviour of square concrete-filled steel tubes. Journal of Constructional Steel Research, 2016, 121: 121–215
Li W, Han L H, Chan T M. Tensile behaviour of concrete-filled double-skin steel tubular members. Journal of Constructional Steel Research, 2014, 99: 99–46
Li W, Han L H, Chan T M. Numerical investigation on the performance of concrete-filled double-skin steel tubular members under tension. Thin-walled Structures, 2014, 79: 79–118
Silva A, Jiang Y, Macedo L, Castro J M, Monteiro R, Silvestre N. Seismic performance of composite moment-resisting frames achieved with sustainable CFST members. Frontiers of Structural and Civil Engineering, 2016, 10(3): 312–332
Shams M, Saadeghvaziri M A. Nonlinear response of concrete-filled steel tubular columns under axial loading. ACI Structural Journal, 1999, 96(6): 1009–1017
Susantha K A S, Ge H, Usami T. Uniaxial stress-strain relationship of concrete confined by various shaped steel tubes. Engineering Structures, 2001, 23(10): 1331–1347
Hajjar J F, Gourley B C. Representation of concrete-filled steel tube cross-section strength. Journal of Structural Engineering, 1996, 122(11): 1327–1336
Inai E, Mukai A, Kai M, Tokinoya H, Fukumoto T, Mori K. Behavior of concrete-filled steel tube beam columns. Journal of Structural Engineering, 2004, 130(2): 189–202
Vecchio F J, Collins M P. The modified compression field theory for reinforced concrete elements subjected to shear. ACI Structural Journal, 1986, 83(2): 219–231
Architectural Institute of Japan (AIJ). Recommendations for design and construction of concrete filled steel tubular structures. Study on Concrete Properties Subjected Impact Loading, 2008, 12: 12–10 (in Japanese)
ANSI/AISC 360-05. Specification for Structural Steel Buildings. Chicago: American Institute of Steel Construction (AISC), 2005
JGJ 138-2016. Code for Design of Composite Structures. Beijing: Ministry of Housing and Urban-Rural Development (MOHURD), 2016 (in Chinese)
Zhou M, Xu L Y, Tao M X, Fan J S, Hajjar J F, Nie J G. Experimental study on confining-strengthening, confining-stiffening, and fractal cracking of circular concrete filled steel tubes under axial tension. Engineering Structures, 2017, 133: 133–199
Xu L Y, Tao M X, Zhou M. Analytical model and design formulae of circular CFSTs under axial tension. Journal of Constructional Steel Research, 2017, 133: 133–230
Rabczuk T, Zi G, Gerstenberger A, Wall W A. A new crack tip element for the phantom-node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599
Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
Zhang Y M, Lackner R, Zeiml M, Mang H A. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 287–366
Zhang Y M, Zhuang X Y. Cracking elements: A self-propagating strong discontinuity embedded Approach for quasi-brittle fracture. Finite Elements in Analysis and Design, 2018, 144: 144–100
Zhang Y M, Zhuang X Y. Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics, 2019, 102: 102–9
Zhang Y M, Mang H A. Global cracking elements: A novel tool for Garlerkin-based approaches simulating quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 2020, 121(11): 2462–2480
Zhang Y M, Gao Z R, Li Y Y, Zhuang X Y. On the crack opening and energy dissipation in a continuum based disconnected crack model. Finite Elements in Analysis and Design, 2020, 170: 103333
Zhang Y M, Huang J G, Yuan Y, Mang H A. Cracking elements method with a dissipation-based arc-length approach. Finite Elements in Analysis and Design, 2021, 195: 103573
Ren H L, Zhuang X Y, Anitescu C, Rabczuk T. An explicit phase field method for brittle dynamic fracture. Computers & Structures, 2019, 217: 217–56
Rabczuk T, Ren H L, Zhuang X Y. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. CMC, 2019, 59(1): 31–55
Ren H L, Zhuang X Y, Rabczuk T. A nonlocal operator method for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2020, 358: 112621
Hognestad E. High strength bars as concrete reinforcement—Part 2: Control of cracking. Journal of the PCA Research and Development Laboratories, 1962, 4(1): 46–62
Xu LY, Nie X, Zhou M, Tao MX. Whole-process crack width prediction of reinforced concrete structures considering bonding deterioration. Engineering Structures, 2017, 142: 142–254
Belarbi A, Hsu T T C. Constitutive laws of concrete intension and reinforcing bars stiffened by concrete. ACI Structural Journal, 1994, 91(4): 465–474
Nie J G, Tao M X, Cai C S, Li S J. Deformation analysis of prestressed continuous steel-concrete composite beams. Journal of Structural Engineering, 2009, 135(11): 1377–1389
Tao M X, Nie J G. Fiber beam-column model considering slab spatial composite effect for nonlinear analysis of composite frame systems. Journal of Structural Engineering, 2015, 140(1): 04013039
Tao M X, Nie J G. Element mesh, section discretization and material hysteretic laws for fiber beam-column elements of composite structural members. Materials and Structures, 2014, 48(8): 2521–2544
Wang Y H, Nie J G, Cai C S. Numerical modeling on concrete structures and steel-concrete composite frames structures. Composite: Part B, 2013, 51(1): 58–67
Denavit M D, Hajjar J F. Nonlinear seismic analysis of circular concrete-filled steel tube members and frames. NSEL Report No. NSEL-023. 2010
Tort C, Hajjar J F. Reliability-based performance-based design of rectangular concrete-filled steel tube (SCFT) members and frames. Structural Engineering Report No. ST-07-1. 2007
Hajjar J F, Molodan A, Schiller P H. A distributed plasticity model for cyclic analysis of concrete-filled steel tube beam-columns and composite frames. Engineering Journal (New York), 1998, 20(4–6): 398–412
Legeron F, Paultre P, Mazars J. Damage mechanics modeling of nonlinear seismic behavior of concrete structures. Journal of Structural Engineering, 2005, 131(6): 946–955
Zhou M. Study on basic theory and method of steel-concrete composite tension problem. Dissertation for the Doctoral Degree. Beijing: Tsinghua University, 2016 (in Chinese)
Acknowledgements
The writers gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51878018). The first author (Meng Zhou) gratefully acknowledges the support provided by Tsinghua Innovation Center in Zhuhai and Zhuhai Institute of Civil Construction-Safety Research Co., Ltd.
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Zhou, M., Wang, J., Nie, J. et al. Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel tubes in tension loads. Front. Struct. Civ. Eng. 15, 1317–1336 (2021). https://doi.org/10.1007/s11709-021-0763-3
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DOI: https://doi.org/10.1007/s11709-021-0763-3