Calculating Shear Capacity: de with Harped Strand

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Josh Pruitt
Calculating Shear Capacity: de with Harped Strand

When comparing PGSuper’s calculated shear capacity with results from another prestress girder design program, the two get very different results. While designing girders with harped strand, PGSuper produces shear results with an extreme “dip” in capacity around the 10th & 90th points. This has been noticed in at least 3 different projects (Two WF girder projects and one DBT). I believe the problem is stemming from the method in which PGSuper calculates de.

The calculation of de is pretty simple when there are no harped strands, since none of the strands are in the compression zone of the member. Calculating dv would then be taken as the greater of: the Moment Arm (de – a/2), 0.9de, or 0.72h. The problem occurs when a girder has harped strands, and the cross section being investigated is located at a region where all of the harped strands are positioned above h/2. Since these strands are in the compression zone, PGSuper removes their contribution to Aps leaving only the Aps of the straight strands, which is correct. The problem is, when PGSuper is calculating de, it appears to be using the CG of the total prestressing group (both harped and straight strands). Unless I understand the code incorrectly, I think this is a mistake.

The PCI Bridge Design Manual mentions this situation briefly in Section 8.4.3.2:

“Any mild reinforcement of strand in the compression zone of the member, which is taken as one-half of the overall depth (h/2), should be neglected when computing As and Aps for use in this calculation. This is very important when evaluating members with harped strand, since near the end of typical beams, harped strands are near the top of the beam. Because of this, it is recommended that the straight and harped strands be considered separately in the analysis. It is the physical location of each strand that is important and not the centroid of the group”

Full text is available online at
http://www.pci.org/view_file.cfm?file=MNL-133-97_ch8_4.pdf

I guess I interpret that to mean that since the location of each strand is to be considered separately, and not the centroid of the group, then strands that are located above h/2 would be neglected from the Aps AND the calculation of the prestressing centroid (therefore de). Maybe this is an incorrect assumption, and PGSuper is correct, but it sure gives funny shear capacity diagrams!

Thanks for your help,
Josh

Rick Brice
Josh, Thanks for your

Josh,
Thanks for your excellent question. Think that PGSuper is computing de correctly. de is the location of the resultant tensile force (not the geometric centroid of the strands) when the girder section has reached its nominal moment capacity (See LRFD Figure C5.8.2.9-1). All strands are engaged when determining nominal moment capacity. It doesn’t make any sense to compute Mn for all strands when evaluating moment and then compute Mn again with only the strands below h/2 when evaluating shear.
If you look at LRFD Figure 5.8.3.4.2-1, the force T (which is the total resultant tensile force at nominal moment capacity) produces strain es. If you re-arrange LRFD Equation 5.8.3.4.2-4 you get an expression of force equilibrium. (EsAs+EpAps)(es) = T. This is an approximation of the resultant tensile force you get from the nominal moment capacity. The force T influences the angle of the diagonal cracks (theta) and the ability of the crack to transmit tension (beta). Defining the flexural tension side by measuring a line through the cross section at h/2 is another approximation to make it easier to estimate the net tensile strain in the section.
Some computer programs use concurrent Vu and Mu when computing the strain es. PGSuper conservatively uses the maximum Mu and Vu. This may explain some of the differences. Also, stirrups size and spacing has a lot to do with capacity. I often see “dips” in capacity where bar sizes change and spacing widen (usually around the 0.1L and 0.9L points).
If possible, can you please provide me with your PGSuper file and a side by side comparison of the various shear calculations in question? I’d like to see side by side values of Mu, Vu, Aps (total and below h/2), es, Theta, and Beta. This should help pinpoint the differences.
Thanks,
Rick
 
Richard Brice, PE
Software Applications Engineer
WSDOT Bridge and Structures Office

Josh Pruitt
Rick, In situations where

Rick,

In situations where there is no mild reinforcement in the bottom flange of the girder, isn’t the resultant tensile force located at the geometric centroid of the strands? This project (as typical to WSDOT W and WF girders) does not have any mild reinforcement in the bottom of the girder. The question is, when computing dv, should the location of the tensile force take into account just the straight strand, or include the harped strands when they are above h/2?

The PCI Bridge Design Manual has an LRFD Design Example in Section 9.4. When they calculate de in section 9.4.11.1.2 they use the equation: de = hc – ybs. In this case they take 80 – 4.22 = 75.78. As expected, hc equals the height of the girder + haunch + deck: 72 + 0.5 +7.5 = 80. The value of ybs is taken as the centroid of the bottom strand group only, excluding the harped strand group. This is where I think PGSuper is wrong.

The Design Example can be found here:

http://www.pci.org/view_file.cfm?file=MNL-133-97_ch9_4.pdf

I have attached a pdf printout of PGSuper output and an alternate programs output for shear capacity. Some of the dead load varies because the alternate program does not account for web end blocks and PGSuper does. The dead loads are within about ~5% and they should not affect the calculation of dv anyway, only the resulting strain. I have also attached the PGSuper file.

PGSuper says the moment arm at (0.1Ls) is equal to 57.843. This is much smaller than the alternate program which has a result of 75.5. PGSuper thinks that 0.72h controls, when in reality the moment arm (which should not include the harped strand while above h/2) should control. The alternate program includes some haunch in its calculation of h, and I would expect there may be a difference between the two programs of maybe an inch or two, but since they had such a drastic difference it was noticeable.

Additionally, in regards to your comment about the “dip” being caused by changes in the stirrup steel, obviously the reinforcement will affect the capacity; but if you ignore the steel altogether, and just look at the PGSuper output for Vc (as shown on page 6 of 14) the capacity of the concrete takes a huge dip at (0.1Ls) which does not make much sense.

Once again, thanks for your help!

Josh

Rick Brice
Josh, I'll look into

Josh,
I'll look into this.
 
One thing to note is that PGSuper is computing the nominal moment capacity (and thus de) using a strain compatiblity analysis. This can yield different results than the approximate method provided in AASHTO. This could also have something to do with the results.
 
The positions of the harped strand are spread out over the height of the girder near the ends. The strain at each level descrease as you go up from the bottom of the girder. We use the PCI Power Formula for the stress-strain relationship. This is a non-linear curve. As such, the CG of the prestress force is not at the geometric centroid of the strands. The strands closer to the bottom carry more force than the ones near the neutral axis. The approximate methods in the AASHTO code makes the assumption that the strands are located very close together and that it is sufficiently accurate to use the geometric CG. The nominal moment capacity equations in AASHTO were developed for mid-span where all of the strands are near the bottom. Those formulas don't do a very good job near the ends of beams.
 
Thanks for the details. I'll look into the differences and report back what I find.
Rick 

Rick Brice
Josh,   Can you provide me

Josh,
 
Can you provide me details as to how the alternative software computes moment capacity?
 
Thanks

Josh Pruitt
Rick, I've attached pretty

Rick,

I've attached pretty much a full report print out for the exterior girder which is controlling. Some of the dead loads (haunches, utilities, sacrifical wearing surface) may vary slightly between this and PGSuper. I was trying to quickly compare and haven't spent the time to fine tune both programs to eachother.

Josh

Rick Brice
Thanks Josh,   I’ve done some

Thanks Josh,
 
I’ve done some more investigating and what I have found is somewhat contradictory. I am in agreement with you that the differences are due to dv and de. I’ve gone through Example 13.9 in “Prestressed Concrete Structures” by Collins and Mitchell. In this example, all of the prestressing (above and below h/2) is used to determine jd (which is the same as de-a/2). However, if you look in PCI BDM Article 8.4.1.2 you’ll see that industry is very clear on this matter. “When determining de, only the steel on the tension side should be considered”.
 
I will embrace the wisdom of industry and update PGSuper to match. A new release is due out on May 1. I should have time to get this change code into the software.
 
Thanks for bringing this issue to my attention and working with me to resolve it.
 
Rick

Josh Pruitt
No problem! Thanks for the

No problem!

Thanks for the very quick responses and support.

Josh

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