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İnternational Design Codes
ACI 318-19 : One-Way Shear Strength
TSC 2018 : TSC One-Way Shear Strength
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Notation in ACI 318-19
Ac-sh = area of concrete used to determine shear stress, in2
Ag = gross area of concrete section, in2
bw = web width or diameter of circular section, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
fc ' = specified compressive strength of concrete, psi
(fc')0.5 = square root of specified compressive strength of concrete, psi
fyt = specified yield strength of transverse reinforcement, psi
h = overall thickness, height, or depth of member, in.
Nu = factored axial force normal to cross section occurring simultaneously with Vu or Tu; to be taken as positive for compression and negative for tension, lb
s = center-to-center spacing transverse reinforcement, in
Vc = nominal shear strength provided by concrete, lb
Vn = nominal shear strength, lb
Vs = nominal shear strength provided by shear reinforcement, lb
Vu = 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 normal weight concrete of the same compressive strength
λs = factor used to modify shear strength based on the effects of member depth, commonly reffered to as the size effect factor
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Nominal one-way shear strength at a section, Vn, is calculated by :
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The shear strength is based on an average shear stress over the effective cross section, bwd. Therefore dimensions of the cross-section should be satisfy ACI Eq. (22.5.1.2).
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For calculation of Vc, Vs 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 bwd is equal to the shear area Ac-sh for rectangular sections. However, in solid, circular sections, the the shear area Ac-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, bw (d = 0.8bw).
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The maximum value of the (fc')0.5 [or 
] used to calculate Vc, Vs or ACI Eq. (22.5.1.2) is 100 psi. For calculation of Vc, Vs or ACI Eq. (22.5.1.2), it is assumed that the unit of (fc')0.5 [or ] is psi. If these values are to be calculated in SI-metric or mks-metric units, the (fc')0.5 [or ] value is changed accordingly. Strength reduction factor ϕ for shear, is determined as described in the Strength Reduction Factors title.
Vc for Nonprestressed Members
For nonprestressed concrete reinforcement members, Vc 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 to 1 for normalweight concrete. Nu is positive for compression and negative for tension.
The maximum value of Vc ;
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The maximum value of Nu/6Ag ;
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The size effect modification factor, λs
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One-way shear reinforcement
At each section where Vu > ϕVc, transverse reinforcement is provided such that ACI Eq. (22.5.8.1) should be satisfied.
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For members reinforced with transverse reinforcement, Vs is calculated using ACI Eq. (22.5.8.5.3).
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Av 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, Av 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, Av and its spacing, s can be calculated as follows.
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The values of fy and fyt used to calculate Vs 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
Beam Shear Design
Joint Shear Strength
Shear Wall Shear Design
For calculation of Vc, Vs or ACI Eq. (22.5.1.2), it is assumed that the unit of (fc')0.5 [or ] is psi. If these values are to be calculated in SI-metric or mks-metric units, the (fc')0.5 [or ] value is changed accordinglyusing concrete and transverse reinforcement properties.
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