Beam Reinforcement Limits per ACI 318-19 with ideCAD

How does ideCAD control beam reinforcement limits according to ACI 318-19?

Notation

A_cp = area enclosed by outside perimeter of concrete cross section, in.²
A_l = total area of longitudinal reinforcement to resist torsion, in.²
A_l,min = minimum area of longitudinal reinforcement to resist torsion, in.²
A_s = area of nonprestressed longitudinal tension reinforcement, in²
A_s,_min = minimum area of flexural reinforcement, in.²
A_t = area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.²
A_v = area of shear reinforcement within spacing s, in.²
A_v,_min = minimum area of shear reinforcement within spacing s, in.²
b_w = web width or diameter of circular section, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
f_c^' = specified compressive strength of concrete, psi
√f_c‘ = square root of specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed reinforcement, psi
f_yt = specified yield strength of transverse reinforcement, psi
h = overall thickness, height, or depth of member, in.
s = center-to-center spacing transverse reinforcement, in
T_cr = cracking torsional moment, in.-lb
T_th = threshold torsional moment, in.-lb
T_n = nominal torsional moment strength, in.-lb
T_u = factored torsional moment at section, in.-lb
V_c = nominal shear strength provided by concrete, lb
V_n = nominal shear strength, lb
V_s = nominal shear strength provided by shear reinforcement, lb
V_u = factored shear force at section, lb
ϕ = strength reduction factor
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength
ρ = ratio of A_s to bd

Minimum flexural reinforcement

According to ACI 9.6.1.2, a minimum area of flexural reinforcement, A_s,_min is equal to the greater of the following relations;

According to ACI 9.6.1.3, if A_s provided at every section is greater than one-third of A_s calculated by analysis, A_s,_min need not be satisfied.

Minimum shear reinforcement

If shear reinforcement is required, minimum shear reinforcement area, A_v,_min, should be considered in accordance with ACI Table 9.6.3.4.

For nonprestressed beams, minimum shear reinforcement area, A_v,_min, should be provided in all sections where V_u >ϕλ √fc‘ b_wd, except for the cases given in ACI Table 9.6.3.1. For the cases given in ACI Table 9.6.3.1., A_v,min, should be provided where V_u>ϕV_c

In other words, if ϕλ√fc‘(b_wd) < V_u < [ V_c + 8√fc‘(b_wd) ], the minimum shear reinforcement area, A_v,min, is calculated given below.

Minimum torsional reinforcement

• If T_u < ϕT_th, torsional effects are ignored.

• If ϕT_cr > T_u ≥ ϕT_th, only minimum torsional reinforcement needs to be provided given below;

Minimum transverse reinforcement (A_v + 2A_t)_min / s

the minimum area of longitudinal reinforcement A_l,min

Reinforcement Limits for Beams of Earthquake-Resistant Structures

Ordinary moment frames

All the conditions and calculations described above are valid for beams of ordinary moment frames.

Intermediate moment frames

All the conditions and calculations described above are valid for beams of intermediate moment frames.

Special moment frames

All the conditions and calculations described above are valid for beams of special moment frames.

According to ACI 18.6.3.1; Longitudinal reinforcement should be satisfied the conditions given below;

• Beams should have a minimum of two continuous bars at the top and bottom faces.

• The reinforcement ratio ρ shall not exceed 0.025 for Grade 60 or S420 reinforcement and 0.02 for Grade 80 reinforcement.