If the rail is supported on a flexible elastomeric pad, the loads
are destabilising and the Standard notes that the loads should
be assumed to be applied at the top of the flange.
In BS 5950, destabilising loads were treated by multiplying
the system length by 1.2 (typically), with further adjustment
depending on the support conditions. The equivalent uniform
moment factor mLT had to be taken as 1.0 (so no benefit from
the shape of the bending moment diagram). The Eurocode deals
with destabilising loads by adjusting the calculated value of Mcr ,
which will lead us to the comment about using software from a
Calculation of Mcr
The background to the problem of Mcr is that BS 5950 presents
bending strengths pb for different values of slenderness, λLT ,
which is very convenient for the designer, as long as one is
not interested how the values have been derived. If interest is
sparked, Annex B of BS 5950 provides the background. With
patience and algebraic dexterity, one can demonstrate that the
BS 5950 terms depend on a familiar friend – the elastic critical
buckling moment, Mcr . This has been discussed previously4.
Mcr can be calculated using a formula. The version of the
formula which allows for destabilising loads is perfectly
amenable to computation by paper, pencil and calculator as
the Verulam correspondence wished. Software solutions merely
make the process easier and, many would say, less open to error.
After extensive experience asking course delegates to complete
a manual calculation of Mcr even without destabilising loads, the
conclusion is that generally over 80% fail to compute the correct
answer. Sadly, the main problem is that delegates attempt to use
inconsistent units within the calculation. Maybe software is safer
The French software mentioned is LTBeam, which has been
discussed several times. Despite the assertion in Verulam,
independently written software from the UK (does that make it
better?) exists and is freely available at steelconstruction.info
If necessary, these two programs could be used for mutual
checking, and then proved by hand calculation – though a
spreadsheet is strongly recommended to remove the tedium of
the latter option.
How to check?
The calculation of Mcr is merely a step on the way to the result,
so checking of the final resistance is probably wise. Options
are available, starting with a ‘sense check’ against the results
from BS 5950. Since the introduction of the Eurocodes the
consistent message has been that the structural mechanics
has not changed, so one would not expect to find significant
differences in the results obtained by either code. Generally, the
LTB resistance according to the Eurocode is a little higher than
according to BS 5950, so that needs to be recognised, as well as
taking mLT = 1.0 for destabilising loads.
The wise authors of BS 5950 recognised that increasing
the effective length of the member was a good way to allow
for destabilising loads. That simple check can be completed
by looking at the calculated member resistances for the two
Simple design assessment
Some straightforward checks of the example presented in
P385 have been completed. The example demonstrates the
verification of a member subject to combined major and minor
axis bending combined with torsion, but if the example is
reconfigured to assume lateral loads (and torsional effects due
to eccentricity) are taken by a plate welded to the top flange, the
exercise becomes a review of the main member.
The vertical loads are destabilising, so according to EN 1993-6
are assumed to be applied at the level of the top flange.
Accounting for the position of the loads, Mcr = 320 kNm*,
according to P385, and Mb = 277 kNm*.
The span of the gantry girder is 7.5 m, so applying a factor of
1.2 results in a span of 9 m. Then one must make a reasonable
estimate of the shape of the bending moment diagram, or
conservatively assume that C1 = 1.0
Looking at the bending moment diagram (Figure 3), it
looks vaguely similar to that for a UDL, admittedly with some