Why are tenons offset from the center (e.g. 1.5" from the edge?) I have a kingpost tenon that I need to cut and it seems to me that it would do its job better if it were centered on the bottom of the post.

Gib...

I'm a newbie, but here's my take on this:

I suspect you are talking about "square rule", were everything is measured from 2 adjointing reference faces. One reason this is done is to assure that the outside faces of timbers in a wall are on the same plane...so it can be sheathed. Same theory with the tops of floor joists...

Joel

The kingpost tenon does not need to be offset, unless there are other mortices which need to be offset on your bottom chord.
I'd agree that offset tenon layout comes from square rule.
In a corner post(or a wall post), offset tenons preserve more continuous fibers than central tenons(because the girts and braces are set to the outside faces of the posts already).

In designing a frame the designer looks at all aspects of the bent/truss/frame.
With square rule joinery there are "General frame rules" that are established, such as 1.5" off the layout face and then a tenon 1.5" thick. But with every rule there is or can be an exception to that rule.
If the joinery is right so that the king post is truly being hung by the support of the two rafters then the king post is holding up the tie beam creating a truss, and if this is so, then the size and location of the bottom tenon may need to be looked at closely and adjusted so that it doesn't fail under load, whatever that load may be, such as a second floor or ceiling.
And the fastener of the tenon to the tie needs to be looked at also.
There has been many articles lately about roof trusses in Timber Framing magazine.
It's possible your frame and king post tenon should be reviewed and a determination as to what size it should truly be and it's location.

Good luck with your project.
Jim Rogers