ACI 318-19

ACI 318-19 Section 22.7 | Torsional Strength & Threshold Torsion

Torsion twists a beam around its longitudinal axis. ACI 318-19 models torsional response using a thin-walled tube space truss where diagonal concrete compression struts spiral around the member, equilibrated by transverse closed stirrups and longitudinal bars distributed around the perimeter.

Code Equation

Governing Formula

T_{\text{ th }} = \phi \lambda \sqrt{f'_c} \left( \frac{A_{cp}^2}{p_{cp}} \right), \quad T_n = \frac{2 A_o A_t f_{yt}}{s} \cot \theta

Standard: ACI 318-19Dual US Customary & SI Metric

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Notation & Variables

T_{\text{ th }}

Threshold torsion below which torsional effects may be neglected

kip-in or kN·m

T_n

Nominal torsional strength resisted by transverse closed stirrups and longitudinal steel

kip-in or kN·m

A_{cp}

Area enclosed by outside perimeter of concrete cross section

in² or mm²

p_{cp}

Outside perimeter of concrete cross section

in or mm

A_o

Gross area enclosed by shear flow path (0.85 * Aoh)

in² or mm²

A_t

Area of one leg of a closed stirrup resisting torsion within spacing s

in² or mm²

Worked Example

Compute cross-section geometric properties

For an 18 in x 24 in spandrel beam: Acp = 18 * 24 = 432 sq in, pcp = 2(18 + 24) = 84 in.

Calculate threshold torsion Tth

With f'c = 4000 psi: Tth = 0.75 * 1.0 * sqrt(4000) * (432^2 / 84) = 105.4 kip-in (8.78 kip-ft).

Check design necessity

If factored Tu > phi * Tth, design closed stirrups and longitudinal reinforcement per Section 22.7.4.

Governing Criteria

When does this govern?

Governs perimeter spandrel beams supporting exterior precast panels and cantilevered canopy beams.

Common Pitfall

Common Mistake

Using standard open U-stirrups for torsion. Torsion requires 100% closed stirrups with 135-degree seismic hooks into the core!

Related Resources

Notation & Variables

T_{\text{ th }}

Threshold torsion below which torsional effects may be neglected

kip-in or kN·m

T_n

Nominal torsional strength resisted by transverse closed stirrups and longitudinal steel

kip-in or kN·m

A_{cp}

Area enclosed by outside perimeter of concrete cross section

in² or mm²

p_{cp}

Outside perimeter of concrete cross section

in or mm

A_o

Gross area enclosed by shear flow path (0.85 * Aoh)

in² or mm²

A_t

Area of one leg of a closed stirrup resisting torsion within spacing s

in² or mm²

Worked Example

Compute cross-section geometric properties

For an 18 in x 24 in spandrel beam: Acp = 18 * 24 = 432 sq in, pcp = 2(18 + 24) = 84 in.

Calculate threshold torsion Tth

With f'c = 4000 psi: Tth = 0.75 * 1.0 * sqrt(4000) * (432^2 / 84) = 105.4 kip-in (8.78 kip-ft).

Check design necessity

If factored Tu > phi * Tth, design closed stirrups and longitudinal reinforcement per Section 22.7.4.