Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 459

spreads from the flange tips into the cross-section, until the flanges become fully
yielded at

M fp = f y b f t f / 4 (10.60)

which corresponds to the fully plastic bimoment

B p = f y d f b f t f / 4 (10.61)

The plastic shape factor for warping torsion of the I-section is therefore given by
B p / B y = 3 / 2.
Expressions for the full plastic bimoments of a number of monosymmetric
thin-walled open sections are given in [18].

10.3.3.2 Plastic analysis of warping torsion

An equal flanged I-section member in warping torsion will collapse plastically
when there is a sufficient number of warping hinges (frictionless or plastic) to
transform the member into a mechanism, as shown for example in Figure 10.29.
Ingeneral,thewarpinghingesdevelopprogressivelyuntilthecollapsemechanism
forms.
A frictionless warping hinge occurs at a point where warping is unrestrained
( φ = 0) so that there is a frictionless hinge in each flange, while at a
plastic warping hinge, the bimoment is equal to the fully plastic value B p
(equation 10.61) and the moment in each flange is equal to the fully plastic value
M fp (equation10.60),sothatthereisaflexuralplastichingeineachflange.Warping
torsionplasticcollapsethereforecorrespondstothesimultaneousplasticcollapse

Bottom
flange

Warping torsion
plastic hinges

Top flange

Frictionless
hinge

End free to
warp

End warping
prevented

(b) Warping torsion collapse mechanism

M fp
M fp

(-)

T

(+)

L

(a) Torsion member and loading

(c) Top flange moment distribution

Figure 10.29 Warping torsion plastic collapse.