Dynamics: How to obtain Mode shapes of a 3D structure

[DimzK]

Dear all,

I have a burning question about Dynamics which I have had in mind for over two years since my graduation which I would like to ask you all.
I know that I can model a 2 storey 2d (that only has 2 mode shapes) frame manually by hand using (in one direction) using the below procedure and I have got my head around that:

What I do not understand is when we model a 3d frame structure in Etabs, it can analyse for 10-20 mode shapes include torsional modes. How does this happen?
Is it too hard to simplify this to understand the theory behind the matrix of Etabs? I thought Etabs lumps the masses of each floor just like how we do in hand calculations, if so , howcome Etabs has so many mode shapes?

Thank you,
Dimuth

 

[ThomasH]

Hi
In your hand calculation you have assumed that the two translations describe the possible movement of the frame. If you instead assume that each of the four top joints has two translations and a rotation that would give you 3 x 4 = 12 DOFs and 12 modes. If you work in 3d you have three translations and three rotations for each joint (6 x 4 = 24 DOFs).

And since each degree of freedom gives you one frequency and one mode shape you can have a lot of mode shapes.

I don't use Etabs so I can't be sure regarding how it works. But usually a "lumped" mass matrix means that the masses are lumped to the nodes, not necessarily a floor.

Thomas