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Reliability-based analysis of the flexural strength of concrete beams reinforced with hybrid BFRP and steel rebars

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Abstract

The durability of reinforced concrete structures has always been an important problem in civil engineering because steel rebars rust easily. Therefore, fiber-reinforced polymer (FRP) rebars possessing good corrosion resistance, low weight, and easy construction has become a substitute for reinforcement. However, since FRP rebar has a low elastic modulus and is a brittle failure material, large deflections and cracks occur in the FRP concrete beam with no obvious warning before failure. A hybrid reinforced concrete beam that combines the advantages of steel rebar and FRP rebar is a good structural form. The reliability of hybrid reinforced beams must be analyzed to ensure their safety. A flexural performance test of the hybrid basalt FRP (BFRP)–steel-reinforced beam was performed, the failure mode was explored, and the numerical models were established. The accuracy of the models was verified by comparing them with the test results. The numerical models were used to establish a database (630 cases) that was combined with existing research results (33 cases), to obtain the statistics of the uncertainty of the prediction model. Reliability analysis of a large-scale design space was conducted to calibrate the BFRP. Finally, the average deviation from the target reliability index suggested that the values of the partial coefficient of the materials range from 1.2 to 1.4.

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Abbreviations

λ i :

ith order of L-moment

E:

Expectation

X:

Random variable

U:

Normal variable

F:

Distribution function of random variable

a, b, c  and  d :

Polynomial coefficients

\({\tau }_{3}\) :

Skewness of L-moment of random variable

\({\tau }_{4}\) :

Kurtosis of L-moment of random variable

Z :

Limit state function

R :

Structural resistance

S :

Structural effect

X i :

Various effects on the structure and various factors affecting the structural resistance

N f :

Number of samples with Z < 0

N :

Total number of samples

\({P}_{f}\) :

Failure probability

\(\Phi\)(·):

Inverse function of normal distribution

f cu :

Cube compressive strength of concrete

A s :

Area of steel rebar

A f :

Area of BFRP rebar

E f :

Elastic modulus of BFRP rebar

ε cu :

Ultimate compressive strain of concrete

β 1 :

Ratio of depth of the equivalent rectangular stress block to the depth of neutral axis

ρ s :

Reinforcement ratio of steel rebar

ρ f :

Reinforcement ratio of BFRP rebar

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

Cylinder compressive strength of concrete

\({f}_{cu,k}\) :

Compression strength of 150 mm cube concrete block

\({\alpha }_{c1}\) :

Coefficient of concrete

\({\alpha }_{c2}\) :

Coefficient of concrete

\({M}_{u,\mathrm{exp}}\) :

Moment result from experiment or numerical model

\({M}_{u,\mathrm{pre}}\) :

Moment result from prediction model

μ :

Error of prediction model

PDF:

Probability density function

k :

Ratio k of live load dead load

γ f :

Material partial factor of elastic modulus of BFRP rebar

H :

Average deviation value

n :

Number of design cases

β i :

Reliability index of ith case

β T :

Target reliability index

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Funding

Financial support of the work by the Natural Science Foundation of Fujian Province (Grant No. 2021J011062) and the Fujian University of Technology (Grant No. GY-Z21181).

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Authors and Affiliations

  1. School of Civil Engineering, Fujian University of Technology, Fuzhou, 350118, China

    Wei Zhang, Xiang Liu & Yiqun Huang

  2. Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague, 19000, Czech Republic

    Wei Zhang

  3. School of Civil Engineering, Zhengzhou University, 100 Kexuedadao Rd, Zhengzhou, 450001, China

    Ming-Na Tong

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  1. Wei Zhang
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Correspondence to Xiang Liu.

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Zhang, W., Liu, X., Huang, Y. et al. Reliability-based analysis of the flexural strength of concrete beams reinforced with hybrid BFRP and steel rebars. Archiv.Civ.Mech.Eng 22, 171 (2022). https://doi.org/10.1007/s43452-022-00493-7

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