Bill Schwab wrote:
Chris,

Thank you for that thoughtful essay on the basis for structural
mechanics. It was well written and I agree with the principles you
outline. Although my structural mechanics may be a little rusty
through lack of use, I did study it to second year university level,
and other branches of mechanics to a higher level. I do consider
myself to have a good understanding of Newton's laws, free body
diagrams, etc. In your 500+ words you have still not explained
precisely why my free body diagram is wrong. If it's wrong, I want to
know why.


You left off the horizontal component of the tension in the "tension
member". I've said that at least three times now. Given the idealized
structure you created, it is simply where Newton takes us.

Whether or not this force is included depends on how you model the
structure. If you look at my diagram of the idealised structure, the
tension member, column and roller support are all connected by the same
pin. In this case the roller support provides a reaction (transmitted
through the pin) against the horizontal component of the tension, and
this force is not seen by the column. The free body diagram is
consistent with my model. You could draw a subtly different idealised
structure in which the tension member is connected to the column, and
the column to the roller support. In this case the horizontal component
of the tension should be shown on the FBD. I chose to take the first
approach as it simplifies the model and I do not believe it will have
much effect on the answer.

Chris