# One-Way Shear Strength

One-way shear strength 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 normalweight concrete of the same compressive strength*

**λ***= factor used to modify shear strength based on the effects of member depth, commonly reffered 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 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. Strength reduction factor*

**f**_{c}^{'})^{0.5}**ϕ**for shear, is determined as described in the Strength Reduction Factors 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 to 1 for normalweight 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

Beam Shear Design

Joint Shear Strength

Shear Wall Shear Design

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}**Next Topic**