Original Research Article
The statistical evaluation of design methods of the load-carrying capacity of flexural reinforced concrete elements strengthened with FRP

https://doi.org/10.1016/j.acme.2014.04.005Get rights and content

Abstract

This article presents a statistical analysis of the design methods for calculating the load-carrying capacity of reinforced concrete elements in flexure strengthened with external FRP reinforcement. To perform calculations a database of experimental research has been created. Calculations of the load-carrying capacity were performed following the ACI440.2R-08, fib bulletin 14, TR55 recommendations. Distribution of experimental and theoretical results was determined on the basis of Wilk–Shapiro test. The evaluation of design methods was done by testing the statistical hypotheses on the difference of the means of the ratio between the experimental and theoretical results. Confidence intervals of the ratios of the experimental and calculated load carrying capacity were also calculated. In order to assess the accuracy of the design methods it is suggested to calculate the coefficient of confidence.

Introduction

Strengthening of reinforced concrete structures with external FRP reinforcement is widely known and applied. Numerous experiments, numerical and analytical research have been performed when analysing reinforced concrete structures strengthened with external FRP reinforcement [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. Research shows that proper strengthening of structures with FRP both reduces the deflections and width of cracks in reinforced concrete elements as well as increases their load carrying capacity.

Although structures strengthened with external FRP reinforcement have been intensively researched and analysed since the 80s of last century, there are still quite a few unsolved issues such as common work of external reinforcement and concrete, effective methods of anchoring FRP reinforcement and design methods.

Most authors [22], [23], [24], [25], [26], [27], [28], [29] as well as design codes [30], [31], [32] suggest design methods for calculating the load carrying capacity of reinforced concrete elements in flexure strengthened with external FRP reinforcement. The essence of all these methods is to solve two equilibrium equations. The first equation is the total of internal forces acting in the cross-section, the second one – the total of moments. Depending on the author or the design code, design methods vary according to the description of stress–strain diagram for concrete in compression, additional coefficients, limits of the effective strain level in FRP reinforcement at the debonding conditions, assumptions of calculations.

When calculations are done applying different methods and recommendations, the received theoretical results of the load carrying capacity will always differ among themselves and they will always be different from the load carrying capacity determined during the experiments. The significance of the difference of the results as well as the accuracy of the design methods may be assessed by applying statistical methods.

This article analyses three design methods for calculating the load-carrying capacity. All these methods are provided in design codes or recommendations [30], [31], [32]. A comparison of the calculated and the experimentally received load-carrying capacity of reinforced concrete structures in flexure strengthened with external FRP reinforcement was performed with the help of statistical methods.

Section snippets

Design methods

Design methods ACI440.2R-08, fib bulletin 14, TR55 (further in text methods are marked as ACI, fib and TR) are based on the following assumptions [30], [31], [32]:

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    the plane sections of element remain plane after loading, so there is a linear distribution of strains;

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    the ultimate strain of concrete according ACI, fib and TR is equal to 0.003, 0.0035 and 0.0035 respectively. The ultimate strain 0.0035 is valid for classes of concrete ≤C50/60;

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    the tensile strength of concrete is not assessed;

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Database and statistical analysis

A database of the results of 80 experimental researches has been created for statistical analysis. All beams included into the database were of rectangular cross-section. During the research all beams were tested in four-point bending. Specimens before the experiment were not additionally preloaded or damaged. The beams were reinforced with steel bar reinforcement and strengthened with externally bonded CFRP reinforcement. External reinforcement was not pre-stressed and not additionally

Conclusions

The performed analysis shows that it is difficult to assess the design methods only on the ground of the means of the results of calculations and variation coefficients. It is proposed here to assess the design methods with the help of statistical methodologies. Wilk–Shapiro test, t test as well as calculation of the confidence intervals of the results were applied in the statistical research of the design methods for calculating the load-carrying capacity.

Based on the results of experimental

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