Minimum Flexural Reinforcement Steel Ratios of High-Strength Concrete Beams

Table 4

Effect of member depth on the minimum reinforcement ratio according to various models.

Source	No. of beams	Notes
ACI318 M-19 [7]	Independent	(i) Employs the criteria  =  (equating the moment capacity associated with steel yielding and the cracking moment)
		(ii) Uses empirical relationships in the derivation
		(iii) Does not consider size effects
		(iv) Assumes that the concrete tensile strength after cracking is zero (conservative assumption)
Eurocode 2-04 [3]	Independent	(i) Uses the same underlying approach as that of ACI318-19
Ozbolt and Bruckner [12]	Increase after reaching a critical beam size	(i) Employs the criteria  = but allows strain-softening within a finite element framework
		(ii) Uses a finite element framework, making it difficult to be considered among the simple analytical models
Gerstle et al. [23]	Increase	(i) Based on nonlinear fracture mechanics (NLFM)
		(ii) Considers the equilibrium of the tensile and compressive forces with concrete tensile softening
		(iii) Defines the minimum reinforcement as that at which the crack propagation becomes stable
		(iv) Does not consider the interaction between concrete and steel or the softening in the concrete
Appa Rao et al. [21]	Increase	(i) Uses the same approach as Gerstle et al. [23]
Bosco et al. [29]	Decrease	(i) Is a linear fracture mechanics approach
		(ii) Proposes a brittleness number, which is a function of the reinforcement ratio and the beam size
		(iii) Does not consider the fracture process zone in concrete (strain softening)
		(iv) Does not consider the interaction between concrete and steel
Ruiz et al. [34]	Decrease	(i) Is a nonlinear fracture mechanics (cohesive model) approach
		(ii) Employs numerical modelling–uses an effective slip
		(iii) Model for reinforcement and concrete interaction
		(iv) Is difficult to apply as it includes many numerical parameters
Carpinteri et al. [18]	Decrease	(i) Uses a numerical approach based on nonlinear fracture mechanics
		(ii) Does not model the interaction between steel and concrete along the reinforcement bar