Original Research ArticleThe statistical evaluation of design methods of the load-carrying capacity of flexural reinforced concrete elements strengthened with FRP
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
References (53)
Bond between FRP and concrete in reinforced concrete beams strengthened with near surface mounted and externally bonded reinforcement
Construction and Building Materials
(2012)- et al.
Influence of surface roughness on the bond of FRP laminates to concrete
Construction and Building Materials
(2013) - et al.
Bond efficiency of EBR and EBROG methods in different flexural failure mechanisms of FRP strengthened RC beams
Construction and Building Materials
(2014) - et al.
Experimental investigation into bond behavior of CFRP sheets attached to concrete using EBR and EBROG techniques
Composites Part B: Engineering
(2013) - et al.
Bond behaviour of substandard splices in RC beams externally confined with CFRP
Construction and Building Materials
(2014) - et al.
Assessment of effectiveness of CFRP repaired RC beams under different damage levels based on flexural stiffness
Construction and Building Materials
(2012) - et al.
Deformability of hierarchic cable roof
Journal of Constructional Steel Research
(2006) - et al.
Long-term behavior of wide shallow RC beams strengthened with externally bonded CFRP plates
Construction and Building Materials
(2014) - et al.
Externally bonded reinforcement in grooves (EBRIG) technique to postpone debonding of FRP sheets in strengthened concrete beams
Construction and Building Materials
(2013) - et al.
Behavior of reinforced concrete beams strengthened with externally bonded hybrid fiber reinforced polymer systems
Materials and Design
(2014)
Assessment of adhesive setting time in reinforced concrete beams strengthened with carbon fibre reinforced polymer laminates
Materials and Design
Effect of groove characteristics on CFRP-to-concrete bond behavior of EBROG joints: experimental study using particle image velocimetry (PIV)
Construction and Building Materials
Interaction of environmental factors on fiber-reinforced polymer composites and their inspection and maintenance: a review
Construction and Building Materials
Static and dynamic behaviour of RC beam model strengthened by CFRP-sheets
Construction and Building Materials
Strengthen and real-time monitoring of RC beam using “intelligent” CFRP with embedded FBG sensors
Construction and Building Materials
Specific challenges of adopting Eurocodes in Latvia
Procedia Engineering
Design method for calculating load-carrying capacity of reinforced concrete beams strengthened with external FRP
Construction and Building Materials
Assessment of available prediction models for the strength of FRP retrofitted RC beams
Composite Structures
Experimental study and analysis of RC beams strengthened with CFRP laminates under sustaining load
International Journal of Solids and Structures
A way for preventing tension delamination of concrete cover in midspan of FRP strengthened beams
Construction and Building Materials
Experimental study on RC beams with FRP strips bonded with rubber modified resins
Composites Science and Technology
Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRP-strengthened beams
Composites Science and Technology
Interfacial shear stress concentration in FRP strengthened beams
Composite Structures
Improved model for plate-end shear of CFRP strengthened RC beams
Cement and Concrete Composites
Experimental performances of RC beams strengthened with FRP materials
Construction and Building Materials
An experimental study of the anchorage length of carbon fibre composite plates used to strengthen reinforced concrete beams
Construction and Building Materials
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