Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 470

influence on the torsional behaviour. Significant distortions occur only in very
thin-walledmembers, forwhichthedistortionalrigidity, whichvariesasthecube
ofthewallthickness,reducesatamuchfasterratethanthewarpingrigidity,which
varies directly with the thickness [27]. These distortions may induce significant
wallbendingstresses,andmayincreasetheanglesoftwistandchangethewarping
stress distributions [28, 29].
Thin-walled closed-section members are very stiff torsionally, and the twisting
deformationsduetouniformtorsionarenotusuallyofgreatimportanceexceptin
curvedmembers.Ontheotherhand,rectangularandtrapezoidalmembersarenot
veryresistanttodistortionalloads,andthedistortionaldeformationsmaybelarge,
whilethestressesinducedbythedistortionalloadsmaydominatethedesign[26].
The distortional behaviour of single-cell rectangular or trapezoidal members
can be classified as uniform or non-uniform. Uniform distortion occurs when the
applied distortional loading is uniformly distributed along a member of constant
cross-section which has no diaphragms. In this case the distortional loading is
resisted solely by the out-of-plane bending rigidity of the plate elements of the
section.Innon-uniformdistortion,thedistortionsvaryalongthemember,andthe
plate elements bend in their planes, producing in-plane shear stresses which help
to resist the distortional loading.
Perhapsthesimplestmethodofanalysingnon-uniformdistortionisbyusingan
analogytotheproblem[30]ofabeamonanelasticfoundation(BEFanalogy).In
this analogy, which is shown diagrammatically in Figure 10.35, the distortional

(a) Elevation of a
box section member

Rigid
diaphragm
free to
warp

Rigid
diaphragm
warping
prevented

Concentrated
distortional
load

Distributed
distortional
load

Flexible
diaphragm

Beam
rigidity EI

Q q

(b) Beam on an elastic
foundation

Foundation modulus k
EI d 4 w/ d x 4 + kw = q

Distortion
In-plane stiffness
Out-of-plane stiffness
Distortional loads
Warping normal stress
Warping shear stress

Deflection w
Beam rigidity EI
Foundation modulus k
Beam loads Q, q
Beam moment
Beam shear

(c) Analogy

Figure 10.35 BEF analogy for box section distortion.