Concrete Threshold and Cracking Torsion (ACI 318-19 22.7)

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.

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).

ACI 318-19 is viewable through ACI's online public-access reader; the lambda x sqrt(f'c) x (Acp^2/pcp) arithmetic is public.

Estimate. AHJ and licensed professional govern.

Field names used by the API: fc_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