Minimum Reinforcement Steel Area Calculator

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Minimum Reinforcement Steel Area Calculator

Civil Engineering and Design
Strength of Materials Basics and Equations | Mechanics of Materials

Minimum Reinforcement Steel Area per. ACI 318 Equations and Calculator

ACI 318 sets limits on the minimum and maximum areas of tension in steel.

The minimum area of tension steel is

Eq. 1(a), SI
A_s,min = f'_c^0.5 · b_w· d / ( 4 · f_y ) ≥ 1.4 · b_w · d / f_y

Eq. 1(b), US
A_s,min = 3 · f'_c^0.5 · b_w· d / ( f_y ) ≥ 200 · b_w · d / f_y

When the bending moment produces tension in the flange of a statically determinate T-beam, the value of A_s,min calculated from Eq. 1 must be increased. For this condition, ACI 318 Sec. 10.5.2 requires that the minimum steel be taken as the smaller of what is calculated from either Eq. 1 (with b_w set equal to the width of the flange) or Eq. 2.

Eq. 2(a), SI
A_s,min = f'_c^0.5 · b_w· d / ( 2 · f_y )

Eq. 2(b), US
A_s,min = 6 · f'_c^0.5 · b_w· d / f_y

Minimum steel provisions of Eq. 1 and Eq. 2 do not have to be followed if the area of steel provided exceeds the calculated amount required by at least 33% [ACI 318 Sec. 10.5.3].

Where:

f '_c = Compressive strength of concrete, lbf/in² (MPa)
b_w = Width of web, ft, (m)
d = Beam effective depth (tension to steel centroid), ft, (m)
f_y = Tension steel yield strength, lbf/in² (MPa)

Reference

ACI 318 Building Code Requirements for Structural Steel, paragraph 10.5 Minimum reinforcement of flexural members
Civil Engineering Reference Manual, Fifteenth Edition, Michael R. Lindeburg, PE