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An Experimental and Numerical Study on Continuous RC Deep Beams Strengthened with CFRP Strips

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Abstract

This paper presents the result of a research program and includes numerical analysis and experimental studies on continuous reinforced concrete deep beams and strengthening of these beams with carbon fiber reinforced polymer (CFRP) strips. Different shear span-to-overall depth ratio (a/h) between 1 and 0.33, and various reinforcing methods with CFRP strips were studied. The cracking behavior and failure modes of these beams were investigated. The experimental and numerical analysis indicated that CFRP strips significantly affect the shear capacity of continuous deep beams and their failure modes. Three experimental specimens strengthened with diagonal CFRP strips at 45° angle showed a 29%, 31%, and 24% increase in the bearing capacity, in comparison to their control beams. Among different CFRP strip arrangements in beam models, diagonal reinforcement at a 45° angle (SS45) was the most effective one, which increased the shear capacity up to 49%. Vertical U-wrap side arrangements (US90) showed the lowest increase in the bearing capacity for the beams. U strengthened beam models’ bearing capacity increased by 16%, 15%, and 13% compared to their control beams. Experimental and numerical results showed that (a/h) ratio is a key factor affecting deformability and the ultimate strength of continuous deep beams. The ultimate strength of continuous concrete deep beams increased when the a/h ratio decreased, and the mid-span deflection decreased with decreasing the a/h ratio. Finally, the load-bearing capacities of beams were compared with the internal and external indeterminate strut–tie analysis. The results of numerical modeling and experimental studies have high compatibility with indeterminate truss analysis with a 1% difference in the final load.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

L :

Overall length

a :

Shear span

h :

Overall section depth

l :

Clear span

d :

Effective depth of beam

b :

Beam width

\({f}_{\mathrm{c}}^{^{\prime}}\) :

Concrete cylinder compressive strength

\({f}_{\mathrm{t}}\) :

Concrete tensile strength

\(E\) :

Elasticity modulus

\({E}_{\mathrm{c}}\) :

Concrete initial elastic modulus

\(d\) :

Damage variable

\({d}_{\mathrm{c}}\) :

Uniaxial compressive damage variable

\({d}_{\mathrm{t}}\) :

Uniaxial tensile damage variable

\({\varepsilon }_{\mathrm{c}}^{\mathrm{pl}}\) :

Compressive plastic strain

\({\varepsilon }_{\mathrm{t}}^{\mathrm{pl}}\) :

Tensile plastic strain

\({s}_{\mathrm{c}}\) :

Compressive stiffness recovery

\({s}_{\mathrm{t}}\) :

Tensile stiffness recovery

ν c :

Concrete Poisson’s ratio

θ:

Angle of dilation

\(\frac{{f}_{\mathrm{b}0}}{{f}_{\mathrm{c}0}}\) :

Ratio of equibiaxial to uniaxial compressive stress

K:

Ratio of the second stress invariant on the tensile meridian to compressive meridian at initial yield

\({f}_{\mathrm{c}}\) :

Concrete compressive stress

\({\varepsilon }_{0}\) :

Strain at peak compressive strength

\(\varepsilon\) :

Compressive strain of concrete

\({\varepsilon }_{\mathrm{u}}\) :

Ultimate concrete compressive strain

\({\varepsilon }_{\mathrm{cr}}\) :

Strain at peak tensile strength

\({\varepsilon }_{\mathrm{tu}}\) :

Concrete ultimate tensile strain

\({\sigma }_{\mathrm{t}}\) :

Tensile stress

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

Compressive stress

\({E}_{x}\) :

Elastic modulus in the longitudinal x direction

\({E}_{y}\) :

Elastic modulus in the longitudinal y direction

\({E}_{z}\) :

Elastic modulus in the longitudinal z direction

\({\nu }_{xy}\) :

Poisson’s ratio in the xy plane

\({\nu }_{xz}\) :

Poisson’s ratio in the xz plane

\({\nu }_{yz}\) :

Poisson’s ratio in the yz plane

\({G}_{xy}\) :

Shear modulus in the xy plane

\({G}_{xz}\) :

Shear modulus in the xz plane

\({G}_{yz}\) :

Shear modulus in the yz plane

K nn, K ss, K tt :

Initial elastic stiffness

\({\sigma }_{n}\) :

Maximum amount of tensile stress

\({\tau }_{\mathrm{s}},\) \({\tau }_{\mathrm{t}}\) :

Maximum amount of shear stresses

\({\sigma }_{n}^{0}\) :

Tensile cohesive strength

\({\tau }_{\mathrm{s}}^{0}\), \({\tau }_{\mathrm{t}}^{0}\) :

Shear cohesive strengths

\(\alpha\) :

Load distribution ratio

\(\rho\) :

Flexural reinforcement ratio

\({\rho }_{\mathrm{b}}\) :

Balanced flexural reinforcement ratio

\(\Upsilon\) :

Reaction distribution ratio

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The authors received no financial support for the research, authorship, and/or publication of this article.

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Authors and Affiliations

  1. Department of Civil Engineering, Amir Kabir University, Hafez Avenue, Tehran, Iran

    Mahsa Zargarian & Alireza Rahai

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  1. Mahsa Zargarian
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Contributions

MZ did the finite element and experimental study. AR directed the research as a professor and was a major contributor in writing the manuscript. All authors read and approved the final manuscript.

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Correspondence to Alireza Rahai.

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Zargarian, M., Rahai, A. An Experimental and Numerical Study on Continuous RC Deep Beams Strengthened with CFRP Strips. Int J Civ Eng 20, 619–637 (2022). https://doi.org/10.1007/s40999-021-00677-x

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