Bending Stiffness or Youngs Modulus 1

[ZeroStress]

Hello

I'd be grateful if someone could shed some light on my problem which is keeping me awake through the nights.

I am assessing a bridge deck and its construction is RC deck (280mm thick) spanning between the abutments (span is 7m). Fairly simple deck. The concrete is of 20.7N/mm2 strength. Here is the cross section of it. [URL unfurl="true"]https://imgur.com/dmCitvq[/url]

I am using a FE software (LUSAS) to analyse the deck by modelling the deck as thick shell.

The main rienforcement (longitudinal) is 22mm @ 150 CRS and the transverse reinforcement is only 10mm @ 300 CRS. As you can see the transverse reinforcement is pretty small. In accordance with British standards (dmrb CS 454), the longitudinal bending capacity would be 95kNm and the transverse bending capacity would be 9kNm.

Now, I want to model the deck in such a way that the stiffness in longitudinal direction is the usual stiffness of concrete which is given by the standard i.e. 25,589,000 kN/m2. However, I want to enter the transverse stiffness lower than the longitudinal one because the deck has relatively lower bending capacity in transverse direction. This would mean that the transverse distribution of the load effects will be limited which is true given the capacity in that direction.

And so I am struggling to work out what this transverse stiffness should be. Lets just assume that the bridge deck is made of longitudinal and transverse beam elements just like a grillage model. My understanding from the Euler-Bernoulli beam theory is that I can work out the bending stiffness of the section from the formula
σ = My/I. See my attached calculations.

Could anyone please advise me whether my calculations for the transverse stiffness are correct? If not, is there any other way to work out the stiffness in transverse direction?

Also am I correct in assuming that the Youngs Modulus E as in Euler-Bernoulli's beam theory is the same as bending stiffness?

Appreciate all your advises which may help me sleep better tonight.

Regards

 

[IDS]

Your calculations are incorrect.

You can’t just reduce the transverse stiffness in the weaker direction so as not to attract load. Especially not by the amount you are imagining.

I disagree, provided there is a valid load path (which there is) reducing the transverse stiffness will increase the maximum load in the longitudinal direction, which is conservative.

The calculated E value is based on the cracked stiffness, assuming a fully cracked section. Allowing for some tension stiffening could more than double the E value, but with such light reinforcement it seems better to me to use a very low value in the analysis.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

I think it (varying stiffness of concrete deck) is best to be carried out by grillage method then?

 

[IDS]

I think it (varying stiffness of concrete deck) is best to be carried out by grillage method then?

Well it would certainly be the simplest to implement, and given the uncertainty of the concrete behaviour, I think any added precision from a plate analysis would be entirely illusory.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Settingsun]

I suggest grillage as well. It will be easier to adjust the stiffness in the various directions to match the capacity, including the twist component (which causes xy moment that must be carried by both reinforcement directions).

I would also do an analysis with best estimate stiffness to see how much redistribution is needed. I once read that torsionless grillage deflection should preferably be limited to three times that of a grillage with torsion stiffness. Maybe something similar here. That's from memory; I can't find the source now.

How old is the bridge? That transverse reinforcement quantity seems a few code editions out of date.

 

[STrctPono]

ZeroStress,

Everyone thinks that slab bridges are easy to analyze but they can be quite cumbersome.... especially if they are skewed and the rebar is not oriented parallel with the direction of vehicular travel. It is hard to equally equate the demand with the capacity. Calculating the capacity is really straightforward and you do it based on a per ft (errgh per meter?) basis. Your force demand results from a finite element analysis using shell elements tells you nothing about what width strip to consider when integrating your stresses to get your forces... this comes from engineering judgement and perhaps some guidance from your code.

It certainly is possible to calculate your transformed section properties and then artificially modify the elastic modulus of your material by using an orthotropic material such that you can set the different properties in the different local directions. However, I have NEVER heard about this being done and I really don't think that this is a prudent approach. If you reduce the stiffness in the transverse direction, won't you actually be reducing the transverse distribution of the stresses and your force demand from LUSAS will show your strip width to have a higher force demand than if you had just left it alone. Also, in order to justify using the effective section properties, your concrete needs to crack in the transverse direction, which I am not convinced it will for this slab bridge. I think your transverse slab stresses will be quite low, maybe even below the modulus of rupture of the concrete. Those upturn curbs on the edges will provide stiffness and may draw load to them so I may be wrong but it's something that's pretty straightforward to check.

What's the reason for you approaching this analysis from this direction? Are the demands higher than the capacity and you're struggling to justify the existing design?

If your numbers are not working out currently, a grillage analysis is worthless. It's way too simplified. Has no ability to account for the torsional rigidity of the slab. You're working with IMO the premier bridge FEA software program on the market, LUSAS, and you should take advantage of it. The most difficult thing is making sure you can interpret the results correctly.

 

[STrctPono]

and given the uncertainty of the concrete behaviour, I think any added precision from a plate analysis would be entirely illusory.

I feel as if a lot of what we do when it comes to the analysis of concrete structures is illusory.

 

[Settingsun]

Is this for a serviceability check or strength check? The bending capacities you gave correspond to around 170 MPa reinforcement stress, assuming the reo is near the face rather than central in the slab.

 

[Settingsun]

I clipped this for another topic but it's (maybe) relevant here too. This is what IDS (Doug) was saying about the valid load path and why I propose a deflection limit after adjusting the stiffness values away from pre-yield estimates. Of course, if the structure works without reducing stiffness and without relying on the concrete in tension, no need. But, if the light transverse reinforcement is overstressed, reducing stiffness in that direction is how the structure will respond. The analysis is then trying to find whether the heavier longitudinal reinforcement is up to the task when less of it is active.