Abstract
Serviceability Limit States (SLS) may govern the design of concrete elements internally reinforced with Fibre Reinforced Polymer (FRP) bars because of the mechanical properties of FRP materials. This paper investigates the design of Fibre Reinforced Polymer reinforced concrete (FRP RC) beams under the SLS of cracking, stresses in materials, and deflections. A formulation to calculate the bending condition at which crack width and stresses in materials requirements are fulfilled is presented based on principles of equilibrium, strain compatibility and linear elastic behaviour of materials. The slenderness limits to comply with the deflection limitation are redefined and a methodology to calculate the optimal height of an FRP RC beam to satisfy all of these serviceability requirements is proposed. This procedure allows optimising the dimensions of an FRP RC beam taking into account the specific characteristics of the element, such as the mechanical properties of materials and the geometric and loading conditions.
Highlights
Corrosion of steel reinforcement in aggressive environments can cause considerable damage in reinforced concrete (RC) structures
Where:Q,G andQP are the instantaneous deflection of the variable, permanent and quasi-permanent loads, respectively; ψ is the coefficient for the quasipermanent value of the variable action and λ is the factor to take into account the long-term deflection, defined as 0.6ξ for fibre reinforced polymer (FRP) RC elements following ACI 440.1R-06 (2006) recommendations
The design of concrete structures reinforced with FRP materials is likely to be controlled by the various criteria imposed at Serviceability Limit States (SLS)
Summary
Corrosion of steel reinforcement in aggressive environments can cause considerable damage in reinforced concrete (RC) structures. DT-203 2006) and Eurocode 2 (2002) is considered for the crack width calculation Comparisons between both limitations are presented in terms of the service moment related to the cracking moment and the corresponding tensile stress at the reinforcement. While ACI 440.1R-06 (2006) adopts this latter approach, a limiting value of 0.45fc’ is explicitly recommended in ACI 440.2R-08 (2008) for concrete elements strengthened with FRPs. Eurocode 2 (2004) imposes a maximum stress in concrete of 0.60fck under a characteristic combination of loads to avoid the appearance of longitudinal cracks, which could affect durability. The tensile strain developed in the reinforcement at the cracked section εf could be a useful parameter of design when considering the SLS (Newhook et al 2002) This parameter can be calculated considering the hypothesis that the concrete stress may be less than 0.45fck and fully cracked section: εf.
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