thermal expansion exercise

[gaz89]

hello to all and good year wishes
I would like to ask if someone can help me with this machine construction exercise, of course I am not asking to solve it for me
However, once you calculate the deformation ɛ how do I calculate the vertical shift?
Thank you very much in advance

 

[cacciatorino]

Then:
you have the delta-t that causes a shortening of the beam l1, contrasted by the reaction of the beam l2. you can imagine working backwards: Consider a vertical beam already shortened, and then a screw that simmers the head of the vertical rod and the intradox of the beam prompted to flesion, the problem does not change.

You have to set up two situations.

1) in the first describe the beam subject to bending, in which you will have an arrow, function of a force applied centrally. for which you will have a dl_fless arrow and a f_fless force

2) in the second, you have a traction-stressed beam, length l1-epsilon (epsilon is thermal contraction). This beam will extend to a certain dl_traz, under the action of a force upwards of f_traz

being the connected system, you get two equations:

f_traz = f_fless
dl_traz

the data of the durable sections and materials you have, so you should get to a solution.

 

[meccanicamg]

the linear expansion or contraction of the structure due to the thermal expansion action (positive or negative) causes an additional tension state, therefore a force.

see attached a page of my machine tool clipboards that is done in unity with regard to structures

 

[gaz89]

Then:
you have the delta-t that causes a shortening of the beam l1, contrasted by the reaction of the beam l2. you can imagine working backwards: Consider a vertical beam already shortened, and then a screw that simmers the head of the vertical rod and the intradox of the beam prompted to flesion, the problem does not change.

You have to set up two situations.

1) in the first describe the beam subject to bending, in which you will have an arrow, function of a force applied centrally. for which you will have a dl_fless arrow and a f_fless force

2) in the second, you have a traction-stressed beam, length l1-epsilon (epsilon is thermal contraction). This beam will extend to a certain dl_traz, under the action of a force upwards of f_traz

being the connected system, you get two equations:

f_traz = f_fless
dl_traz

the data of the durable sections and materials you have, so you should get to a solution.

Thank you very much to both of us.
However, I think I have understood what the 2 eq. are to be matched, practically :

(ii)[EA/(L1-epsilon)]_

but the second equation to solve the system?

 

[Legs]

Thank you very much to both of us.
However, I think I have understood what the 2 eq. are to be matched, practically :
(ii)[EA/(L1-epsilon)]_
but the second equation to solve the system?

you must consider that for the principle of action and reaction the mountaineer will be subject to the same force (changed of sign) of that applied to the traverse (probably this is the second equation that told you ie equal the forces exchanged).
But I prefer to write the equation of congruence by highlighting directly the x force exchanged between the two rods (force method).
in practice the mount will extend the alpha*deltat*l1 quantity (positive hypotize the delta. However, nothing changes if it is negative) and will notice the quantity x*l1/(e*a) while the traverse will have an arrow at the center of x*l2^3/(48*e*j).
It will be enough to say that the shift of the point to is the same for both auctions, namely:
(e*a) = x*l2^3/(48*e*j) from which x.
It is however easier if you refer to the following image where I highlighted the force x:


p.s.
I have speculated that the two auctions can only exchange strength x.

 

[gaz89]

Thank you very much!!! very nice