Torsion applied to a member produces internal stresses which may contribute to certain failure modes. The stresses are identified as pure (St. Venant) torsion shear stress (τsv), warping shear stress (τw), and warping longitudinal stress (σw).
τsv = Tsvt/J = –Gtϕ' for open sections
τsv = Tsv/2Amt = –2Gϕ'Am/Sm for closed sections
τw = TwSw/Cwt = ESwϕ'''/t
σw = Bωn/Cw = Eωnϕ''
See also Torsion Properties.
The AISI Specification (2022 and later) calculates the nominal bimoment strength (Bn) as the first yield bimoment (By). In S100-24, the bimoment strength may alternatively be determined using DSM based on the Bcr values for buckling of the web or flange. This often gives a higher bimoment strength. For earlier editions, CFS determines the nominal bimoment strength as By.
The AISI Specification (2020 and earlier) has design provisions for combined bending and torsion, where longitudinal stresses from torsion may reduce the flexural strength of the member. If a member check includes a torsional bimoment (B), a moment reduction is calculated using the ratio of the maximum bending stress to the maximum combined bending and warping stress.
If the section contains more than one part, the nominal bimoment strength (Bn) is approximated as the sum of the individual part bimoment strengths, and the maximum warping stress is calculated as FyB/Bn. This is conservative because: 1) the bimoment strength should be greater than the sum of the parts, 2) the maximum stresses for warping and bending may not occur at the same location with the same sign, and 3) no strength increase is considered based on the controlling location (i.e., flange/web junction).
If the section has an override value for Cw, CFS has no information about the expected warping behavior of the section and is not able to calculate the bimoment strength. Therefore CFS cannot check combined bending and torsion for that case.
See also Torsion Analysis and Torsion Diagrams.