Beam Reinforcement Limits.

International Design Codes

ACI 318-19 : Beam Reinforcement Limits per ACI 318-19 with ideCAD

TSC 2018 : Longitudinal Reinforcement Limits for Beams Transverse Reinforcement Detailing for Beams.

Notation in ACI 318-19

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