Mechanics of materials -- deformation problem

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Discussion Overview

The discussion revolves around a deformation problem in mechanics of materials, specifically focusing on the movement of point N in a statically indeterminate structure involving beams and supports. Participants explore various approaches to analyze the deformation and the forces acting on the structure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in determining the downward movement of point N and proposes equations of deformation based on the assumption of static indeterminacy.
  • Another participant questions the clarity of the posted diagram and seeks to understand the cause of node N's downward movement.
  • A participant identifies that a uniform load on the beam causes member NM to stretch, leading to the bending of the upper structure.
  • There is a query about whether node M is perfectly articulated in all directions, suggesting that link TM could be removed without affecting the problem.
  • A participant clarifies that the structure is indeed twice statically indeterminate and emphasizes the rigidity of the connections in the diagram.
  • One participant introduces the method of superposition as a potential approach to analyze the deflection at point N, suggesting that the deflection can be determined from the contributions of individual loads.
  • The original poster acknowledges the method of superposition but expresses uncertainty about the correctness of their approach and seeks validation of their reasoning.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the analysis of the structure. There are multiple competing views regarding the assumptions about the supports and the methods to analyze the deformation.

Contextual Notes

Participants mention the complexity of the structure and the difficulty in interpreting the diagram, which may affect the clarity of the discussion. There are unresolved questions regarding the assumptions of static determinacy and the effects of loads on the structure.

Yossi33
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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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The posted diagram is very difficult to read.
What is causing node N to move downwards?
 
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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
 
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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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.
 
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?
 
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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