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

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

One-way shear strength is calculated automatically.

Shear strength provided by concrete is calculated automatically.

Transverse reinforcement is calculated automatically.

**Notation**

* A_{c-sh }= *area of concrete used to determine shear stress, in

^{2}

*gross area of concrete section, in*

**A**_{g }=^{2}

*web width or diameter of circular section, in.*

**b**_{w }=*distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.*

**d =***specified compressive strength of concrete, psi*

**f**_{c }^{'}_{ }_{ }=**(**

*square root of specified compressive strength of concrete, psi*

**f**_{c}^{'})^{0.5 }_{ }=*specified yield strength of transverse reinforcement, psi*

**f**_{yt }_{ }=*overall thickness, height, or depth of member, in.*

**h =***factored axial force normal to cross-section occurring simultaneously with*

**N**_{u }=*or*

**V**_{u}*; to be taken as positive for compression and negative for tension, lb*

**T**_{u}*center-to-center spacing transverse reinforcement, in*

**s =***nominal shear strength provided by concrete, lb*

**V**_{c }=*nominal shear strength, lb*

**V**_{n }=*nominal shear strength provided by shear reinforcement, lb*

**V**_{s }=*factored shear force at section, lb*

**V**_{u }=*strength reduction factor*

**ϕ =***= modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal-weight concrete of the same compressive strength*

**λ***= factor used to modify shear strength based on the effects of member depth, commonly referred to as the size effect factor*

**λ**_{s}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_{w}d*. Therefore dimensions of the cross-section should be satisfy

**ACI Eq. (22.5.1.2)**.

For calculation of * V_{c}*,

*or*

**V**_{s,}**ACI Eq. (22.5.1.2)**,

*is taken as the distance from extreme compression fiber to centroid of longitudinal tension reinforcement. In*

**d****ACI Eq. (22.5.1.2)**the product of

*is equal to the shear area*

**b**_{w}d*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*

**A**_{c-sh}**ACI 22.5.2.2**,

*is allowed to be taken as 0.8 times the diameter,*

**d***(*

**b**_{w}*= 0.8*

**d***).*

**b**_{w}The maximum value of the **(*** f_{c}^{'})^{0.5}* [or :fcuss:] used to calculate

*,*

**V**_{c}*or*

**V**_{s}**ACI Eq. (22.5.1.2)**is 100 psi. For calculation of

*,*

**V**_{c}*or*

**V**_{s,}**ACI Eq. (22.5.1.2)**, it is assumed that the unit of

**(**

*[or :fcuss:] is psi. If these values are to be calculated in SI-metric or mks-metric units, the*

**f**_{c}^{'})^{0.5}**(**

*[or :fcuss:] value is changed accordingly. The strength reduction factor*

**f**_{c}^{'})^{0.5}**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.

*is positive for compression and negative for tension.*

**N**_{u }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

*, for each rectangular tie, stirrup, hoop, or crosstie. For each circular tie or spiral,*

**s***is two times the area of the bar or wire within spacing*

**A**_{v}*.*

**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,

*can be calculated as follows.*

**s**

The values of * f_{y}* and

*used to calculate*

**f**_{yt}*shall not exceed the limits in*

**V**_{s}**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}*,

*or*

**V**_{s}**ACI Eq. (22.5.1.2)**, it is assumed that the unit of

**(**

*[or :fcuss:] is psi. If these values are to be calculated in SI-metric or mks-metric units, the*

**f**_{c}^{'})^{0.5}**(**

*[or :fcuss:] value is changed accordingly.*

**f**_{c}^{'})^{0.5}