Derivation of minimum steel ratio: based on service applied stresses

Abstract

Reinforced concrete beams undergo several design stages starting with the immediate application of loading and till the ultimate failure of the beam. In many practical applications, the beam is designed to function in the service stage during which steel plays a major role in the determination of the location of the Neutral axis. The ACI code implements several provisions on the minimum steel ratio in order to encourage ductile behaviour of the beam and to prevent against the unfavourable scenario of a sudden failure. The ACI 318-08 provisions encompass a derived expression to calculate the minimum amount of flexural reinforcement that is independent of concrete strength. This paper suggests an expansion to the formula by deriving the minimum steel ratio based on the modulus of rupture and the applied service stresses. The special case for a cracking bending moment is extrapolated from the suggested formula and the result is compared to different minimum steel area formulas.