One-Way Shear Strength per ACI 318-19 with ideCAD

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

Notation

A_c-sh = area of concrete used to determine shear stress, in²
A_g = gross area of concrete section, in²
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^')^0.5 = square root of specified compressive strength of concrete, psi
f_yt = specified yield strength of transverse reinforcement, psi
h = overall thickness, height, or depth of member, in.
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
s = center-to-center spacing transverse reinforcement, in
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 normal-weight concrete of the same compressive strength
λ_s = factor used to modify shear strength based on the effects of member depth, commonly referred to as the size effect factor

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

The shear strength is based on an average shear stress over the effective cross-section, b_wd. Therefore dimensions of the cross-section should be satisfy ACI Eq. (22.5.1.2).

For calculation of V_c, V_s, or ACI Eq. (22.5.1.2), d is taken as the distance from extreme compression fiber to centroid of longitudinal tension reinforcement. In ACI Eq. (22.5.1.2) the product of b_wd is equal to the shear area A_c-sh for rectangular sections. However, in solid, circular sections, the shear area A_c-sh should be found as shown in the picture below. According to ACI 22.5.2.2, d is allowed to be taken as 0.8 times the diameter, b_w (d = 0.8b_w).

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The maximum value of the (f_c^')^0.5 [or ] used to calculate V_c, V_s or ACI Eq. (22.5.1.2) is 100 psi. For calculation of V_c, V_s, or ACI Eq. (22.5.1.2), it is assumed that the unit of (f_c^')^0.5 [or ] is psi. If these values are to be calculated in SI-metric or mks-metric units, the (f_c^')^0.5 [or ] value is changed accordingly. The strength reduction factor ϕ for shear is determined as described in the Strength Reduction Factors per ACI 318-19 with ideCAD title.

V_c for Nonprestressed Members

For nonprestressed concrete reinforcement members, V_c is calculated using ACI Table 22.5.5.1.

The modification factor λ, given for concrete class specified in ACI 19.2.4.3, and equals 1 for normal-weight concrete. N_u is positive for compression and negative for tension.

The maximum value of V_c ;

The maximum value of N_u/6A_g ;

The size effect modification factor, λ_s

One-way shear reinforcement

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

For members reinforced with transverse reinforcement, V_s is calculated using ACI Eq. (22.5.8.5.3).

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.

The values of f_y and f_yt used to calculate V_s shall not exceed the limits in ACI Table 22.2.2.4(a).

Shear strength provided by bent-up longitudinal reinforcement is neglected.

In earthquake-resistant structures, there are additional requirements for shear design strength. These requirements are described in the headings below.

Column Shear Design per ACI 318-19 with ideCAD
Beam Shear Design per ACI 318-19 with ideCAD
Joint Shear Strength per ACI 318-19 with ideCAD
Shear Wall Shear Design per ACI 318-19 with ideCAD

For calculation of V_c, V_s or ACI Eq. (22.5.1.2), it is assumed that the unit of (f_c^')^0.5 [or ] is psi. If these values are to be calculated in SI-metric or mks-metric units, the (f_c^')^0.5 [or ] value is changed accordingly.