Mechanics of materials -- deformation problem

In summary, the diagram is very difficult to read and it is not clear what is causing node N to move downwards. Without knowing more about the diagram, it is difficult to say if the method of superposition is correct.
  • #1
22
3
Homework Statement
find the deformation of the structure and find delta(N).
Relevant Equations
deformations equations
Motif-1.jpg

Hi, i'm struggling with that problem , i need to find the distance that point N went down.My way of thinking is that the structure is twice not statically determined because of the beam MN and beacuse of the left support which is also unnecessary in order for equilibrium. My 2 equations of deformation in order to find the variables are d(N)-d(M)=d(Lmn) and d(N) of the left beam equal to the d(N) of the right beam.
i thought to denote the force of the beam as N and then to divide to to each beam (pic 1) then i got the problem that i have a beam with no support and a force that causing it do go down, so i tought (pic 2 ) that the beam NM is equal to support there and got the problem that if there is a support it wont get down. in addition to that i cant figure out if the force that bending one beam is causing the torsion of the other , because the left doesnt resist that its only has a translational resistance. I wonder if my initial analysis is somehow correct and what other perspective there is to solve problems like this. thank you.
 
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  • #2
The posted diagram is very difficult to read.
What is causing node N to move downwards?
 
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  • #3
W the uniform load acts on the beam , that casues the member NM to stretch and as a result , bending down the upper structure.
Note 10 Jan 2023 (1)-1.jpg
Note 10 Jan 2023-1.jpg
 
  • #4
Thank you.
Is node M perfectly articulated in the three directions of the links converging at it?
If so, it seems that link TM can be removed with no consequences for our problem.
 
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  • #5
no , also in the diagram you can see that it is a half node and the upper structure TMS is continous . and i did some extra black there to emphasize the rigidity of the 90 degree.
.- edit - that is why i said that the structure is two times statically indeterminate.
 
  • #6
Have you studied the method of superposition, which states that the deflection at any point on the beam is equal to the resultant of the slopes or deflections at that point caused by each of the load acting separately?
 
  • #7
yes, that is why i stated that my first try was to compare the displacements of point M , and the solution is 2 equations of deformations because the structure is twice statically indeterminate but i try to solve that and i dont know if its right or no . can you tell me if its ok or if im in the right direction? , its in the pdf
 

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