# Torsional Strength (v12)

Torsional strength is calculated automatically

**Notation**

* A_{o }= *gross area enclosed by torsional shear flow path, in.

^{2}

*area enclosed by centerline of the outermost closed transverse torsional reinforcement, in.*

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

*area enclosed by outside perimeter of concrete cross section, in.*

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

*gross area of concrete section, in*

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

*total area of longitudinal reinforcement to resist torsion, in.*

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

*minimum area of longitudinal reinforcement to resist torsion, in.*

**A**_{l,min }=^{2}

*area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.*

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

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

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

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

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

**f**_{c}^{'})^{0.5 }_{ }=*compressive stress in concrete, after allowance for all prestress losses, at centroid of cross section resisting externally applied loads or at junction of web and flange where the centroid lies within the flange, psi.*

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

**f**_{yt }_{ }=*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}*outside perimeter of concrete cross section, in.*

**p**_{cp }_{ }=*perimeter of centerline of outermost closed transverse torsional reinforcement, in.*

**p**_{h }_{ }=*center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.*

**s =***cracking torsional moment, in.-lb*

**T**_{cr }_{ }=*threshold torsional moment, in.-lb*

**T**_{th }_{ }=*nominal torsional moment strength, in.-lb*

**T**_{n }_{ }=*factored torsional moment at section, in.-lb*

**T**_{u }_{ }=*factored shear force at section, lb*

**V**_{u }_{ }=**ϕ**

*strength reduction factor*

**=****λ**= modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength

Torsional design is made with the reinforcement requirement determined by comparing the factored torsional moment * T_{u}* value with the threshold torsion

*and cracking torsion*

**T**_{th}*values.*

**T**_{cr}Torsional effects can be neglected if the factored torsional moment at section

is less than threshold torsion multiplied by strenght reduction factor**T**_{u}Torsional moments that do not exceed the threshold torsion**ϕT**_{th}(T_{u}<ϕT_{th}).will not cause a structurally significant reduction in either flexural or shear strength and can be ignored.**T**_{th}If

**T**_{u}**≥**it is assumed that the torsional resistance is provided by closed stirrups, longitudinal bars, and compression diagonals. Therefore, the reinforced concrete member is designed to resist**ϕT**_{cr}.**T**_{u}If

**ϕT**_{cr}**>****T**_{u}**≥**, only minimum tension rebar needs to be provided**ϕT**_{th}**ACI 9.6.4**.

**Threshold Torsion**

Threshold torsion * T_{th}* is calculated in accordance with

**ACI**

**Table 22.7.4.1(a)**and

**22.7.4.1(b)**. Factored axial force

*is positive for compression and negative for tension. The modification factor*

**N**_{u}**λ**, given for concrete class specified in

**ACI Table 19.2.4.2**and equals to 1 for normalweight concrete.

**Cracking Torsion**

Cracking torsion * T_{cr}* is calculated in accordance with

**ACI**

**Table 22.7.5.1.**Factored axial force

*is positive for compression and negative for tension. The modification factor*

**N**_{u}**λ**, given for concrete class specified in

**ACI Table 19.2.4.2**and equals to 1 for normalweight concrete.

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

*and*

**T**_{cr}*is 100 psi.*

**T**_{th}**Torsional strength**

For nonprestressed reinforced concrete members, nominal torsional moment strength * T_{n}* is the minimum value of given equations below.

* A_{o}* is determined by using analysis results, θ is between 30 degrees and 60 degrees;

*is the area of one leg of a closed stirrup resisting torsion;*

**A**_{t}*is the longitudinal torsional reinforcement area; and*

**A**_{l}*is the perimeter of the centerline of the outermost closed stirrup.*

**p**_{h}If

torsional effects is ignored.**T**_{u }< ϕT_{th}If

**ϕT**_{cr}**>****T**_{u}**≥**, only minimum torsional reinforcement needs to be provided given below;**ϕT**_{th}

Minimum transverse reinforcement **(A _{v} + 2A_{t})_{min} / s**

minimum area of longitudinal reinforcement **A _{l,min}**

If

**T**_{u}**>**total area of longitudinal reinforcement to resist torsion**ϕT**_{cr}is calculated bu using nominal torsional moment strength**A**_{l}. In addition, minimum reinforcement requirements are checked.**T**_{n}

There is an upper limit of the combination of * V_{u}* and

*. Cross-sectional dimensions should be satisfied the*

**T**_{u}**ACI Eq. (22.7.7.1a)**;

**Special Section Properties for Torsional Strength**

* A_{cp}* =

**b**_{w}h* A_{oh}* =

**(b**_{w}− 2c)(h − 2c)* A_{o}* =

**0.85**

**A**_{oh}**p _{cp} = 2b_{w} + 2h**

**p _{h} = 2(b_{w} − 2c) + 2(h − 2c)**

For calculation of Torsional strength it is assumed that the unit of **(*** f_{c}^{'})^{0.5}* [or :fcuss:] is psi. If these values are to be calculated in SI-metric or mks-metric units, the

**(**

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

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