Semi rigid diaphragm 2

[dougantholz]

I am trying to model a semi-rigid diaphragm in a finite element program. I am looking for very accurate results and would like some help.
The diaphragm is a standard wide rib 1 1/2" deck. But the shear deflection calculation uses a G' for the shear modulas, which combines a lot of factors in it. I am currently modeling using flat plate elements with a mesh that is about 5% of the total area. My idealized model (pined on one corner with rollers at the support nodes) doesn't deflect anywhere close to where the diaphragm design guide says it should. I have reduced the shear modulas so that it matches G', but it doesn't come close (off by more than a factor of 10).
I could sure use some help.

 

[austim]

Hi, dougantholz,

Is it possible that your software develops its own G from E and Poisson's ratio? It might be worth changing the diaphragm E as well, to see what happens.

 

[JAE]

We've attempted to do what you are doing on various 3D models. Essentially, we added the finite elements to correctly model the behavior of the diaphragm so we could design the supporting beams and columns and distribute lateral loads properly.

For a given steel deck spanning a distance L and extending a depth B(parallel with the applied load), the maximum lateral diaphragm deflection at midspan is:

D = q x L^2 / (8 x G' x B)

where q is the lateral load in kips per inch
G' is the diaphragm stiffness.

If you try a particular deck, you can hand calculate the G' from the diaphragm charts provided by SDI or the manufacturer. Calculate D from the above equation using a distance L and depth B which is similar to your model. When you create your model, add you finite elements with E = 29000 ksi and G = 11,200 (for basic steel).

What we do is vary the finite element thickness. Compare your hand calculation under a unit load with the computer model under the same unit load, varying the thickness until the deflections are close. You now have a diaphragm that should behave pretty close to what the deck will provide.

Your calcs won't be perfect...there is a level of approximation and variation in deck behavior (second order buckling between the supports).

 

[dougantholz]

JAE,
Thanks for the tips. I have used the varied thickness of deck and E & G for steel, and I have also used the 1 inch deck varying the shear modulas. The G = 20 ksi seems to give me the most consistant answer (at least one that I can more easily justify mathematically).
What I think that I am running into is that the finite element plates are derived using beam theory, with varying levels of shear deformation accuracy (often ignored in classic beam theory).
What I would like to do is to get the stiffness right so that I can model a 3-sided box correctly. Does any one know of a program that models the finite elements correctly for shear deformations, especially along non-orthagonal axis.
I need a way to do this, if by hand or by computer. So if ANYONE can give me guidence, it would help.
Thanks
Doug.

 

[StephenEd]

When you day a three-sided box, do you mean a tunnel of sorts?

 

[dougantholz]

Three sided box means a building with lateral support on three sides, and the fourth side has to be supported by the torsional rigidity of the diaphragm.