I remember reading somewhere that the most efficient common purlin design normally turns out to be a nearly square timber. I guess it would depend on the pitch of the roof. I've looked through all my books and can't find an explanation. Can anyone give me a reference for this or explain why it is--or isn't?
Kjell

this is true on a 45 degree pitch.

We all know that the depth of the beam is more important to it's strength/stiffness than the width. So on shallower pitches, the deeper the beam the better, just like any beam.

As you go over 45 degrees, you actually want to orient the purlin so that the depth is in the plane of the roof, which is opposite what you might think.

Not a very clear explanation I'm afraid. And it is simplified, because it is hard to join deep common purlins to principal rafters without weakening one or both members.