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Flexural Stiffness Analysis of the PVC–CFRP-Confined Concrete Columns with RC Ring Beam Joint Under Eccentric Load

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Abstract

An experimental study on 24 PVC–CFRP-confined concrete (PCCC) columns with reinforced concrete (RC) ring beam joint under eccentric load is conducted, and several experimental parameters (i.e., width and height of ring beam, reinforcement ratio, eccentricity and CFRP strips spacing) are considered. Two failure modes, the damage of PCCC columns and the crushing of joint concrete, are observed in the experiments. The initial stiffness increases with the decrease in the ring beam height, eccentricity or CFRP strips spacing. The stiffness degradation rate increases with the increase in the ring beam height, eccentricity or CFRP strips spacing, while it decreases with increasing ring beam width. According to the experimental study, a theoretical model for estimating the flexural stiffness of PCCC columns with RC ring beam joint is established based on the cross-sectional strain equilibrium condition. Additionally, considering the impact of axial compression ratio \(n\) and equivalent confining effect coefficient \(\xi _{{{\text{ef}}}}\), a simplified moment–curvature model of PCCC columns with RC ring beam joint is proposed. The proposed models agree well with the test results.

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Abbreviations

\(A_{{\text{s}}}\) :

Total sectional area of ring reinforcement in the ring beam

\(A_{{\text{c}}}\) :

Concrete area of PFCC column

\(A_{{\text{f}}}\) :

CFRP strips section area

b :

Ring beam width

\(B_{{\text{s}}}\) :

Flexural stiffness of PCCC columns with RC ring beam joint

\(e_{0}\) :

Eccentricity

\(e'\) :

Distance from the action point of axial force to resultant point of tensile steel bars

\(E_{{\text{c}}}\) :

Elastic modulus of core concrete

\(f_{{\text{c}}}\) :

Compressive strength of core concrete

\(f_{{\text{f}}}\) :

Tensile strength of CFRP strips

h :

Ring beam height

\(h_{0}\) :

Effective height of column section

\(I_{{\text{c}}}\) :

Inertia moment of core concrete

\(k_{{\text{g}}}\) :

Confinement effect coefficient of CFRP strips

\(K_{{\text{e}}}\) :

Elastic stage stiffness of PCCC columns with RC ring beam joint

\(K_{{\text{p}}}\) :

Strengthening stiffness of PCCC columns with RC ring beam joint

M e :

Measured moment of mid-span section of PFCC columns in Group F

M u :

Measured moment of mid-span section of PFCC columns in Group S

\(N_{{\text{e}}}\) :

Measured bearing capacity of specimens in Group F

\(N_{{\text{u}}}\) :

Measured bearing capacity of specimens in Group S

\(n_{{\text{f}}}\) :

Layer of CFRP strips

\(s_{{\text{f}}}\) :

Spacing of CFRP strips

\(s^{\prime}_{{\text{f}}}\) :

Width of CFRP strips

\(\sigma _{{\text{c}}}\) :

Axial compressive stress of concrete approach axial force

\(\sigma _{{\text{s}}}\) :

Tensile stress of steel bars far from axial force

\(\varepsilon _{{\text{s}}}\) :

Measured tensile strain of the longitudinal bars of columns

\(\varepsilon _{{\text{c}}}\) :

Measured compressive strain of core concrete in PVC–CFRP tube

\(\phi\) :

Curvature of the mid-span section of PFCC column

\(\varphi _{{\text{c}}}\) :

Strain inhomogeneity coefficients of concrete

\(\varphi _{{\text{s}}}\) :

Strain inhomogeneity coefficients of steel bars

\(\eta\) :

Eccentricity enhancement factor of RC columns

\(\eta _{{\text{k}}}\) :

Coefficient of internal force arm

\(\zeta\) :

Confining effect coefficient of PVC tube on core concrete

\(\xi _{{{\text{ef}}}}\) :

Equivalent confinement effect coefficient

\(\xi ^{\prime}_{{{\text{ef}}}}\) :

Equivalent confinement effect coefficient considering the effect of eccentricity

\(\rho _{{\text{s}}}\) :

Reinforcement ratio of tensile steel bars

\(\rho\) :

Reinforcement ratio of ring beam

\(\nu\) :

Reduction coefficient of elastic modulus of compressive concrete

\(\psi\) :

Influence coefficient of the flexural stiffness of PCCC columns

\(\gamma _{{\text{e}}}\) :

Influence coefficient of eccentricity on the bearing capacity of PCCC columns

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Acknowledgements

This study was sponsored by the National Natural Science Foundation of China (Nos. 51578001, 51878002, 52078001), Outstanding Youth Fund of Anhui Province (No. 2008085J29) and University Natural Science Research Project of Anhui Province (Nos. KJ2020A0234, KJ2020A0261).

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Authors and Affiliations

  1. Department of Civil Engineering and Architecture, Anhui University of Technology, Maanshan, China

    Ping Wu, Jie Liu, Feng Yu, Yucong Guan, Yuan Fang & Shuangshuang Bu

  2. Shanghai Baoye Group Corp., LTD, Shanghai, China

    Jie Liu & Yucong Guan

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  1. Ping Wu
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  2. Jie Liu
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  3. Feng Yu
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Correspondence to Feng Yu or Yucong Guan.

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Wu, P., Liu, J., Yu, F. et al. Flexural Stiffness Analysis of the PVC–CFRP-Confined Concrete Columns with RC Ring Beam Joint Under Eccentric Load. Iran J Sci Technol Trans Civ Eng 46, 1825–1840 (2022). https://doi.org/10.1007/s40996-021-00693-w

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