Question on Number of Degrees of Freedom in a Simple Structure

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Discussion Overview

The discussion revolves around determining the number of degrees of freedom in a lumped mass structure, focusing on the implications of bending stiffness while considering various scenarios. Participants explore theoretical aspects and implications for further calculations such as equations of motion and natural frequencies.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes that the structure could have either 6 or 2 degrees of freedom, leaning towards 2 based on the assumption that only bending stiffness is relevant.
  • Another participant suggests that the first attempt at determining degrees of freedom is better, implying a preference for the scenario with 6 degrees of freedom.
  • A participant questions the reasoning behind the number of degrees of freedom, considering small vertical and horizontal displacements in fixed cases as potentially negligible.
  • Another participant introduces the possibility of 4 degrees of freedom, suggesting one vertical and one rotational degree of freedom at each node, while questioning the absence of horizontal degrees of freedom.
  • A participant inquires about the moment of inertia value for the elements, indicating a need for specific parameters in the analysis.
  • One participant clarifies that the elements have general properties (E, I, L) and emphasizes that the number of degrees of freedom affects subsequent calculations like equations of motion and natural frequency.
  • Another participant acknowledges that while axial deformation could be included, it would likely be negligible, supporting the second attempt in the initial post.

Areas of Agreement / Disagreement

Participants express differing views on the number of degrees of freedom, with no consensus reached. Some support the idea of 2 degrees of freedom, while others advocate for 6 or even 4 degrees of freedom, indicating an ongoing debate.

Contextual Notes

The discussion lacks specific values for moment of inertia and other parameters, which may influence the conclusions drawn about degrees of freedom. Additionally, assumptions regarding the neglect of axial and shear resistance are not universally accepted.

Pooty
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I have attached the problem drawing. Please refer to it. This is a lumped mass structure and all elements have the same Modulus of Elasticity and Moment of Inertia.

Determine the number of degrees of freedom of the structure

So I am thinking between 2 different scenarios. 1 scenario where it has 6 degrees of freedom and a second scenario where it has 2. I have attached my attempt on the same picture. Since the problem statement didn't include anything about the element areas, shear areas, or radius of gyration I think we can ignore axial and shear resistance. We are only taking bending stiffness into account... correct? So I am leaning more toward the 2nd attempt of only 2 degrees of freedom. Both rotational degrees of freedom at the nodes where the columns connect to the upper beam. Does this seem logical or do you see something else?

Thanks everyone
 

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I think your first attempt is better.
 
Any reasons? I considered it because I felt like if the beam deflects, there will be very small vertical and horizontal displacements. However, usually for fixed, fixed cases we never really take in account those displacements since they are so negligible. Right? I am really trying to understand why it would be one of the 2... or maybe even something else?
 
Wait, what if it was 4 degrees of freedom. 1 degree of freedom in the vertical direction at each node and 1 degree of freedom in the rotational direction at each node? NO HORIZONTAL Degrees of Freedom? Maybe?
 
What moment of inertia value is given for the elements?
 
Last edited:
It's all just general. Each element has Modulus of Elasticity "E" Moment of Inertia "I" and the lengths are just general "L" I have a lot of problems that I need to solve for this diagram (i.e. Equation of Motion, Natural Frequency, and Mode Shapes) but they are ALL dependent on how many degrees of freedom there are
 
You could assume the element cross-sectional area is A. Then you could include axial deformation. However, like you said in post 3, axial deformations would be relatively very small, and thus negligible. Therefore, your second attempt in post 1 seems correct.
 

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