Technical
The design of tee sections in bending
David Brown of the SCI looks at the lateral torsional buckling resistance of tee sections,
considering the rules in BS 5950 and BS EN 1993-1-1
26 NSC
July/Aug 19
A tee section? In bending?
A tee section seems an unlikely choice for a member in bending,
but judging by the calls to SCI’s Advisory Desk, designers do wish
(or are perhaps required) to use them. Normally, a tee might be
used as a tie between floor beams. The vertical web fits between
floor units and the flange sits just below the units, making little
impact on an uninterrupted soffit. Before hollow section trusses
became popular, tees would have been a good choice for the
chords of roof trusses. The web of the tee (if cut from a UB section)
provides enough room to connect the angle internal members,
either by bolting or welding.
This article considers the alternative ways to design a tee section
in both BS 5950 and BS EN 1993-1-1, illustrated with a worked
example, so that designers have a resource if faced with the
challenge of an unrestrained tee in bending.
BS 5950 guidance
The verification of a tee is covered in Section B.2.8, which provides
rules to calculate the equivalent slenderness for lateral torsional
buckling (LTB). The first point to note is that guidance is given on
when LTB should be considered, and when not. To avoid confusion
with Eurocode terminology, the axis on the web centreline will be
referred to as the minor axis and the perpendicular axis, the major
axis.
In B.2.8.2 a), the Standard advises that if Imajor = Iminor LTB does
not occur and λLT is zero. The same applies to doubly-symmetrical
sections where there is no reason for the section to buckle in the
minor axis.
The reverse is true for tees cut from a UB – major axis inertia is
larger than the minor axis inertia and LTB is possible.
Part b) of the clause notes that “if Iminor > Imajor LTB occurs about
the major axis and λLT is given by:
LB
0.5
= 2.8( we) LT T2 ”
where B is the flange breadth and T is the flange thickness. Many
tees will fall into this category – notably those cut from UC sections
where the web is short and the flange is wide and thick. A simply
supported tee section with Iminor > Imajor , loaded so as to put a short
unrestrained stem in compression will buckle by twisting to reduce
the compression in the stem.
This clause may lead to some significant confusion, because the
expression for λLT for a tee is the same as the equivalent expression
for a plate bent about its major axis, given in clause B.2.7. The
expression is based on the St Venant torsional stiffness of the
flange only; the stem of the tee and any warping stiffness are
ignored, hence the similarity with the expression for buckling of a
flat plate.
Finally, part c) of the clause describes when Imajor > Iminor (the
common situation for tees cut from UB) and provides the familiar
(for designers of a certain age!) expression:
LT = uv Bw
The clause goes on to provide expressions for the relevant
section properties needed to evaluate λLT , but designers will mostly
obtain these from section property tables. In this case, the warping
stiffness of the section is included in the determination of λLT .
BS EN 1993-1-1 guidance
For tees, there is no change from the normal procedure. To
calculate the non-dimensional slenderness λLT the elastic critical
buckling moment, Mcr is needed. This challenge is conveniently
addressed by using software.
Verification methods
In the particular example chosen, the tee is cut from a UB, and thus
has a relatively long web. Classification to either Standard leads to
the conclusion that the tee is slender (BS 5950) or class 4 (BS EN
1993-1-1).
Two approaches are then possible in both Standards. Either
the design stress can be reduced until the section becomes Semicompact/
Class 3, or an effective section can be determined by
neglecting the ineffective parts of the cross-section. This latter
approach becomes more involved in the Eurocode, because the
effective section depends on the stress ratio in the web, which
depends on the position of the neutral axis, which moves as the
effective section reduces – so an iterative process is needed.
BS 5950 is more straightforward as uniform stress in the web is
assumed.
Worked example
The tee is a 152 × 229 × 30, in S355, with a buckling length of
4 m. The applied moment is in the plane of the web about the
major axis and the web is in compression. The section is shown in
Figure 1.
Method 1 – BS 5950 reduced design stress
From look-up tables, d/t for the web = 28
From Table 11, the Class 3 limit is 18ε, and as ε = 0.88, the limit is
15.84. The section is therefore slender.
Clause 3.6.5 allows the use of a reduced design stress, pyr given by:
15.84
2
p=( ) × 355 = 114 N/mm2 yr 28
Various section properties are needed from section tables:
minor axis radius of gyration, ryy = 32.3 mm
buckling parameter, u = 0.648
monosymmetry index, ψ = -0.746 (negative as the flange is in
tension)
28
Figure 1: Tee section dimensions
/Trusses
/Steel_construction_products#Standard_open_sections
/Welding
/Member_design#Lateral_torsional_buckling_resistance
/Design_codes_and_standards#Introduction_to_Eurocodes