Calculate Normal Force

[Calvin Murphy]

I am hoping to settle a debate between two engineers.

I have created a simple diagram of the part of the structure we are investigating.

It can be solved in 5 minutes or less by anyone familiar with static equilibrium problems.

The goal is simple enough: find Fn.

Yet, the discussion over whose solution was correct is still unresolved. I build a rig to physically measure it, but the disagreement persisted. Then I reached out to 5 university professors to see if they would help, but I have not heard a response. So here I am. Please help.

 

[human909]

None additional requirements or caveats are necessary calculate the static equilibrium answer. The fact that it is stated that the system is in static equilibrium is enough. Of course we should all recognise that this static state is inherently unstable and hence this is a academic exercise not a real world exercise.

As I said earlier if you need extra confirmation then your favourite frame analysis software should give you an answer. Here is my result for what should be a simple statics problem. I've provided two diagram simply to show that geometric length is not relevant.

 

[GregLocock]

5/tan(30) obviously for the horizontal component. I think it is stable, it is very similar to the jammed kitchen drawer problem, and can be 'fixed' the same way, pulling up at the centre. The constraint at the LH wall is hard to achieve in practice, the reality is the upper wheel will lift off and then there will be an expensive noise.

 

[human909]

5/tan(30) obviously for the horizontal component. I think it is stable, it is very similar to the jammed kitchen drawer problem, and can be 'fixed' the same way, pulling up at the centre. The constraint at the LH wall is hard to achieve in practice, the reality is the upper wheel will lift off and then there will be an expensive noise.

No. It is not a stable structure by definition.

Even the slightest variation away from "perfect" a horizontal of the first beam will remove static equilibrium you end up with a mechanism. A perfectly vertical needle balancing on its tip is in static equilibrium, but it is unstable because even the smallest deviation will lead to a situation where static equilibrium is not possible.

Sure, if you have a real world scenario with roller static friction then you can achieve some stability. But that isn't what we have here we have zero vertical restraint on the left end of the beam.

Again if you want to check these claims try to calculate a static equilibrium for the case where the angle of the horizontal member is 0.1degree off horizontal.

 

[GregLocock]

Agreed.