Reinforcement Area Limits

The area of flexure reinforcement A_s is subject to the following limits:

The lesser of:

A_{s, \min} = \frac{3 \sqrt{{f^{'}}_{c}}}{f_{y}} b d

From ACI 10-3

A_{s, \min} = \frac{200}{f_{y}} b d

From ACI-10.5.1

or:

A_{s, min}= 4/3 A_s Required from analysis.

From ACI-10.5.3

A_{s, max} = 0.75ρ_bbd

From ACI-99-10.3.3

Note that for negative moment, use b_w instead of b

where

ρ_b	=	$0.85 β_{1} \frac{{f^{'}}_{c}}{f_{y}} \frac{87, 000}{87, 000 + f_{y}}$ From ACI-10.3.2
β₁	=	$0.85 - 0.05 \frac{{f^{'}}_{c} - 4, 000}{1, 000}$ From ACI-10.2.7.3

Limited by:

0.65 ≤ β₁ ≤ 0.85

Note: ACI 10.5.2 is not implemented because all designed beams are considered continuous. If the beams have end releases the user may need to perform some additional checks.