Beam Shear Design per ACI 318-19 with ideCAD

How does ideCAD calculate beams' shear strength according to ACI 318-19?

Notation

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 = width of compression face of member, in.
c₁ = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
D = dead load
E = earthquake load
f_c^' = specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed reinforcement, psi
f_yt = specified yield strength of transverse reinforcement, psi
l_n = length of clear span measured face-to-face of supports, in.
l_u = unsupported length of column or wall, in.
L = live load
L_r = roof live load
M_n = nominal flexural strength at section, in.-lb
M_pr = probable flexural strength of members, with or without axial load, determined using the properties of the member at joint faces assuming a tensile stress in the longitudinal bars of at leasts 1.25f_y and a strength reduction factor ϕ of 1.0, in.-lb
P_n = nominal axial compressive strength of member, lb
P_u = factored axial force; to be taken as positive for compression and negative for tension, lb
R = rain load
S = snow load
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.
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_e = design shear force for load combinations including earthquake effects, lb
V_e^b = Capacity shear force of the column based on the maximum probable moment strengths of the beams framing into the column, lb
V_e^c = Capacity shear force of the column based on the maximum probable flexural strengths of the two ends of the column, 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
V_u,z = factored load per unit length of beam or one-way slab, lb/in.
W = wind load
ϕ = strength reduction factor
Ω_o = overstrength factor for the lateral-force-resisting system given in ASCE Table 12.2-1.

Beam required strength is calculated in accordance with the factored load combinations in https://idecad.atlassian.net/wiki/spaces/IKP/pages/1539605249 title. The required shear strength of a beam V_u is obtained from Load Combinations given in ACI Table 5.3.1.

Shear design strength at all sections should satisfy the condition ϕV_n ≥ V_u.

Strength reduction factors ϕ is determined according to using ACI Table 21.2.1. Interaction between load effects is considered.

Nominal one-way shear strength at a column, V_n, is calculated by:

The nominal shear strength V_n is calculated as the sum of the nominal shear strength provided by concrete, V_c, and nominal shear strength provided by shear reinforcement V_s as shown in ACI Eq.(22.5.1.1).

The nominal shear strength V_n for a column is calculated in accordance with https://idecad.atlassian.net/wiki/spaces/IKP/pages/1547764956 title. In addition, V_s and V_c calculations are also described in the same title with details.

At each section of a beam where V_u > ϕV_c, transverse reinforcement is provided such that ACI Eq. (22.5.8.1) should be satisfied.

Vs is calculated using ACI Eq. (22.5.8.5.3) for a beam reinforced with transverse reinforcement.

A_v is the effective area of all bar legs or wires within spacing s, for each rectangular tie, stirrup, hoop, or crosstie. For each circular tie or spiral, A_v is two times the area of the bar or wire within spacing s.

Using equations ACI Eq. (22.5.8.1) and ACI Eq. (22.5.8.5.3), the required area of shear reinforcement, A_v, and its spacing, s can be calculated as follows.

According to ACI 9.6.3.4; If shear reinforcement is required, A_v,_min is equlat to the greater of the following relations;

A minimum area of shear reinforcement, A_v,_min should be provided in all sections where V_u > 0.5ϕV_c.

Strength reduction factors ϕ is determined according to using ACI Table 21.2.1.

Beams of Earthquake Resistant Structures must satisfy (A_v)_min condition.

Shear Design for Columns of Earthquake Resistant Structures

Ordinary moment frames