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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

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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;

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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.

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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.

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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;

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• 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.

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