## 1565 Minimum Reinforcement for Flexure

The primary role of minimum reinforcement is to provide adequate reserve of strength after cracking. ACI 318-02 and NZS 3101-95 code expressions for the minimum reinforcement ratio for rectangular sections are

3 f 200 As min = f c bwd > 2— bwd in.2 (psi and in.)

ffiffi fy (15.10)

As,min = bwd > — bwd mm2 (MPa and mm) 4f fy where bw is the web width and d is the effective depth. For a statically determinate T-beam, with the flange in tension, ACI 318-02 requires that bw be taken as the smaller of 2bw or the flange width.

The approach used by CSA A23.3-94 for determining minimum reinforcement is based on the ACI approach for prestressed concrete members, requiring that the factored flexural strength be at least 1.2 times the cracking moment. The cracking moment is determined with a modulus of rupture f = 0.6y f MPa. This philosophy is applied equally to non-prestressed as well as prestressed concrete members. CSA A23.3-94 provides slightly lower values of As,min than the ACI Code.

where bw is the width of the tension zone and h is the overall depth of the member. ACI 318-02, CSA A23.3-94, and NZS 3101-95 codes allow the minimum reinforcement requirement to be waived if the ultimate or factored flexural strength is at least one-third larger than the factored moment. This represents a trade-off between ductility and over-strength.

EC2-02 requires that the minimum area of flexural reinforcement must satisfy the following expression:

Asmin > 0.26tcm btd > 0.0013btd ( MPa and mm ) ( 15.12)

Jyk where bt is the mean width of the concrete zone in tension, taken as the web width for a T-beam with the flange in compression, and fctm is given by Equation 15.9. The 1995 Recommended Extensions to MC-90 require a minimum reinforcement ratio equal to 0.23f-tkjmax/fk, where _/ctk,max = ftk,0.95, which is a function of the maximum tensile strength.

Figure 15.22 compares the minimum flexural reinforcement ratio pmin = As min/bwd, required by ACI 318-02, CSA A23.3-94, and EC2-02, as a function of the concrete compressive strength. It is noted that EC2-02 requires less minimum reinforcement for beams than ACI 318-02 and CSA A23.3-94.

Unlike the requirements for the EC2-02, the minimum reinforcement requirements for slabs, given by ACI 318-02 and CSA A23.3-94, are not a function of concrete strength.

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