Slab-beam stiffness matrix assembly

[StructMnguy]

Hi everyone,

I have a topic on my mind, Has someone ever seen the assembly matrix of a beam and a slab? Does Anyone know if there is a book that shows matrix algorithms used in structural software?
I'm curious about that.

Sorry for my writing but English is my second language.


Thank you,

StructMnguy

 

[ANE91]

Matrix Analysis of Structures by Sennett
Elementary Structural Analysis by Norris et al.
Structural Analysis by Kassimali has 1 chapter on it
Structural Analysis in Theory and Practice by Williams

 

[StructMnguy]

@ANE91 Thanks for the help!

Do you know exactly how a shell element and a bar element are assembled in the stiffness matrix?

 

[ANE91]

Bar element is the first thing you learn — 2x2 stiffness matrix. I don’t do plates.

 

[StructMnguy]

Yes @ANE91 , I know the first thing you learn is a 2x2 stiffness matrix.

But I'm looking for an example of the connection between the shell and bar stiffness matrix.

Thanks BTW.

StructMnguy

 

[Celt83]

The elements stiffnesses are summed based on degree of freedom, at this stage there is nothing unique about either element.

Matrix Analysis of Structures by Kassimali has pseudo code for up to 3D bar structures first edition of the book can be found relatively inexpensive online and covers the topic sufficiently.

A First Course in the Finite Element Method by Logan any edition of the book has a section that addresses plate elements.

 

[StructMnguy]

@Celt83 Thank you.

But have you ever seen a book or an example that covers the connection between a plate and a bar element?

BTW thanks for the books, I will check them.

StructMnguy.

 

[IDS]

You might find my attached conference paper of interest, relating to analysis of bridge decks. It doesn't go into details of the FEA matrix, but does look at alternative ways of modelling the interaction between beams and slabs, and compares results from alternative approaches.