Shear Wall Combined Flexural and Axial Design per ACI 318-19 with ideCAD

How does ideCAD calculate shear wall combined flexural and axial strength according to ACI 318-19?

Notation

A_g = gross area of concrete section, in²
A_s = area of nonprestressed longitudinal tension reinforcement, in²
A_st = total area of nonprestressed longitudinal reinforcement, in²
α = depth of equivalent rectangular stress block, in.
b_w = width of compression face of member, in.
c = distance from extreme compression fiber to neutral axis, in.
C_c = concrete compressive force, lb
C_s = reinforcement tension force, lb
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
L = live load
L_r = roof live load
M_n = nominal flexural strength at section, in.-lb
M_u = factored moment at section, in.-lb
P_n = nominal axial compressive strength of member, lb
P_n,max = maximum nominal axial compressive strength of a member, lb
P_nt = nominal axial tensile strength of member, lb
P_nt,max = maximum nominal axial tensile strength of member, lb
P_o = nominal axial strength at zero eccentricity, lb
P_u = factored axial force; to be taken as positive for compression and negative for tension, lb
R = rain load
S = snow load
V_n = nominal shear strength, lb
V_u = factored shear force at section, lb
W = wind load
ϕ = strength reduction factor
ε_t = net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
β₁ = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

Required strength

According to ACI 11.4.2.1, walls should be designed for the maximum factored moment M_u combined with P_u for each applicable load combination. The required strength is calculated in accordance with the factored load combinations in Load Factors and Combinations per ACI 318-19 with ideCAD title. Combined Axial and Flexural Required strengths of a shear wall P_u and M_u co-occur for a shear wall. Therefore, for each applicable factor load combination specified in ACI Table 5.3.1, the most unfavorable P_u and M_u co-occurring condition is considered.

Designed strength

P_n and M_n are calculated in accordance with Axial strength or Combined Flexural and Axial Strength per ACI 318-19 with ideCAD title. Combined Axial and Flexural strengths create a three-dimensional interaction failure surface. In addition to axial compression and biaxial bending, the formulation allows for axial tension and biaxial bending considerations. An interaction surface of a shear wall is shown below.

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P_n means nominal axial compressive strength, and M_n means nominal flexural strength. M_n takes a different value for each axial force level. Therefore, a three-dimensional interaction failure surface is formed in the picture above. Nominal flexural strength M_n is calculated according to the assumptions described in Flexural Strength per ACI 318-19 with ideCAD title. Flexural design strength ϕM_n is obtained by calculating M_n and strength reduction factor ϕ at each axial force level. While finding the flexural design strength, combined with axial force ϕM_n, should be found in which control zone the cross-section is. When the section is tension controlled, a ϕ factor for tension control is used. When the section is compression controlled, a ϕ factor for compression control is used.

As described in the title of Axial strength or Combined Flexural and Axial Strength per ACI 318-19 with ideCAD, for nonprestressed concrete members nominal axial strength P_o and the maximum design compressive strength ϕP_n,max values are calculated as given below;

Strength reduction factor ϕ shown in section (a) of Table 21.2.1, for moment, axial force, or combined moment and axial force, are given in ACI Table 21.2.2.

Nominal flexural strength M_n with zero compression is calculated as described in the title of Flexural Strength per ACI 318-19 with ideCAD. Similarly, combined nominal flexural and axial strength M_n and P_n are calculated with the same design assumptions.

Demand/Capacity Ratio of Shear Walls

Because of the axial force and biaxial bending interaction in shear walls, the demand/capacity ratio is calculated using the interaction curve. The point (P_u, M_u) is placed in the interaction space shown as point D in the picture below. If point D (P_u, M_u) is within the acceptable range, the column's capacity is adequate. However, the shear wall is overstressed if point D (Pu, Mu) is outside the interaction volume. The capacity ratio is calculated using point C obtained by extending the line passing through points O and D to the interaction curve. The capacity ratio is given by the ratio OD/OC.

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Earthquake Resistant Structures

Special structural walls

According to ACI 18.10.5.1, structural walls subject to combined flexure and axial loads should be designed in accordance with ACI 22.4, also described in Axial strength or Combined Flexural and Axial Strength per ACI 318-19 with ideCAD title.