Physics problems - where to find similar exercices

[gildasd]

This thread demonstrates that in class as well as in real life, clarity in stating and understanding the problem is at least as important as the engineering and physics used in solving it.

Moving goalpost are the standard fare of any project 

[gildasd]

Here is a follow-up exercise:
The 3 supports are of different materials, we need to find the pressure on each one in MPa's.
(The weight is horizontal and can't tilt).
In the second half, the 3 supports are heated by 50°C and we need to check if the weight can touch all 3.
(Sorry about the French, but it's pretty self explanatory).

More seriously:
The 3rd image is a simplification of a problem that I often encounter, but the methods and formulas that we have been given can only get you a rough approximation at best.
And they take a couple of pages to resolve...

[IanB]

The 3rd image is a simplification of a problem that I often encounter, but the methods and formulas that we have been given can only get you a rough approximation at best.
And they take a couple of pages to resolve...

That third image is a matter of resolving forces. The snag is that when the trusses AB and AC stretch the angles will alter. So for an exact solution it is necessary to write equations that apply to the final state with the final angle unknown. I think it will be necessary to use some triangle formulas like the cosine rule or the sine rule.

[gildasd]

The 3rd image is a simplification of a problem that I often encounter, but the methods and formulas that we have been given can only get you a rough approximation at best.
And they take a couple of pages to resolve...

That third image is a matter of resolving forces. The snag is that when the trusses AB and AC stretch the angles will alter. So for an exact solution it is necessary to write equations that apply to the final state with the final angle unknown. I think it will be necessary to use some triangle formulas like the cosine rule or the sine rule.

I'm going in that general direction... But it's HARD!
This will probably need a small integral at one stage to cover the zone between the two angles...
It's a bit frustrating that for such a common problem there is not a formula (digging through textbooks right now).

[gildasd]

I've tried to solve a problem nearly all day...
With the tools at my disposition (only a 12 course on material science), I finally took an indirect route:

I calculated the truss with a "wet finger in the breeze" force that was within the magnitude.
With the resulting lengths I made a coefficient.
With that coefficient, I obtained the proportion of deformation on the simplest part of the truss.
Did a simple multiplication to get an "about there" result...

Really trying to get this out of the way to do some electronics for my final project (concept validated today -  yay!).

[IanB]

You can exploit the symmetry of the problem and consider only one half of the system. See the diagram below. Does this give you a hint? (I haven't solved it myself, but having gone thus far I am confident the solution will be attainable.)

[gildasd]

You can exploit the symmetry of the problem and consider only one half of the system. See the diagram below. Does this give you a hint? (I haven't solved it myself, but having gone thus far I am confident the solution will be attainable.)

Thanks!
I used the symmetry too but used Pythagoras at the end to find EA'.
I like what you did, but what does "k" represent?

http://skyciv.com/free-truss-calculator/
This is cool little tool to check final truss results.

[IanB]

k is the "spring constant" of the truss.

If we assume that the truss is a bar of cross-section A, length L and Young's modulus E, then we can write:

    F = EA/L dL

or

    F = k dL

where

    k = EA/L

[F4CPY]

Hello
I think there's a better way to solve this.
Try to apply PFS (principe fondamental de la statique  ) fundamental principle of static  at node A
Evaluate each force in the bars (parametric function of F)
Evaluate the sum of the traction energy of the three bars (N²*L)/(2*S*E)
Apply Castigliano theorem : dérivative of the sum of the energy by the external force F equal displacement. (little displacements)
Knowing displacement you will find F.

Didier

[gildasd]

Hello
I think there's a better way to solve this.
Try to apply PFS (principe fondamental de la statique  ) fundamental principle of static  at node A
Evaluate each force in the bars (parametric function of F)
Evaluate the sum of the traction energy of the three bars (N²*L)/(2*S*E)
Apply Castigliano theorem : dérivative of the sum of the energy by the external force F equal displacement. (little displacements)
Knowing displacement you will find F.

Didier

That's either brilliant or rather rude...

[mrflibble]

Evaluate each force in the bars (parametric function of F)
Evaluate the sum of the traction energy of the three bars (N²*L)/(2*S*E)
Apply Castigliano theorem : dérivative of the sum of the energy by the external force F equal displacement. (little displacements)
Knowing displacement you will find F.

Hey, that sounds suspiciously much like D'Alembert's principle.

That's either brilliant or rather rude...

Well, if it's like the D'Alembert method like I think it is then it just might be brilliant. The concept of virtual work makes solving this type of problem totally easy.

[IanB]

The theory is easy, but the algebra can become messy.

The system here is non-linear for large displacements because the angle of the truss changes. The non-linearity introduces complexity. I am not sure that applying the principle of virtual work will in and of itself simplify this.

However, if you assume that displacements are small relative to the dimensions of the system then you can linearize the system equations around the initial point and get a much simpler solution which is correct to the first order. This would probably be acceptable if the trusses were steel girders, but likely not be acceptable if the trusses were rubber bands.

[gildasd]

Had the exam today and it went ok.

I don't know how much an internet thanks is worth, but this is one.
Thank-you to all that contributed, I might have not used your methods to the letter, but they certainly do open "mind doors".

Thanks again!

G.

[Vgkid]

What class are you taking.

[gildasd]

Engineering Watch Officer - Unlimited.
That means ships of a minimum of 500Gt and 7.5kW to be relevant.