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# Determining the Reduction Factor in Predicting the Contribution of Concrete to Shear Strength by Using a Probabilistic Method

• 52 Accesses

## Abstract

The reliability of a structure can be defined as the probability of the structure to fulfil its intended purpose throughout its design lifespan. In the codes, it is aimed to provide the target failure probability by means of safety factors in the form of load factors and strength reduction factors. This paper presents an investigation of the reduction factor for the contribution of concrete to the shear strength of reinforced concrete beams without stirrups designed according to the Turkish Code. In this code, the contribution of concrete to the shear strength is calculated by multiplying the diagonal cracking strength by a reduction factor of 0.8. In this study, based upon a second moment probabilistic analysis procedure, the change in the strength reduction factor was investigated for various coefficients of variation of concrete compressive strength and failure probabilities by using experimental data available in the literature. It is assumed that the considered random variables are statistically independent, and the correlation effects are not taken into account. The results show that the reduction factor decreases with the increase in the coefficient of variation of concrete compressive strength and the reduction factor given by the Turkish Code corresponds to a variation coefficient of 0.12 and a failure probability of 10−6.

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## Abbreviations

$$a/d$$ :

Ratio of the shear span to effective depth of beam

$$f_{\text{ck}}$$ :

Compressive strength of concrete

$$g(X)$$ :

Performance function

$$m_{{X_{i} }} ,m_{{_{{X_{i} }} }}^{N}$$ :

Mean value, mean value of equivalent normal distribution

$$p_{\text{F}}$$ :

Failure probability

$$v_{\text{cr}}$$ :

Cracking shear strength of beam

$$v_{c}$$ :

Contribution of concrete to shear strength

$$V$$ :

Coefficient of variation

$$X_{i} ,X_{i}^{{\prime }}$$ :

Random variable, reduced variates

$${\mathbf{x}}^{*}$$ :

Most probable failure point

$$\alpha_{i}$$ :

Sensitivity coefficient

$$\beta$$ :

Reliability index

$$\phi$$ :

Strength reduction factor

$$\gamma$$ :

Safety factor

$$\lambda_{R} \cdot \lambda_{S}$$ :

Mean value of lognormal distribution

$$\rho$$ :

Longitudinal reinforcement ratio

$$\sigma_{R} \cdot \sigma_{S}$$ :

Standard deviation of normal distribution

$$\sigma_{{_{{X_{i} }} }}^{N}$$ :

Standard deviation of equivalent normal distribution

$$\zeta_{R}^{{}} \cdot \zeta_{S}^{{}}$$ :

Standard deviation of lognormal distribution

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