# Two-Way Shear Strength

Two-Way shear strength of two-way members is calculated automatically

**Notation**

* A_{v }= *area of shear reinforcement within spacing s, in.

^{2}

*perimeter of critical section for two-way shear in slabs and footings, in.*

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

**d =***nominal diameter of bar, wire, or prestressing strand, in.*

**d**_{b}=*specified compressive strength of concrete, psi*

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

**√f**_{c}‘*square root of specified compressive strength of concrete, psi*

^{ }_{ }=*specified yield strength of transverse reinforcement, psi*

**f**_{yt }_{ }=*stress corresponding to nominal two-way shear strength provided by concrete, psi*

**v**_{c }=*equivalent concrete stress corresponding to nominal two-way shear strength of slab or footing, psi*

**v**_{n }=*equivalent concrete stress corresponding to nominal two-way shear strength provided by reinforcement, psi*

**v**_{s }=*maximum factored two-way shear stress calculated around the perimeter of a given critical section, psi*

**v**_{u }=*= constant used to calculate*

**α**_{s}*V*in slabs and footings

_{c}*ratio of long to short dimensions; clear spans for two-way slabs, sides of column, concentrated load or reaction area; or sides of a footing*

**β =***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 shear strength of the two-way members withour shear reinforcement should be calculated by using **ACI Eq.(22.6.1.2),**

Nominal shear strength of the two-way members with shear reinforcement should be calculated by using **ACI Eq.(22.6.1.3),**

According to **ACI 22.6.1.4, **two-way shear strength should be calculated using a section with depth and critical perimeter * b_{o}*, (defined in

**ACI 22.6.4**).

According to **ACI 22.6.2.1, **for calculation of * v_{c}* and

*for two-way shear,*

**v**_{s}*should be the average of the effective depths in the orhogonal directions.*

**d**According to **ACI 22.6.3.1, **the maximum value of * √f_{c}‘* is 100 psi.

**Critical Sections for Two-way Members**

According to **ACI 22.6.4.1, **for two-way shear, critical sections should be located so that perimeter * b_{o}* is a minimum but need not be closer than

*to given two cases given below;*

**d/2**Edges or corners of columns, concentrated loads, or reaction areas

Changes in slab or footing thickness, such as edges of capitals, drop panels, or shear caps

According to **ACI 22.6.4.1.1, **concerntrated loads, or reaction areas, critical sections for two-way shear in accordance with **ACI 22.6.4.1 (**case 1 and case2**) **can be defined assuming straight sides for square or rectengular columns.

According to **ACI 22.6.4.1.2,** critical sections for two-way shear in accordance with **ACI 22.6.4.1 (**case 1 and case2**) **can be defined assuming a square column of equivalent area for a circular or regular polygon-shaped column.

According to **ACI 22.6.4.2,** for two-way members with single (or multi) leg stirrup or headed stud shear reinforcement, one more critical section with perimeter * b_{o}* located

*beyond the point where shear reinforcement is dicontinued. The shape of this critical section should be a polygon selected to minimize*

**d/2***.*

**b**_{o}Value of * b_{o}* is shown in

**ACI Fig. R22.6.4.2a, b**and

**c.**

According to **ACI 22.6.4.3,** If there is an opening located closer than * 4h* from the periphery of a column, concentrated load, or reaction area, the portion of

*enclosed by straight lines projecting from the centroid of the column, concentrated load or reaction area and tangent to the boundaries of the opening should be considered ineffective.*

**b**_{o}**Two-way Shear Strength Provided by Concrete in Members Without Shear Reinforcement**

According to **ACI 22.6.5.2,** For nonprestressed two-way members, * v_{c}* shall be calculated in accordance with

**ACI Table 22.6.5.2.**

According to **ACI 22.6.5.3, ****α _{s}**

**value is**

40 for interior columns

30 for egde columns

20 for corner colums

**Two-way Shear Strength Provided by Concrete in Members With Shear Reinforcement**

According to **ACI 22.6.6.1,** for nonprestressed two-way members with shear reinforcement, * v_{c}* at critical sections should be calculated in accordance with

**ACI Table 22.6.6.1.**

The size effect modification factor, **λ _{s}**

According to **ACI 22.6.6.2, **the value of * λ_{s}* can be taken as 1.0 if two conditions below are satisfied;

Stirrups are designed and detailed in accordance with

**ACI 8.7.6**and**A**_{v}/s ≥ 2√f_{c}‘b_{o}/f_{yt}Smooth headed shear stud reinforcement with stud shaft length not exceeding 10 in. is designed and detailed in accordance with

**ACI 8.7.7**and**A**_{v}/s ≥ 2√f_{c}‘b_{o}/f_{yt}

For shapes other than rectangular, * β* is taken to be the ratio of the longest dimension of the effective loaded area to the largest overall perpendicular dimension of the effective loaded area, as illustrated for an L-shaped reaction area in

**ACI Fig. R22.6.5.2**

According to **ACI 22.6.6.3, **for two-way members with shear reinforcement, maximum effective depth should be selected such that * v_{u}* calculated at critical sections is given in

**ACI Table 22.6.6.3**

**Two-way Shear Strength Provided by Single (or multiple) Leg Stirrups**

According to **ACI 22.6.7.1, **Single (or multiple) leg stirrups fabricated from bars or wires can be used as shear reinforcement in slabs and footings satisfying given two conditions below;

**d ≥ 6**inches,where**d ≥ 16d**_{b}is the diameter of the stirrups**d**_{b}

According to **ACI 22.6.7.2, **for nonprestressed two-way members with single (or multiple) leg stirrups, * v_{c}* should be calculated in accordance with

**ACI Eq. 22.6.7.2.**

* A_{v}* is the sum of the area of all legs of reinforcement on one peripheral line that is geometrically similar to the perimeter of the column section, and

*is the spacing of the peripheral lines of shear reinforcement in the direction perpendicular to the column face.*

**s****Two-way Shear Strength Provided by Headed Shear Stud Reinforcement**

According to **ACI 22.6.8.1, **Headed shear stud reinforcement scan be used as shear reinforcement in slabs and footings if the placement and geometry of the headed shear stud reinforcement satisfies **ACI 8.7.7**.

According to **ACI 22.6.8.2, **for nonprestressed two-way members with headed shear stud reinforcement, * v_{c}* should be calculated in accordance with

**ACI Eq. 22.6.8.2.**

* A_{v}* is the sum of the area of all shear studs on one peripheral line that is geometrically similar to the perimeter of the column section, and

*is the spacing of the peripheral lines of headed shear stud reinforcement in the direction perpendicular to the column face.*

**s**According to **ACI 22.6.8.3, **If headed shear stud reinforcement is provided, * A_{v}/s* should satisfy

**ACI Eq. 22.6.8.3.**

**Next Topic**