AASHTO 17th Ed. ASD for Concrete

[labeattie]

Hi all,

I'm working on a pretty simple bridge substructure, but am required to use the ASD provisions in AASTHO 17th Ed (2002). I'm not very familiar with this, as my previous experience and education focused on LRFD. With regards to the concrete design, I see that design for some limit states other than flexure (8.15.4 for example) there are some specification for applying safety factors to the more familiar (to me) LFD procedures for design. Forgive me if I'm missing something obvious, but there is very little guidance in 8.15.3 on designing for flexure in ASD. Does the straight line theory of stress and strain mentioned in 8.15.3.1 imply a linear stress distribution in a concrete beam? If so I'll need to ask a supervisor for an older textbook in WSD for beams. I expected to find a safety factor applied to a Whitney stress block type of design (used in LFD as far as I know), as I think ACI stopped using WSD long before this code's release. Any clarification would be greatly appreciated.

Thanks in advance,
labeattie

 

[bridgebuster]

Here's an old California DOH abutment design - using WSD. You're assumption is correct, WSD assumes a linear relationship.

 

[labeattie]

Thanks bridgebuster! I really appreciate it. It's hard to find ASD designs examples via google nowadays it seems. I haven't finished reading this yet, but I can tell it's going to be helpful. One preemptive question though. I'm designing drilled shafts with the abutment. I think 8.15.4 and its safety factor for combined flexural axial analysis may do the trick, but out of curiosity, how would one usually go about designing a circular cross section for flexure with WSD. I assume engineers aren't going to be finding the resultant and centroid of the stress distribution with double integrals. And i haven't seen this question addressed in what little WSD procedures I have come across so far.

 

[IDS]

I'm a bit puzzled by the US approach to limit state design. It's called LRFD design, as though only the strength limit state was included, but the codes have similar requirements for the serviceability limit state as other international codes. Deflection checks and crack width checks (amongst other things) are usually calculated assuming linear elastic behaviour for concrete in compression, and I assume text books still cover the procedures for carrying out these calculations.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[labeattie]

Hi Doug,

I love your excel site by the way. I just discovered it a few weeks ago. But our deflection checks are performed using either a moment area deflection method (uncommon) or an equation for an "effective moment of inertia" based on some interpolation factor between the gross section MOI and the fully cracked MOI (based on the applied load vs the capacity). Without getting into some pretty intense math, I've only seen this cracked MOI determined for rectangular sections. As far as I know (which admittedly might not be too much), the crack width equations are highly empirical. So neither have helped me with regards to WSD.

However I do understand the mechanics of RC with a triangular compressive stress distribution, but wonder how circular cross sections are commonly treated. Because I doubt most designers are doing the double integral to find the resultant and centroid of the stress distribution, or using some approximation technique, like using rectangular strips to approximate the circular segment. I'm thinking there must be some rules of thumb or simpler approximation techniques. Perhaps changing the cross section to some sort of representative square? Although that is just totally spit-balling. My WSD background and resources are few, so any insight is certainly appreciated. I guess AASHTO took a lot longer to accept ultimate design than ACI, and Alabama took even longer than AASHTO!

 

[jreit]

Not much WSD experience here either, but could you conservatively assume an equivalent square cross-section, by considering the largest possible square that could be inscribed within the circular pile?
The diagonal of the square would be equal to the diameter of the pile and each side would be 0.707d.
A very rough approximation, and might be too conservative because you lose 35% of the concrete cross-sectional area, but if your numbers work out, it might get the job done.

 

[bridgebuster]

I agree; use an equivalent square. That's what we did recently a bunch of circular drilled shafts for noise walls. We designed them as columns with moments then checked the shear capacity along the shafts. Everyone was OK with that approach.

 

[jreit]

@bridgebuster how did you treat the reinforcing steel within the drilled shaft?
Would you also need to reduce the area of the steel proportional to the area of concrete reduced to get it to fit within the smaller square cross-section?
It would depend on the amount of concrete and steel, but if so, it would seem as if a completely different square shaft would have to be analyzed, with the only link being that it had less capacity than the original circular shaft.

 

[bridgebuster]

@jreit: The way we did it has nothing to do with WSD. There was no reduction of area. The sides of the square are the square root of the circle area. The same amount of rebar is used. This is the way I've always seen it done. Granted for deflection it would be based on "I" of the circular section.

 

[labeattie]

Thank you all for the responses. I will keep the "equivalent" rectangle cross section in mind, but as I have already made a program that calculates circular cross section capacity with the whitney stress block, i will most likely just be using 8.15.4, where I just multiply those results by 0.35. But I was very interested how anyone else had approached the problem, so thanks! You all have been helpful as always.

 

[Waxwing]

Love WSD and still use it.

There are plenty of detailed and extensive books to download for free on Google books. Interesting stuff "bending and direct stress"; cohesion to calculate development length (very interesting to calculate the allowable concrete stresses on hooked bars); it's especially usefully for designing substructures.

AASHTO LFD only allows WSD for calculating moment and shear in beams without axial force. The other provisions are not really WSD, but calculating by LFD and than reducing by an artificially high loadfactor over phi, and then calling it "WSD".

Transforming a column into a rectangular section doesn't have anything to do specifically with WSD vs LFD/LRFD. I believe that method is probably still explained in ACI 318 (I don't have a current edition).