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A gross analysis of the forces on a crane boom

Picture 1. The top of a crane boom from some government archive pictures.

It is time for the rubber to meet the road on starting to figure out how to build the popsicle crane boom. As you know, I have been looking at many pictures and researching crane sites to try to understand what kind of forces to expect on a crane. I also have been sketching some force diagrams. Things are starting to fall out and now I am ready to discuss those forces. First, I do need to write a disclaimer in case someone is visiting and thinking they will learn how to build a real crane.

I am not a civil or structural engineer and I doubt very either of those would consider taking on the job of designing a real crane. It is something to be done by an organisation with lots of resources. experience, and facilities. What we are designing and playing with is going to be a model where at most we might get a sore toe if we are stupid enough to put our foot under the load and the crane fails. The skills we will be learning are transferable to larger things, but always education and experience and knowledge of codes and standards are required.

Picture 2: The crane boom height cable and forces.

Several months ago I presented a couple of posts about statics and splitting a force into its component parts. (Episode 25 & Episode 27). In Picture 2 I am doing exactly that but I have changed things a little.  The blue box frame is a schematic representation of the boom frame and the magenta line represents the cable used to raise and lower the boom.  I randomly chose a 45 degree angle for the boom.  The boom is hinged on the bottom so it is free to rotate.  The weight of the boom and the load will attempt to make the boom rotate counter clockwise and the only thing preventing that is the tension on the boom cable.as shown by the solid arrow.  (Tension is a force on a rope or structural element attempting to stretch it.  Compression is a force on a structural element attempting to crush it.)  Instead of taking components of the force that are horizontal and vertical it makes more sense at this point to divide the force into components parallel and perpendicular to the boom frame.  These components are shown in the dashed line.  These components taken together must from a right triangle with the actual force on the cable being the hypotenuse.

In this exercise we are not going to attempt to calculate the actual forces.  There really is no use in doing that because there are too many unknowns.  All we are trying to do is get an understanding of what kind of forces and the interaction between the forces.  As seen from Picture 2, because of the relatively small angle between the boom and the cable, the cable will supply a comparatively small force lifting the boom, the force perpendicular to the boom.  It will supply a much larger force compressing the boom.   Increasing the angle between the rope and boom will reduce this ratio.  (More on that subject later.)

Picture 3: The hoist cable & forces.

Picture 3 shows the hoist cable. Keep in mind that in this picture I did not use a block and tackle assembly to reduce the force on the hoist cable running inside the boom. I touched upon a block and tackle way back in Episode 7, but for now just know that it is a way of reducing the force on a cable.  The load on the crane is hanging on the vertical cable.  The components of this force is one making the boom want to rotate counter-clockwise and another force parallel to the boom.   This second force is compressing the boom.   The rope running down the middle of the boom is also attempting to compress the boom.  A block and tackle would have no effect on the load, but it could reduce the force on the cable inside the boom.

Picture 4: Hoist Cable Routing on Older Cranes.

The older crane shown in the video in a previous post had the hoist cable running from above the cab of the crane to the top of the boom.  The force diagrams are shown and are basically a combination of the way we described the boom lift cable and the previous hoist cable.  I think probably the advantage of doing things this way was it was the only way of achieving it with the technology at the time.  Even the real crane I show in Picture 1 is closer to the the routing in Picture 3 than this routing so we will not talk about this version any more and will only consider the Picture 3 routing for the rest of this discussion.

Picture 5: The Weight of the Boom

Now we will consider a completely different force, the weight of the boom.   This force is completely different than the others because it is not acting at the common point the top of the boom.  The weight is shown as a concentrated load in the middle of the boom section, but it really is distributed throughout the whole boom length.  The component that is perpendicular to the boom will cause the boom to want to  bow in the middle.  Hopefully when we get this completed the weight of the boom will be minor compared to the load lifted by the crane so we can pretty much forget this in our considerations.  Half of this load will be lifted by the boom lift cable, and half of it will rest on the hinge point at the cab.

Picture 6: All of the loads acting on the boom.

Picture 6 shows all of these loads in one picture so we can start considering all the interactions.  The first thing to notice:  All of the forces parallel to the boom are acting in the same direction.  All are tending to compress the boom.

The second thing to notice is all the forces perpendicular to the boom will tend to cause it rotate counter-clockwise, except the boom lift cable.  Remember none of these forces are drawn to scale.  All we have been trying to understand is the angles and types of forces involved.  The next step will be starting to get an understanding of magnitude of these forces.  That will probably be the next post about this crane analysis.  The important thing for right now is:  The crane boom is in compression!   The boom is basically a tower structure that can rotate in the vertical direction.

Dealing with compression will cause to have to think about many things.  If you think about pushing the ends of a popsicle stick together think about what will happen to the stick.  More than likely it will start to bend perpendicular to the “skinny side”.   That will be our greatest difficulty.

I am sorry that this post became fairly long and detailed, but I think the detail is necessary to understand what is going on inside the boom.   Time for a break for both of us now and we will pick this up in a new post very soon.

Gary.

P.S. if you really want to get a feel for what we are talking about get an old broomstick and ties some strings  and weights on it and experiment.  It would be the best way to test the model we have started.

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