Shear Wall Shear Design per ACI 318-19 with ideCAD

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

Notation

A_cv = gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered in the case of walls, and gross area of concrete section in the case of diaphrams. Gross area is total area of defined section minus area of any openings, in.²
A_cw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear, in².
b_w = width of compression face of member, in.
D = dead load
E = earthquake load
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.
h_w = height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.
h_wcs = height of entire structural wall above the critical section for flexural and axial loads, in.
l_n = length of clear span measured face-to-face of supports, in.
l_u = unsupported length of wall, in.
l_w = length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.
L = live load
L_r = roof live load
M_u = factored moment 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
n_s = number of stories above the critical section
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
N_u = factored axial force normal to cross section occurring simultaneously with V_u or T_u; to be taken as positive for compression and negative for tension, lb
positive for compression and negative lb
V_e = design shear force for load combinations including earthquake effects, 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
w_u = factored load per unit length of beam or one-way slab, lb/in.
W = wind load
α_c = coefficient defining the relative contribution of concrete strength to nominal wall shear strength
ϕ = strength reduction factor
Ω_v = overstrength factor equal to the ratio of M_pr/M_u at the wall critical section
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength
ω_v = factor to account for dynamic shear amplification
ρ_l = ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement
ρ_t = ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement

Wall required strength is calculated in accordance with the factored load combinations in Load Factors and Combinations per ACI 318-19 with ideCAD title. The required shear strength of a wall V_u , is obtained from Load Combinations given in ACI Table 5.3.1.

The shear wall is designed leg by leg for each of the design load combinations given above.

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

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

According to ACI 11.5.4.3, nominal shear strength V_n is calculated by ACI Eq. (11.5.4.3) given below;

• α_c = 3 for h_w/l_w ≤ 1.5

• α_c = 2 for h_w/l_w ≥ 2.0

• α_c is calculated by linear interpolation between 3 and 2 for 1.5 < h_w/l_w < 2.0.

• For walls subjected to a net axial tension, α_c is calculated according to ACI Eq. (11.5.4.3);

According to ACI 11.5.4.2, the maximum in-plane shear strength of the shear wall or shear wall leg is given below;

Earthquake Resistant Structures

Special structural walls

Concrete Shear Wall Design per ACI 318-19 §11, §18.10 title also contains requirements for the dimensions and details of special structural walls and all components. Design provisions for special structural walls depend on the ratio of the wall dimensions, such as (h_w/l_w) and (l_w/b_w).

Design shear forces for structural shear walls are obtained from lateral load analysis with suitable load factors increased to account for two approaches given below.

• flexural overstrength at critical sections where yielding of critical sections is expected,

• dynamic amplification due to higher mode effects,

According to ACI 18.10.3.1, the design shear force V_e should be calculated by ACI Eq. (18.10.3.1);

The required shear strength of a wall V_u is obtained from lateral load analysis with factored load combinations given in ACI Table 5.3.1.

The overstrength factor, Ω_v, is calculated in accordance with ACI Table 18.10.3.1.2 given below.

M_pr given in ACI Table 18.10.3.1.2 is calculated by using a strength reduction factor, ϕ of 1.0 and longitudinal reinforcement with an effective yield stress equal to 1.25f_y.

According to ACI 18.10.3.1.3, if h_wcs/l_w < 2.0, ωv should be taken as 1.0 for shear walls. Otherwise, ω_v should be calculated by ACI Eq. (18.10.3.1.3);

n_s is the number of stories above the critical section, and the minimum value of n_s is 0.007*h_wcs.

According to ACI 18.10.4.1, shear strength, V_n, should be calculated by ACI Eq. (18.10.4.1) given below.

• α_c = 3 for h_w/l_w ≤ 1.5

• α_c = 2 for h_w/l_w ≥ 2.0

• α_c is calculated by linear interpolation between 3 and 2 for 1.5 < h_w/l_w < 2.0.

λ=1 for normalweight concrete.

According to ACI 18.10.4.3, shear walls should have distributed shear reinforcement in two orthogonal directions in the plane of the wall. If h_w/l_w ≤ 2.0, the reinforcement ratio ρ_l should be at least the reinforcement ratio ρ_t.

According to ACI 18.10.4.4, for all vertical wall segments that resist lateral loads, the maximum value of V_n should be 8√f_c‘A_cv. For any one of the individual vertical wall segments, the maximum value of V_n should be 10√f_c‘A_cw.

According to ACI 18.10.4.5, For horizontal wall segments and coupling beams, the maximum value of V_n should be 10√f_c‘A_cw.