It is known that
the lateral torsional buckling resistance of a simple supported beam can be
significantly increased if its compressed flange is connected adequately to a
trapezoidal decking.

Eurocode allows
to consider the compressed flange as fully restrained laterally, if the
following condition is met (EN 1993-1-1 BB2.):

If the condition
is not met, Eurocode doesn’t provide too much guidance how the contribution of
the less rigid sheeting can be considered.

The following
graph shows the effect of shear stiffness on the ultimate load capacity of a 10
m long simple supported IPE purlin loaded at the level of the top flange. It is
assumed that several of these purlins are uses with 3 meters of distance
between their centers.

The blue line in
the graph shows the ultimate load carried by this purlin, in function of the
actual shear stiffness. The graph has been built with the help of ConSteel
software, using 7DOF beam finite elements. Such beam elements are adequate to
consider the presence of any shear restraint.

In case of S=0,
the value is calculated without any contribution. The line reaches the maximum
value of 1, which is the ultimate load of this purlin, when lateral buckling
checks are disregarded.

The required
value of S, using the above formula is 16900 kN. If a typical roof sheeting of
35 mm depth is used and connecting screws are used at every rib, this condition
can be fulfilled.

But if the screws
are placed at every second rib only, the S value provided by the sheeting must
be reduced by a factor of 5. The S values reduced by this factor of 5 would
come to the range of 3000-7000 kN, being considerable below the required minimum
S value, to disregard lateral torsional stability checks. These reduced S
values are marked with vertical lines (yellow, orange and gray) on the
following graph.

The very last
vertical light blue line is placed at the required minimum S value of 16900 kN.

It is very well
visible, that shear stiffnesses well below this minimum limit value can still
provide almost 100% restraining effect, even if the screws are used at every
second rib. In case of the thinner sheeting there appears although already a
reduction of the ultimate load.

This picture shows the buckling shape of this simple supported purlin, under the presence of a shear restraint well below the minimum limit required by Eurocode.

There are not only screwed-down roofs used in the practice. On roofs on larger building often floating roofs are used. Such roofs can slide within certain limits independently from the sub-structure, allowing large areas to be built without interruption and dilatation which is very beneficial from water tightness point of view. In case of such roof systems, the lateral stiffness is much lower. Is there are test values available, they can be considered for design, but in such case evidently a full lateral restraint cannot be assumed and the lateral torsional buckling check must be performed by considering the actual values provided by the sheeting.

With the help of
the mentioned 7DOF beam finite elements, these values can be considered in the
analysis and in the forthcoming design step, built on the results of analysis.
As visible from the graph, even a slightest actual shear stiffness can provide
an increase of the ultimate load.

There might be also sheeting produced from aluminium, which can provide considerably lower stiffness than sheeting produced by steel. Or at parts there might be translucent panels made of plastic which is normally not considered as a load bearing component. But the analysis and design must be inline with the real structure, at such locations no restraint should be considered. This can also be correctly considered in the proposed analysis and design approach.