Torsional Stiffness (J or Ix) of a Prestressed Conc. Beam

[asixth]

Hi guys

I recently had a situation where I had prestressed concrete planks spanning 60' with a bonded slab topping spanning transversely. I had to make and assumption about how much torsion is taken by the prestressed beams and positive moment that is put into the slab that spans transversely. Initially, I just took down the torsion stiffness (J or Ix) of the beam by several orders of magnitude so it doesn't attract any torsion and throws all the moment into slab. My supervisor thought this wasn't the best way to model the structure so I started looking for more realistic values for the torsional stiffness. The value that I arrived at for a rectangular cross section was 0.2*x^3*y where x and y are the short and long dimension of the cross-section respectively. I will need to check how much torsion the planks attract and whether the cracking torque of the beam has been exceeded.

What are other peoples torsional stiffness they assume both pre and post cracking.

 

[rowingengineer]

Torsion, The one design item that will keep an engineer awake at night.
for Jt (torsion modulus), which i believe is diffrent to Ix.
I approximate with:
0.4*x^2*y for solid rectangular sections
0.4*Sum(x^2*y) for solid T-, L-, or I-shaped sections.
or use St Venant torsional stiffness can't rember the rules of the top of my head.





When in doubt, just take the next small step.

 

[rowingengineer]

These are all pre cracking
post cracking I have no input of benefit


When in doubt, just take the next small step.

 

[rowingengineer]

Just because I hate working on a Sunday, and hence love a distraction i have been able to go through my papers and found this article worth a read.

When in doubt, just take the next small step.

 

[asixth]

Rowingengineer,

Judging by your post I get the feeling that you are any Australian engineer. And the paper you uploaded was supervised by one of my old professor's at UQ.

The torsional modulus as called up in AS3600 (I haven't cross checked it with ACI or Eurocode) is for the torsional modulus (similar to the elastic modulus b*d^2/6). To convert the torsional modulus to the torsional stiffness it needs to be multiplied by x/2 (where x is the smaller dimension of a rectangular cross-section). This is consistent with most mechanics textbooks that will give a value of 0.2*x^3*y for square cross-sections.

Because concrete isn't an elastic material and the presence of cracking can affect the behavior quite significantly, I wanted to know how people treat torsion and what assumptions they make post-cracking. The torsion we are dealing with is not an equilibrium torsion so it isn't critical but I do want to make sure I have made the most correct assumption on the behaviour of the structure.

For example, when considering flexural stiffness, I will reduce the Iz to 0.6*Ig to account for cracking, do people do the same for torsional stiffness, I have a concrete design textbook written to Australia Standards that recommends a loss in 90% stiffness from the onset of cracking.

Also, some FE programs assigned the torsional stiffness J and I have seen others call it Ix, I did not want to create any confusion with the notations.

 

[rowingengineer]

asixth,
You are correct, I am an Australian engineer. Sorry about the confusion regarding Ix and Iz, was looking at a steel beam when I studied your post.
Your question is hard one with regards to the post behaviour because you have a deck, I assume this is a box girder or similar. There will be a reduction in stiffness like Iz something like 90% (asuming no extra torsion steel detailed) as you suggest if your beam is treated as a single beam however the reduction will not be as great due to the presences of the deck (assuming fully bonded. For example the strength of a beam subject to shear and torsion with a slab has been of debate for a while, ragan & Hall 1983 suggests 4 times the strength. Now do you have 4 times the stiffness? I don’t know but I find it Interesting.
As I said i really have no input of benefit but I do suggest the following references:
Hambly EC . Bridge Deck Behaviour
AS5100 suggests not more than 20% torsion stiffness for modelling.
Joe Wyche has written a lot of articles in regards to box girders, torsion/shear and modelling.
I believe the ACI has a number of good publications but the one i know of is Thomas T.C. Hsu 1973.

All this being said I would prefer to incease the torsion capcaity and not have to worry about torsion cracking.

When in doubt, just take the next small step.

 

[asixth]

I checked out AS5100 this morning and it does say to use no more than 20% of the gross torsional stiffness to account for the loss of stiffness after cracking has occurred. The commentary to the code also recommends this. I am going to set up a spreadsheet that calculates the cracking torque for the cross-section I have set up so I can determine if the section has actually cracked when loaded. Otherwise I am only going to use 20% of the gross torsional stiffness for the analysis.