Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel tubes in tension loads

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.

Graphical abstract

Keywords

square concrete filled tubes / confine-stiffening / confine-strengthening / fractal cracking / fracture

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Notations

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

{\epsilon }_{\text{p,initial}}^{\ast }: initial plastic strain of steel

{\epsilon }_{\text{t}}^{\ast }, f_{\text{t}}^{\ast }: cracking strain and cracking stress of concrete in SCFT

{\epsilon }_{\text{y}}^{\ast }, f_{\text{y}}^{\ast }: modified yield strain and stress of steel tube in SCFT

{\epsilon }_{\text{resi}}^{\ast }: residual strain of cocnrete (defined as the strain corresponding to the time when the primary concrete crack is fully open, i.e., ω = ω_u)

f_{\text{resi}}^{\ast }: residual stress of cocnrete

ε_s,l, ε_s,t: longitudinal strain and hoop strain of steel tube

ε_c,l, ε_c,t,ε_c,r: longitudinal strain, hoop strain, and radial strain of concrete

{\overline{\epsilon }}_{\text{l}}: average longitudinal strain of steel

{\overline{\epsilon }}_{\text{t}}, {\overline{\epsilon }}_{\text{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, σ_c,r: longitudinal stress, hoop stress, and radial stress of concrete

{\overline{\sigma }}_{\text{c,l}}, {\overline{\sigma }}_{\text{c,r}}: average longitudinal stress and average radial stress of concrete

{\overline{\sigma }}_{\text{s,l}}, {\overline{\sigma }}_{\text{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

\overline{\tau }: average interface friction stress between steel tube and concrete

k: friction coefficient for Coulomb’s law

τ₀: 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

R₀: initial value of R (before concrete cracking)

R: average transverse strain to average longitudinal strain ratio of steel tube

t: steel tube thickness

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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2021 Higher Education Press 2021.