A design methodology for fibre reinforced concrete elements in serviceability conditions integrating tension softening and stiffening effects

Abstract

This paper proposes a design methodology to derive an analytical bilinear moment‒curvature diagram ( M ana – χ ana ) for the cross-section of fibre reinforced concrete (FRC) elements that also includes conventional steel flexural reinforcement (R/FRC). This bilinear diagram is obtained by determining the post-cracking tensile capacity of FRC ( N tc FRC ), which integrates not only the tensile stiffening capacity of the FRC surrounding the conventional flexural reinforcement due to the bond stress transference between this reinforcement and FRC, but also the tensile softening of the cracked FRC out of this zone. This M ana – χ ana is defined by two points, the first corresponding to the cracking moment and its corresponding curvature ( M cr ana , χ cr ana ), while the bending moment of the second point of this diagram ( M u ana ) is a multiple of the analytical cracking moment ( C u M cr ana ), where C u is dependent on the fibre volume percentage (V f ). The curvature corresponding to M u ana , χ u ana , is obtained by assuming the flexural stiffness of a fully cracked RC section. Therefore, the M ana – χ ana is determined by geometric and material properties of directly assessed by a designer. For demonstrating the applicability of the proposed design methodology, a database of beams of distinct cross-section aspect ratios and compressive strength classes, reinforced with different percentages of steel fibres and reinforcement ratios of conventional steel bars was established. By using the bilinear M ana – χ ana , and applying the principle of virtual work, the deflection of these beams was estimated with sufficient accuracy for design purposes, when compared to experimental records. Although the formulation has been applied to beams made by steel fibre reinforced concrete (SFRC), it is conceptually general and applicable to elements of concrete reinforced with other types of fibres.