Last night’s post, Popsicle Crane Update 3 was almost completely about construction of the crane boom hinge end (the “butt” end – a real term used by the crane industry.) I realized on the way to work today I did not talk about why I did what I did. I did not do an analysis while I was designing it, but I did put a lot of though. This is an attempt to describe that thought process.

In an earlier post Crane Boom Analysis part 2, I determined that the boom experiences almost 100% compressive forces and these forces will be about 5 times the load on the hook. This is because of the angle of the cables pulling the boom upward. For this discussion we will assume a 20 pound load on the hook so the compressive force will be about 100 lbs. The assumption is that each of the four columns forming the boom will share the load equally. That means 25 lbs force on each of the four connection points to the two butt sections.

I used CAD and drew the vectors down the center of each beam. Beam A is not included in this because it is really part of the boom and we are only interested in the butt assembly. I will be playing “fast and easy” with this analysis because I am doing the simple analysis assuming the forces run down the center of the beams. That cannot be the case because the pivot point is not in the center of the diagonal beams, and the whole end piece, the four vertical members, will be assumed away. That greatly simplifies the analysis, and these make the whole assembly stiffer. Similarly I am not going to include member D in the analysis.

D was put in the design so the center of the “A frame” would not be hollow and the shaft would have more surface area to share the load. Members B & C were included for two reasons. First, they are there to butt up against the ends of the crane boom. Second they are there to keep the diagonal members from wanting to spread apart. The “spread apart” forces are the main focus of this analysis. This analysis is pretty much following the same procedure describe in Episode 27 – Statics Part II – Moments.

Next I copied only the force vectors to another part of the drawing. This eliminates the clutter of the actual physical members in the drawing. We will be looking primarily at the point where the butt meets the boom. Both of members will be compressing that connection point so the arrows are facing each other.

The next step was to simplify the problem. Based upon symmetry half of the problem was eliminated very quickly. I then combined the two column B & C into one vector, the blue one. I drew the diagonal line from the splice point to the center of the shaft. (This is the “fast and easy” assumptions I talked about earlier.) The diagonal line was then broken up into the component vectors. (The red arrows.)

The final step was to scale these vectors so I could directly take measurements from them using the CAD program. I know the horizontal force is 25 so that is the side I used to scale the rest of the vectors. The horizontal forces cancel because the boom will be pushing on the diagonal beam with 25 lbs force and the shaft will be pushing back also with 25 lbs. (It will actually be pushing back with 50 lbs but one-half of that force will be going to the bottom diagonal of the butt assembly.) The problem is the 9.125 lbs of upward force on the end of the diagonal beam. This will tend to push the diagonal beam clockwise around the shaft. If we neglect the short vertical pieces near the shaft the only force that can oppose that is the blue arrow which represents a combination of members B &C. This force can be calculated from the known upward force and the two lever arms. (I will calculate in some bogus units because the distance units will cancel out.) 9.125 X 25 = Blue Arrow X 17.625. Blue Arrow = 12.943 lbs.

Again I did not do these actual calculations, but the thought process was used to create the design. The actual numbers are actually meaningless, because of all the assumptions I made, but the thought process is very close to correct. Besides there really is no design criteria or standards for allowable forces on popsicle sticks and glue joints. We could “nerd out” and do a lot of testing on the sticks and joints, but I don’t really care to spend that kind of time, and I doubt if anyone really would want to read all the details.

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As always, thank you for your time. I hope I have made it worth the time.

Gary

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