Effective reinforcement ratio of RC beams: Validation of modelling assumptions with high‐resolution strain data

Abstract

Concrete tensile stresses influence the cracking behaviour and the stiffness of reinforced concrete (RC) members. Most design codes account for this tension stiffening effect using an effective reinforcement ratio. Although this ratio has a significant influence on the design of RC structures, its quantification is controversial in many cases, and typically relies on empirical geometry-based expressions. One main reason for this knowledge gap is that the area of concrete in tension can only be verified indirectly, for example, through crack widths and spacings and using a suitable mechanical model. This indirect validation is subject to considerable uncertainty as it depends on parameters that scatter (e.g., bond stresses and the concrete tensile strength), and further assumptions relating internal stresses to the applied loads are required. This article outlines

Scaled concrete beams containing maximum levels of coarse recycled aggregate: Structural verifications for precast‐concrete building applications

“…Based on conventional methods, 60,61 the structural behavior of a beam upon which a point load (or the resulting equivalent load) is applied at the midpoint of its span depends on the quotient between its span and its depth: If the quotient is less than two, it is considered to be a “short shear beam.” Under those circumstances, the shear stress will therefore be much greater than the bending moment, so that the beam will be working exclusively under shear stress and any bending stresses may be disregarded. If the quotient is greater than five, it can be considered that the beam almost behaves to an ideally De Saint Venant beam 62,63 . Under typical load conditions, the bending stress will be much more relevant than the shear stress, and the beam will experience a banding failure if it incorporates a conventional reinforcement.…”

“…• If the quotient is greater than five, it can be considered that the beam almost behaves to an ideally De Saint Venant beam. 62,63 Under typical load conditions, the bending stress will be much more relevant than the shear stress, and the beam will experience a banding failure if it incorporates a conventional reinforcement. The load should therefore be applied at a point close to a beam support when a shear test is performed.…”

Modeling statically indeterminate reinforced concrete slabs and beams under fire conditions

“…where d is the effective depth, x is the depth of the compression zone, n = E s /E c is the modular ratio = ratio of the Young's moduli of reinforcing steel and concrete at ambient temperature, and EI II is the fully cracked elastic cross-sectional stiffness. [25][26][27] It is assumed here that Equation (2) also holds if a normal compressive force develops due to restraint during fire exposure, because the cracking moment M cr is generally smaller than the bending moment originating from initial sustained loads in regions where cracking is predominant. This definition of the equivalent geometrical reinforcement ratio in the tension chord is valid with a single reinforcement layer in the tensile zone as common in slabs.…”

“…This definition of the equivalent geometrical reinforcement ratio in the tension chord is valid with a single reinforcement layer in the tensile zone as common in slabs. Kaufmann et al 6 proposed an approach to define the equivalent reinforcement ratio with several layers; for a discussion of different approaches see for example, 27 Using the TCM, the maximum and minimum theoretical crack spacing s r follow from the condition that the concrete stress at the center between two cracks equals f ctm 4 :…”

“…This definition of the equivalent geometrical reinforcement ratio in the tension chord is valid with a single reinforcement layer in the tensile zone as common in slabs. Kaufmann et al 6 proposed an approach to define the equivalent reinforcement ratio with several layers; for a discussion of different approaches see for example, 27 …”