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from The Natural Philosopher contains these words:

Or more relevantly when using the roof space as a room, you can add
another set of binders at 'loft ceiling' level bolted to the rafters.

Which doesn't do anywhere near as much as a purlin would to stop the
rafters bending under load.

Actually it does *more*.

Materials in bending are never as good as in compression. The binder
across a rafter pair effectively locates the end points of the binder
precisely. However it leaves a large trapezoid structure underneath. The
maximum sag will be about halfway between the tie point and the eaves.

How that structure behaves will depend on the stability of the footing
in the eaves. Take a triangular truss with a 'binder' half way up and
the binder will be in compression, not tension as you suggested earlier.
Take an A shape structure and the binder can be in compression, neutral,
or in tension depending on how much movement there is in the feet as a
result of the uniformly distributed roof load. Should the binder be in
tension then far from strengthening the roof structure it is weakening
it by increasing the bending moment on the rafter. It might be
convenient to view each joint as a pin joint but treating the binder
location that way gives a false impression of the stresses involved.

On the other hand a purlin will always provide support for the rafters
resting on it. (If the ends are not supported it is not a purlin).

Which is why the nasty modern trusses use W bracing at about halfway
down the rafters.

At the point where a roof full of rafters would have had a purlin
(assuming it didn't require two).

With full triangulation any bending stresses are limited to much shorter
lengths of timber.

The only reason I can see to use structural ridges and purlins is when
you have cheap wood no machinery and expensive labour. i.e. its easier
to square off a couple of tree trunks and support them on some masonry
and add a few bits of broomstick over, than make up a few 6x3 rafters.


Today there is no excuse for that waste of wood.

Still a choice between waste of wood and waste of loft space.

--
Roger Chapman