The message
from Tim Lamb contains these words:

OK again. So provided the rafters/sheets are rigid and the wall plate
prevented from spreading by the truss tie, the purlin and ridge are
mainly decorative?

That is not what I intended to impart. Looking at one side of the roof
in isolation the wall plate and the ridge will take 25% of the total
weight of the roof and the purlin 50%. As the ridge is also supporting
the other side of the roof its actual loading is the same as the purlin.

I was writing in jest:-)

I am afraid that passed me by.

My construction is such that there are no rafters. The building has
three trusses at roughly 3m intervals. There is no ridge board but a
purlin close to the ridge and a second midway (it may not be proper to
call these *purlins* as they are load carrying members). I can secure
the ridge such that a rigid triangle is formed taking all the load to
the wall plates. Assuming snowloading, windloading and thrust on walls
are not issues (the building has withstood these for the last century) I
am concerned that there will be some sagging midway between the trusses
with the additional sheeting weight.

I am not 100% convinced I understand your explanation but my current
assumption is that you have a barn some 40 feet long and at every
intermediate 10 feet there is a triangular roof truss which supports 4
horizontal timbers (2 at approximate mid points, 2 near the ridge) to
which the original roof sheeting was fixed.

If that is the case and your only worry is the new sheeting sagging
there is a very simple solution. Ask the supplier what the maximum
allowable clear span is. If the roof is shallow enough to be walked on
it might also be worth establishing whether that would require a shorter
clear span.

AIUI you were also worried about the strength of the horizontal supports
but not of the supporting trusses. In the above set-up the horizontal
members should be relatively lightweight* but the rafter (for want of a
better word) sections of the truss would probably have to be more
substantial (carrying more load than the purlin), considerably more
substantial if there is little or no cross bracing.

The agricultural solution is to try it and see: beefing up the structure
if necessary.

Doesn't work too well if failure precedes beefing up. :-)

*I have a gut feeling that 6" x 2" (floor joist for 10 feet span) might
be overkill, 4" x 2" would need checking out but to do that you would
need to know what to add for weather and safety constraints and there I
can't help.

--
Roger Chapman