Concrete Threshold and Cracking Torsion (ACI 318-19 22.7)
The two torsion thresholds every spandrel and edge beam is checked against: torsion 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 and source
Acp = 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.
ACI 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).
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