3D Beam transformation matrix?

[mlevett3]

Anyone have an online resource for programming the transformation matrix for a 3D beam (or better yet, frame) element? I can only find one which omits the rotation of the axis along the beam to describe how the major and minor axes are defined.

 

[IDS]

The spreadsheet here:
3D Beam

Has open source VBA code.

Look at the rigid_jointed function for code to set up a full 3D stiffness matrix.

The code is based on Fortran code in Programming the Finite Element Method by Smith and Griffiths, which is worth getting if you want to program this yourself.

There are also some on-line resources, but I'll need to look them up.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

Chapter 4 in the link below should have what you want:
Matrix Structural Analysis

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mlevett3]

Thanks both of you, the book is on order (I've seen it recommended often) and I've got the other materials until it arrives.

 

[rb1957]

check out MIT opencourseware as an online source of references and study material.

another day in paradise, or is paradise one day closer ?

 

[LRJ]

The link above by IDS does not work for me - it says the root object is missing. Could the link be re-posted please?

 

[IDS]

The link above by IDS does not work for me - it says the root object is missing. Could the link be re-posted please?

Both links work for me, but I have attached the pdf file from the second link.

The first link is to my blog. Please let me know if that is the one that didn't work.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[LRJ]

Sorry, I meant for the second link. The first link works fine. And thanks for providing the PDF.

 

[mlevett3]

Can someone explain the "alpha" angle in section 4.2.2.2 of the book IDS linked to earlier? That's a user input right?

i.e. If I have beam I want to input and I know the orientation of the section in space, then how do I come up with alpha? I can see it has something to do with the angle between some intermediate coordinate system and the principle axes.

 

[IDS]

Alpha is the rotation of the beam local axis system, relative to the global "horizontal" plane.

See:
Defining beam orientation in 3D

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mlevett3]

So if I'm understanding correctly, the most efficient (least irritating) method of inputting sections for a user would be for them to provide the principle moments and then the rotation angle (alpha) of the principle axes from the horizon (XZ plane)?

They should have all this information from a section analysis tool in the procedure where this simple 3D frame FEA computation will come into play.

 

[IDS]

So if I'm understanding correctly, the most efficient (least irritating) method of inputting sections for a user would be for them to provide the principle moments and then the rotation angle (alpha) of the principle axes from the horizon (XZ plane)?

That's the easiest way in a structural engineering context, where the rotation is usually zero. In other contexts it may be easier to define one of the planes of the local member axes with a third node, and calculate the rotation from that.

They should have all this information from a section analysis tool in the procedure where this simple 3D frame FEA computation will come into play.

Or have a database of standard shapes with the required properties that users can select from.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mlevett3]

Hey Doug,

I've looked through your source code of 3DFrame and it seems like to me there's a discrepancy in the second and third row of the rotation matrix between that code (R0 array) and Saoma's notes (eq. 4.39) which you linked to. It repeatedly uses something proportional to (x2-x1)^2+(z2-z1)^2 and yours is proportional to (x2-x1)^2+(y2-y1)^2. What is the reason for the difference?

 

[IDS]

mlevett3 - it's probably due to the convention used for the global vertical direction. Saoma's notes appear to treat Y as vertical, whereas my code has Z as the vertical direction.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/