Question on Number of Degrees of Freedom in a Simple Structure

In summary, the conversation discusses the determination of the number of degrees of freedom for a lumped mass structure with uniform properties. The two scenarios considered are 6 degrees of freedom and 2 degrees of freedom, with the latter being the more logical choice due to the negligible vertical and horizontal displacements. The possibility of 4 degrees of freedom is also mentioned, but it is concluded that the second attempt with 2 degrees of freedom is the most accurate. The value for the moment of inertia is not specified and is considered general, but it is noted that it will affect the calculations for the equations of motion, natural frequency, and mode shapes. It is also suggested to assume a cross-sectional area for the elements to include axial deformation, but it
  • #1
Pooty
32
0
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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  • #2
I think your first attempt is better.
 
  • #3
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?
 
  • #4
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?
 
  • #5
What moment of inertia value is given for the elements?
 
Last edited:
  • #6
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
 
  • #7
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.
 

FAQ: Question on Number of Degrees of Freedom in a Simple Structure

What is the concept of degrees of freedom in a simple structure?

The concept of degrees of freedom in a simple structure refers to the number of independent ways in which a structure can move without being constrained. In other words, it represents the number of variables or parameters that can be changed without affecting the overall stability or functionality of the structure.

Why is it important to consider the number of degrees of freedom in a simple structure?

It is important to consider the number of degrees of freedom in a simple structure because it affects the overall stiffness, stability, and strength of the structure. A higher number of degrees of freedom can result in a more flexible and less stable structure, while a lower number can result in a more rigid and stable structure.

How is the number of degrees of freedom determined in a simple structure?

The number of degrees of freedom in a simple structure can be determined by counting the number of independent movements or variables that are allowed in the structure. These can include translations, rotations, and deformations in different directions.

What are some factors that can affect the number of degrees of freedom in a simple structure?

The number of degrees of freedom in a simple structure can be affected by various factors such as the type of material used, the geometry and shape of the structure, and the type of connections between different components of the structure. These factors can influence the overall stiffness and flexibility of the structure, and therefore affect the number of degrees of freedom.

How does the number of degrees of freedom impact the design and analysis of a simple structure?

The number of degrees of freedom is a crucial factor in the design and analysis of a simple structure as it determines the structural behavior and response to external forces. It is important to consider the number of degrees of freedom in order to ensure the structural integrity and functionality of the structure, and to make accurate predictions and calculations in design and analysis processes.

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