Torsional strength is calculated automatically
Ao = gross area enclosed by torsional shear flow path, in.2
Aoh = area enclosed by centerline of the outermost closed transverse torsional reinforcement, in.2
Acp = area enclosed by outside perimeter of concrete cross section, in.2
Ag = gross area of concrete section, in2
Al = total area of longitudinal reinforcement to resist torsion, in.2
Al,min = minimum area of longitudinal reinforcement to resist torsion, in.2
At = area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.2
bw = web width or diameter of circular section, in.
fc' = specified compressive strength of concrete, psi
(fc')0.5 = square root of specified compressive strength of concrete, psi
fpc = 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.
fyt = specified yield strength of transverse reinforcement, psi
Nu = factored axial force normal to cross section occurring simultaneously with Vu or Tu; to be taken as positive for compression and negative for tension, lb
pcp = outside perimeter of concrete cross section, in.
ph = perimeter of centerline of outermost closed transverse torsional reinforcement, in.
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.
Tcr = cracking torsional moment, in.-lb
Tth = threshold torsional moment, in.-lb
Tn = nominal torsional moment strength, in.-lb
Tu = factored torsional moment at section, in.-lb
Vu = factored shear force at section, lb
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 Tu value with the threshold torsion Tth and cracking torsion Tcr values.
Torsional effects can be neglected if the factored torsional moment at section Tu is less than threshold torsion multiplied by strenght reduction factor ϕTth (Tu<ϕTth). Torsional moments that do not exceed the threshold torsion Tth will not cause a structurally significant reduction in either flexural or shear strength and can be ignored.
If Tu ≥ ϕTcr 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 Tu.
If ϕTcr > Tu ≥ ϕTth, only minimum tension rebar needs to be provided ACI 9.6.4.
Threshold torsion Tth is calculated in accordance with ACI Table 22.214.171.124(a) and 126.96.36.199(b). Factored axial force Nu is positive for compression and negative for tension. The modification factor λ, given for concrete class specified in ACI Table 188.8.131.52 and equals to 1 for normalweight concrete.
Cracking torsion Tcr is calculated in accordance with ACI Table 184.108.40.206. Factored axial force Nu is positive for compression and negative for tension. The modification factor λ, given for concrete class specified in ACI Table 220.127.116.11 and equals to 1 for normalweight concrete.
The maximum value of the (fc')0.5 [or :fcuss:] used to calculate Tcr and Tth is 100 psi.
For nonprestressed reinforced concrete members, nominal torsional moment strength Tn is the minimum value of given equations below.
Ao is determined by using analysis results, θ is between 30 degrees and 60 degrees; At is the area of one leg of a closed stirrup resisting torsion; Al is the longitudinal torsional reinforcement area; and ph is the perimeter of the centerline of the outermost closed stirrup.
If Tu < ϕTth torsional effects is ignored.
If ϕTcr > Tu ≥ ϕTth, only minimum torsional reinforcement needs to be provided given below;
Minimum transverse reinforcement (Av + 2At)min / s
minimum area of longitudinal reinforcement Al,min
If Tu > ϕTcr total area of longitudinal reinforcement to resist torsion Al is calculated bu using nominal torsional moment strength Tn. In addition, minimum reinforcement requirements are checked.
There is an upper limit of the combination of Vu and Tu. Cross-sectional dimensions should be satisfied the ACI Eq. (18.104.22.168a);
Special Section Properties for Torsional Strength
Acp = bwh
Aoh = (bw − 2c)(h − 2c)
Ao = 0.85 Aoh
pcp = 2bw + 2h
ph = 2(bw − 2c) + 2(h − 2c)
For calculation of Torsional strength it is assumed that the unit of (fc')0.5 [or :fcuss:] is psi. If these values are to be calculated in SI-metric or mks-metric units, the (fc')0.5 [or :fcuss:] value is changed accordingly.