LKN wrote:I believe that bending only occurs if there is "give" in the boomilever, most likely the tension strips. When the tension members begin to bend, the main compression shape of your boom should begin to bend as well.
I would not characterize bending like this. I would say, the boom has three joints (assuming we are talking about a simple triangular shape). Each joint undergoes certain amount of rotation and displacement. These rotations and displacements define the deformed shape of the boom. Put simply, the deformation of the structure has to be determined by looking at the entire system instead of its individual parts.
Basically, if buckling and compressive failure moments haven't began in the structure, the structure could in theory bend out of shape until the bending becomes a mode of failure.
Not quite. See my explanation below.
Now, how should I go about thinking of places that will be subject to a larger force of bending in a boomilever?
Bending stress is going to be maximum near the wall (see below).
I believe that the shape of the boom is crucial to resist this bending failure...
Absolutely!
Generally speaking, structures with rigid joints (e.g., when members common to a joint are glued together) bend. Whether we are dealing with a bridge, a tower or a boom, bending is going to be present. The question is: how significant is it?
Bending in a boom is a function of its geometry, wood density and the cross-sectional shape (read moment of inertia) of its members. The best way to determine how a particular boom bends is to analyze it using a frame (not truss) analysis software.
Stress due to bending is called bending stress. For the compression and tension members in the boom this stress would be maximum at the wall end, not at the mid-point of the member or at the load end.
If bending stress is present (if it is significantly large) in the compression member, then it would amplify the amount of axial compressive stress in the member. That is, if the compression member has a cross-sectional area of A and carries an axial force of P, then axial compressive stress in the member is P/A. If the member is also bending, then maximum compressive stress in the member becomes (P/A) + (M/S) where M is maximum bending moment in the member and S is called section modulus (a property of the cross-section of the member). So, we need to look at the combined effect of bending and compression instead of examining them individually. The same is true for the tension member.
I would say as long as the moment of inertia of the vertical member is smaller than that of the other two, bending stress probably would be negligible. If however, the vertical member has a moment of inertia comparable to the horizontal member, then a significant bending stress may be present in all three members.
As for your models, I would go with either 1 or 2. The other ones do not help with bending. Since bending stress is maximum at the wall, the most economical section (if only bending is being considered) would be a tapered shape where the member is wider at the wall (has the largest moment of inertia at the wall) and narrower near the load.