Bridge load rating question

[bluetree]

Need some advice from any bridge engineers. Reviewing a bridge load rating report for a single span multi girder bridge for the std AASHTO truck loads. Bridge span is 26 ft and the width is 17 ft, single lane. Bridge consists of five W18x50 beams spaced at 3.96 ft, simple span. Deck consists of 8” th precast concrete deck planks. The ends of each plank are connected to only the exterior beams with shear studs. The planks only bear on the interior beams, there is no connection. There is no bracing from beam to beam, so the unbraced length of the interior beams is 26 ft, and they are the controlling member. The rating was performed using both the AASHTO Load Factor Design and Allowable Stress Design methods from the Std Specs for Highway Bridges manual. The report results using the LFD method give moment inventory and operating ratios of 0.4 to 0.7, so the bridge would have to be posted for lower loads. . The report results using the ASD method give moment inventory and operating ratios of 1.4 to 2.0, so the bridge would not have to be posted. The report summary concludes by ignoring the LFD results and using the ASD results, stating that the bridge does not need posting and has a capacity greater than the std AASHTO truck loading. There is no explanation on why engineer chose to ignore the LFD rating results.
The AASHTO ASD method seems very simplistic and does not address unbraced length with any degree of complexity. The LFD method seems to be a more extensive analysis method. The calcs appear to be correct and follow the AASHTO methods. Am I missing something here? Is one method better than the other? I am not experienced with bridge design and analysis. It makes no sense to me to have very divergent results, and then just go with the favorable result. Seems like poor engineering judgement at a minimum. Also, I did a capacity analysis of the bridge beams using the AISC ASD manual, and the results are similar to the AASHTO LFD results. Any suggestions?

 

[cap4000]

What is your max. moment??

 

[wiktor]

Both methods should provide very similar results, as the major difference in between LFD and ASD is application of the variable safety factors for different loadings versus 1.82 SF for allowable stress method.
So the rating should be almost the same for 40' spans, and lower for LFD for shorter spans, and higher for ASD for longer spans, where the DL participation w/ SF of 1.3 is smaller. In short, it's just different accounting philosophy.
In your case, the mistake is your assumption that the unbraced length is 26'. Buckling of the top compression flange involves rotation of the beam, or part of beam, which will be prevented by the planks bearing on the top flanges, so your beams are at list partially braced, as the flange under loaded plank will not rotate.

 

[bluetree]

104 ftk from the HS20 LL, and 37.7 ftk from the DL, not factored.

 

[bluetree]

wiktor, is that std practice to consider a steel beam as least partially braced by a concrete deck bearing on the top flange with no physical connection? seems by that logic no bridge of this type would need bracing, which does not seem to be what you see in practice.

 

[DWHA]

I am confused, how can you have shear studs connected to precast plank?

 

[Qshake]

DWHA - these shear studs can easily be accounted for by grout pockets that are open when placing the planks and then grouted for composite action. Recall that this is only on the exterior W sections.

It is not common practice to assume the WF beams as partially braced. If a large enough load were to cross the bridge the beams would simply rotate - no stopping that - short of mechanically fastening them.

While the methods should give similar results, they will differ. The newer 2008 Manual for Condition Evaluation of Bridges can offer some insight to this and should be consulted.

ASD is always thought to be the most conservative of methods available and that alone may have played a role in the originator's decision.

As a reviewer, it is well within your role to ask the originator to provide additional back-up or to explain his decision thoroughly so that you and your client understand it. There may very well be a mistake.



Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[wiktor]

Yes, it will be a standard practice to consider a beam to be partially braced by a bearing deck, even without physical attachment of the planks to the flanges.
This type of construction is commonly used in temporary or make up bridges where only outside beams are attached to the deck.

 

[cap4000]

Your moment of 104 k-ft seems low. Can you describe how thats obtained.

 

[miecz]

bluetree

I've run some quick and dirty numbers on your bridge, and it appears that the calculated ratings are correct. It is unusual for this magnitude of discrepancy between ASD and LFD, but in this case, the result is due to the assumed unsupported length. The rating under LFD is governed by Eq 10-103c, which has a similar format to the allowable stress shown in Table 10.32.1A.

Article 10.48.4 reads: Members not meeting the lateral bracing requirements of Article 10.48.2(c) shall be braced at discrete locations...Bracing shall be provided such that lateral deflection of the compression flange is restrained and the entire section is restrained against twisting. I don't believe precast deck on steel beams meets this definition of Bracing.

If this bridge were originally designed under ASD rules, then some DOTs will allow load rating under ASD. That may be why the designer took this route. However, seeing the magnitude of the discrepancy, I agree with you that it was a bad choice. If I were you, I would not sign off on this.

 

[bluetree]

thanks for everyones input. I found the reason for the discrepancy between the LFD and the ASD results. I guess I will describe it for anyone who may be interested. The ASD equation in Table 10.32.1A gives an allowable bending stress using Sxc, section modulus with respect to the compression flange, which is about 37 in3. In the report, when they calculated the inv and operating ratios they calculated the DL and LL bending stresses by dividing the DL and LL moments by the full Sx of the W18 beam, 89 in3. As a result, the DL and LL bending stresses are lower than they should be, resulting in inv and operating ratios well over 1.0. If you correct the DL and LL bending stresses using the Sxc value, you get ratios that match the LFD results.

 

[miecz]

I have to admit, I would have used Sxc=89in3. How do you get Sxc=37 in3? Where does AASHTO show how to do this?

 

[cap4000]

miecz,

I agree with you. Sounds like a grocery store math mix up. Whats worse is that there is no W18 bracing. Signing off on this design would be a huge mistake.

 

[bluetree]

I did not find in AASHTO how to calculate Sxc, it was done in the report. I have not come across Sxc before, but I do not use AASHTO much. It was calcuted in the report as below, and seems logical to me. I assume the AASHTO ASD method uses this lower value Sxc to account for lower beam capacity with large unbraced lengths.

Sxc = (1/12*b*d^3 + a*D^2) / D

b = 7.5" W18 fl width
d = 0.57" W18 fl th
a = 7.5 x 0.57
D = 9" - 0.57"/2 distance from fl centroid to W18 centroid

 

[paddingtongreen]

I have to join in on the unbraced length disagreement. The requirement is to prevent displacement or rotation. If a rigid deck is crossing it, it cannot rotate without vertical deflection to clear the underside of the deck. it must go through a higher stored energy of the vertically deflected shape to get to the lower stored energy of the buckled shape, it ain't gonna do it.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[cap4000]

paddingtongreen

Take a look at the LFD inventory rating of 0.4. That is the design level. Not good. If it was a slab that was poured I would agree but not precast planks.

 

[paddingtongreen]

That Sxc does not does not have an unbraced length component. It makes no sense to arbitrarily reduce it for all cases except continuously braced beams. The reduction should vary in some proportion with the unbraced length.


As an aside, we once looked at the frictional resistance to lateral beam deflection as a function of the load. By the time the unbraced length became critical, there was enough friction to resist with a good safety factor.

@cap4000, I trust precast, usually pre-tensioned, more than CIP, because there is better QC.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[cap4000]

I have seen testing done for poured slabs but not precast. The problem comes about when a heavy truck load deflects the beam and separates the flange from the slab. The friction must be strong enough to transfer horizontal shear stresses to brace the beam. I just don't see that working for a precast slab bridge designed for 75 to 100 years.

The Sxc looks somewhat like a composite slab design whereby the c represents the compression component of the slab and the entire steel beam is in tension or the Sxt. Just a guess about the section modulus values.

 

[paddingtongreen]

I see that miecz quotes "Bracing shall be provided such that lateral deflection of the compression flange is restrained and the entire section is restrained against twisting." so I'm shot down.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[miecz]

Cap4000 makes excellent points.

bluetree-

The formula for Sxc doesn't make sense to me. The numerator adds two components. The 1/12*b*d^3 term is the contribution to the moment of inertia of the flange about the vertical axis, while the a*D^2 term is the contribution of the flange to the moment of inertia about the horizontal axis.

paddingtongreen-

On AASHTO's definition of lateral bracing. I'm merely quoting AASHTO 10.48.4, which requires both. Not saying I agree with that, but if your have to meet AASHTO, DOT's tend to want you to follow the letter of the code.