any good book for modeling bridge? 1

Hi koo,

When I model a bridge, typically I do a grillage. This is a 2-d model of the bridge which excludes the cross-frames. The accuracy of this type of analysis has been shown, time and time again, to be the most useful for its simplicity. That being said there are things one needs to know in order to model the grillage correctly. Firstly the aspect ratio of the rectangles within the grillage, as well as the section properties of the combined deck and girders. For example the torsional properties of the deck within this combined section should be halfed to account for the two way nature of bridge decks.


Modelling by FE is, for most cases, beyond normal requirements unless you have a very unusual bridge. Typical short and medium span highway bridges don't warrant this kind of analysis.

HTH

Regards

VOD

VOD,

I've seen people mentioning this grillage method many times here, but couldn't find a detailed procedure other than concepts. I can imagine tranforming the composite deck into a grid of frame members that simulate the composite section properties, but when it comes to details, I am not sure how.

For example, you have a 40' simple bridge with 4 W21 girders spaced 6' apart, 8" conc. deck. Longitudinally, one can use the AASHTO defined effective deck width and transform the composite deck into 4 frame members; but transversely, how would you transform the deck into frame members? what effective width to use? I guess this is related to the aspect ratio you mentioned, right? say use 4' deck section properties in transverse direction(that would be 9 transverse grid lines) versus 5'? What aspect ratio you think is good?

koo,

Aspect ratios tend to reflect the span:deck width ratio. Typically for a long bridge, one uses a ratio of transverse grillage beams to the spacing of longitudinal grillage beams of 2:1. For wider, more square 1:1. There is no increase in accuracy below 1. Many bridges come in around 1.5:1. It is recommended to have an odd number of total transverse grillage beams.

In your case, you can use 10' transverse concrete sections. The end sections will have concrete section properties for a tributary width of 5'.

Regards

VOD

VOD,

Do you place the transverse grids in the same plane as the longitudinal girders? I mean, the N.A. of the deck is actually above the girders. How would this affect the accuracy?

2ndly, does it make a deference if you define the transverse grid members to be concrete sections or transform them into equiv. steel sections?

3rdly, when applying the moving load, do you apply it only along the girder lines or it can also on top of the transverse grids?

Many thanks.

koo,

1. Yes, the accuracy is more than sufficient.

2. I would not know as I have not done so, you may want to try both and see. However, when checking global deck moments, you would want results based on the torsional stiffness of the concrete deck.

3. This question is going to lead to deck moments. For deck moments investigate Westergaard analysis for local deck moments and combine with the global effects. For the grillage, the moving loads are applied to the girders only.

Regards

VOD

VOD,

very interesting. so when applying the wheel load, do you multiply it with impact and distribution factors? (I would think yes to both.)

Would you load multiple girders simultaniously and use the multi-lane reduction factors to the results, or load only one lane at a time?

Do you know any literature that deals with computer modeling in details?

VOD

koo,

When doing a grillage or FE analysis you will not use the simplified AASHTO distribution factors. The factors were derived parametrically in order to simplify a number of girders and lanes down to one single "effective" girder.

In order to distribute your wheel loads for a grillage, you will need to locate the worst-case transverse wheel locations on the transverse cross-section, this will become apparent, and calculate the girder reactions using an additive process for each deck span considered as simply supported. This simplification to simple supports has been proven accurate for the overall bridge compared to using a continuous span deck over the girders.

Yes, you will include impact.

Yes, you will load multiple girders simultaneously for 1, 2, 3, etc. lanes with appropriate multi-lane reduction factors, to find which one governs.

I do not quite fully understand your last question.

Regards

VOD

koo,

My previous response,

"Typically for a long bridge, one uses a ratio of transverse grillage beams to the spacing of longitudinal grillage beams of 2:1. "

Should have stated

"Typically for a long bridge, one uses a ratio of transverse grillage beam spacing to the longitudinal grillage beams spacing of 2:1. "

VOD,

thanks for your elaboration on the load distribution. It helps a lot.

My last question asked if you know any books/manuals that have instructions of the grillage modeling. I don't know how people, like you, learnt these nuances (e.g., aspect ratios, redueced torsional constant, etc.), from books, passed down by generations, or trial and error? I just want to find a good resource of modeling techniques.

Regards,
Koo

VOD,

regarding a skewed bridge, at about what skew angle, you would make the grillage perpendicular to the girders, 30deg?
If doing so, how do you model the 4 portions of deck at the corners, since they are not rectangulars?

if grid is parallel to abutment (not perpendicular to girders), the deck portions are parallelograms, should the deck width be corrected to the width that is perpendicular to the deck grid?

Koo

koo,

Do not model the transverse beams parallel to the abutment. In the areas of skew extend lines perpendicular to the girder from each of the bearings to the far girder. Do not draw transverse lines from bearing to bearing. Generally for angles less than 35 degrees, these perpendicular lines from every other bearing will do. This will define your transverse slab section size. End portions of the transverse slab fronting on the skew should be averaged.

To answer your question of how I learned this analysis, these were passed down to me like many other bridge engineers who were confronted with bridge design.

I would recommend you consult with an experienced bridge engineer in your office or a sub-consultant with regards to you designing a bridge.

Regards

VOD

VOD,

If would be nice to have somebody as knowledgeable as you in the office.

I found 2 books called Grillage Analogy in Bridge Deck Analysis and Bridge Deck Analysis. I'll try to get them. What do you thing the book called "Bridge modeling by microcomputer"? Is it a good one to have? It's out of print.

Many thanks.

Koo

Koo,

You need an experienced bridge engineer in your office. Personally I do not think this is the best way to go about bridge design. You need to solve this problem first. A company should not attempt this from a liability perspective. I understand this must be hard for you.

Anyway, to explain about the book "Bridge Analysis by Microcomputer". This book is from Canadian authors, who have adopted a different approach for load distribution factors. The approach is somewhat pioneering and it is continually improving its flexibility while maintaining its simplicity. This is the reason the book, which is the basis of our Canadian Bridge Code, is now out of print. New research and understanding has prompted revisions to various parameters within the text. If you need to understand the beginnings of the Canadian approach to understanding bridge structural response, give it a read from a library.

I doubt it will help you from a grillage perspective since the reaserchers' intent was to approach bridge design from the "simplified method" I alluded to earlier. AASHTO's and Canadian distribution factors were developed independently, approach parameters differently and thus cannot be used together.

Again, do your analysis, but have an experienced bridge engineer review your work!

Hope this helps.

Regards

VOD

VOD,

Is it normal for a highly skewed (60deg) bridge to give high (12kips) lateral load in a FE or grid model? Where does the lateral load come from, torsion? Thanks

Koo

VOD,
sorry, not sure it's 12k or not,but large. The lateral load is on the bearings. Besides breaking force could have a lateral component, what else could cause it? torsion, vertical load?

Koo

koo,

Are you modelling it as flat or placing it from bearing elevation to bearing elevation?

VOD

VOD,
I'm not sure. It's not my project. seems flat, because they couldn't figure out where's the huge lateral load come from...could be from a software bug. I asked just because I'm curious to see if there are things about skewed bridges that I'm not aware of. When I did skewed bridges, I used AASHTO load dist. guideline to get the more accurate load distribution factors for increased shear and reduced moment. But that is based on a line girder analysis. This one I am asking is a MDX FE analysis. I'm not aware of any lateral adjustment in AASHTO for skewed bridge.

Koo

koo,

If the FE analysis is accounting for slope along the road, then bearing elevations may be creating the lateral force. The anchor bolts at the lower end of the bridge can then be designed for the lateral force.

Make sure the end conditions of the analysis match the bearing design, ie. It is recommended to release most of the interior and exterior girder bearings for lateral movement since fixing all these bearings creates internal transverse deck forces due to temperature variations.

Regards

VOD

VOD,

It seems you suspect the lateral load could come from the slope. Is it possible for a skewed bridge to generate lateral load from its vertical loading? torsion?

BTW, I started modeling a small 2lane simple span bridge (38')in sap7. I got much larger reaction (1/5 more) and smaller moment (1/3 less) than the AASHTO based results. (sort like a deep beam?) I suspect it's the dist. factor made the difference, but it's a big difference. I didn't use a grillage though, I put shell eleement between girders and used the auto generated moving load in sap. I'll try model it as a grillage some time.

Koo