Bill:
Your contact area is not really assumed, you set that and the lever arm btwn. them, as part of your design and your experience with these type problems. Since you have to keep in mind fabricating tolerances, straightness of the sections, etc. there is some clearance designed into the boom sections. Your “x” length is a replaceable wear and min. friction pad, as you have them located, and you provide a fixed stop so the lever arm btwn. them can’t get smaller than a set design amount. Start designing out at the boom tip and that tip boom section is a fairly simple canti. beam, with a back span of only a few feet. You apply that couple to the tip of the next section back, etc. I just glanced at BA’s link, and will try to look closer later, it was difficult to load and read. You can calc. the deflection of the tip section as you would any canti., but then you must just add some rotation at its semi-fixed end because of the built-in clearances. I never worried much about deflections, crane booms and spreader beams deflect quite a bit, as long as they aren’t over stressed and don’t buckle. There is no new magic way, that I know of, to do this problem, other than the general tack you have suggested, that’s exactly what I would do too.
