Question on Number of Degrees of Freedom in a Simple Structure

[Pooty]

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

 

[nvn]

I think your first attempt is better.

 

[Pooty]

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?

 

[Pooty]

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?

 

[nvn]

What moment of inertia value is given for the elements?

 

[Pooty]

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

 

[nvn]

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.