Concrete Threshold and Cracking Torsion (ACI 318-19 22.7)
The two torsion thresholds every spandrel and edge beam is checked against.
Example
You enter
- Specified strength f'c (psi) 4000
- Section width b (in) 12
- Section height h (in) 20
- Lightweight factor lambda (1.0 normal) 1
You get
- Threshold torsion Tth 56,921 in-lb (4.74 ft-kip)
- Neglect if Tu below phi x Tth 42690.7
- Cracking torsion Tcr = 4 Tth 227684
Checked against published worked examples from: StructurePoint.
Details, formula, and sources
ScopeTorsion may be neglected when the factored torque is below phi x Tth, where the threshold torsion Tth = lambda x sqrt(f'c) x (Acp^2/pcp) with Acp = b x h the outside area and pcp = 2(b+h) the outside perimeter; the section cracks in torsion at Tcr = 4 x Tth (phi = 0.75). A 12 x 20 in beam on 4,000 psi concrete has Tth = 4.74 ft-kip, so torsion is ignored below 3.56 ft-kip and the section cracks at 18.97 ft-kip; an 18 x 24 in beam raises the threshold to 11.7 ft-kip -- torsion capacity grows fast with section size. Above phi x Tth closed stirrups and longitudinal steel must be designed. A design aid, not a substitute for a licensed engineer's design.
Formula or tableAcp = b x h; pcp = 2(b + h); Tth = lambda x sqrt(f'c) x (Acp^2 / pcp); neglect if Tu < phi x Tth (phi = 0.75); Tcr = 4 x Tth.
Source and editionACI 318-19 (Building Code Requirements for Structural Concrete), by name: §22.7.4.1 (threshold torsion Tth), §22.7.1.1 (the neglect criterion Tu < phi x Tth), §22.7.5 (cracking torsion Tcr = 4 x Tth).
Free accessACI 318-19 is viewable through ACI's online public-access reader; the lambda x sqrt(f'c) x (Acp^2/pcp) arithmetic is public.
What governsEstimate. AHJ and licensed professional govern.
API field namesfc_psi, b_in, h_in, lambda, tth_inlb, neglect_inlb, tcr_inlb
- Threshold torsion Tth = lambda x sqrt(f'c) x (Acp^2/pcp), nominal without phiACI 318-19 §22.7.4.1
- Solid rectangular section Acp = b x h and pcp = 2(b + h) for a solid non-prestressed rectangular section; a hollow or flanged section changes Acp/pcpACI 318-19 §22.7
- Design separate above phi x Tth the closed-stirrup At/s and longitudinal Al torsion reinforcement is a separate design stepACI 318-19 §9.5.4