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 (τ_{sv}), warping shear stress (τ_{w}), and warping
longitudinal stress (σ_{w}).

τ_{sv} = T_{sv}t/J = –Gtϕ' for open sections

τ_{sv} = T_{sv}/2A_{m}t = –2Gϕ'A_{m}/S_{m} for closed sections

τ_{w} = T_{w}S_{w}/C_{w}t = ES_{w}ϕ'''/t

σ_{w} = BW_{n}/C_{w} = EW_{n}ϕ''

See also Torsion Properties.

The AISI Specification 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.

The available bimoment strength shown on the member check report is the magnitude of B at
which the maximum longitudinal warping stress is equal to the yield stress (F_{y}), with
the appropriate safety or resistance factor applied. If the section contains more than one part,
the nominal bimoment strength (B_{n}) is approximated as the sum of the individual
part bimoment strengths, and the maximum warping stress is calculated as F_{y}B/B_{n}.
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 C_{w}, 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.