Need to solve a mechanical problem that's due on Wednesday

[zalmoxis]

Homework Statement

The system is composed of 3 competing ( one after another) beams, like in the drawing. They are all from the same material, with the same admissible strain σ and the same elasticity module E.
It is required to calculate the optimum configuration for the system, considering the main objective function to be the material's weight.

I put the drawing in the attachment.

Homework Equations

Need to find:
σ=? ( admissible strain)
P=?
L=?
E=?

I don't need the scalar values.

The Attempt at a Solution

Nobody in my class knows how to solve this, our professor didn't want to help at all, even if he was asked several times. Everybody just gave up and nobody even knows where to start.

 

[CWatters]

Not sure i can solve it but can you write equations for the length of each member in terms of some angle, then sum those together to give a total length. That should be representative of the total material mass. Then find the minima for that equation. Then check that in that configuration the load on each member is less than some limit.

Problem is the max load in one of the members might be exceeded in that configuration. My maths isn't good enough but I suspect that instead of solving for the minima of a curve you need to do something similar in multiple dimensions.

 

[zalmoxis]

The length isn't really an issue, it can be formulated using the angles. Or at least that's just an idea, but length is also dependent on the admissible tension, which I can't figure out. I don't think I even know what I'm saying anymore, this whole problem, when I think about it all at once, just confuses the hell out of me.

At any rate, I got no idea what to do.

 

[pongo38]

If it's all in one plane (the plane of the paper) then you should be able to draw a range of scale force diagrams for the loaded node. In 2-d it is statically indeterminate, but in 3-d it is determinate. The diagrams could imply a way of minimising the weight (length).

 

[rezeew]

As a scientist, it is important to approach problems with a systematic and logical approach. In this case, the first step would be to clearly define the problem and understand the parameters involved. From the given information, it seems that the main objective is to find the optimum configuration for the system in order to minimize the weight of the material used. This can be achieved by considering the admissible strain, elasticity module, and the competing beams in the system.

Next, it would be beneficial to review any relevant equations or principles related to this problem. This could include concepts such as stress and strain, beam bending, and optimization techniques. It may also be helpful to look at similar problems or examples to gain a better understanding of the approach needed.

Once the problem has been clearly defined and relevant equations have been identified, the next step would be to set up a plan for solving the problem. This could involve breaking down the problem into smaller, more manageable parts and determining the necessary steps to find the optimum configuration.

It is also important to communicate with others, whether it be classmates, professors, or online resources, to gain further insight and potentially find a solution. Collaboration and discussion can often lead to new ideas and approaches to solving a problem.

Overall, it is important to remain persistent and determined when faced with a difficult problem. With a clear understanding of the problem and a systematic approach, a solution can be found.