Calculating reactions for multiple column pier 2

Hello!
I am a structural engineer. But, I have no experience in designing a bridge or have any understanding of calculating/distributing loads to a multiple column pier bridge.

The reference I have is "Bridge Substructure and Foundation Design" by Petros Xanthakos. I am trying to following the example in the reference, example 4-5 p. 261. But, I am having difficulty understanding the load distribution from the superstructure to the substructure/interior and exterior columns.

If anyone could explain to me the steps and how to calculate the loads to the interior and exterior columns, I would greatly apreciate it. Specifically, I do not understand the factors to get the shear/reaction and moment to the columns. Thank you.

 

[Qshake]

While I am familar with that reference, I am not familar with that example.

However, I will try to explain the process the best that I can. This, of course, means that I am assuming the load you are having most difficulty with is the live load distribution.

Please keep in mind that many engineers have different methods to do this and that all may be considered accurate (likewise a few may not!).

Looking at a non-skewed bridge, and beginning with the roadway width we must determine the vehicle (actually the axle) arrangement that will produce maximum reactions at the beams(stringers/girders) that will effect the maximum load to the concrete beam cap (flexure and shear) and to the column (compression).

You can determine the number of lanes to be loaded by dividing the roadway width by 10'. Use whole number. This will give the number of vehicles to be used (one per lane).

Look at how the stringers sit atop the concrete beam. Determine which beams have to be loaded heavily in order to produce the maximum flexural, shear, compression (column) and any beam overhang responses. Assume that a stringer sits atop the concrete beam between two concrete columns. Loading this stringer will produce a maximum positive moment in the concrete beam below. So place one wheel line right atop this stringer and place the second wheel line 6' from this load. Now using simple beam distribution calculate the reaction of the second wheel line (the 6' offset) on the adjacent stringers. This will include the first wheel line that is right over the stringer and thus the reaction of that stringer should be (P+kP) where P is the wheel line load and "k" is a fraction determined by simple beam distribution. For now you can just work with P. The second or adjacent stringer to the one with the entire wheel load will also have a reaction to the remaining fraction of the wheel line inbetween the stringers, and is equal to (1-k)*P. That is for one vehicle. As you can imagine, the largest load may be produced in loading the remaining lanes. Keep in mind that the closest a wheel line can be next to another vehicle is 4' by AASHTO. Remember six feet is the distance for the axle of one vehicle.

Once you have looked at a number of load cases and are satisfied that you have all the responses completed, tabulate them according to response - Max Positive Moment, Max negative moment, Max. Compressive load etc. And you might have several load cases to look at for each. You may now multiply these "P" by the apprpropriate reaction that results from a longitudinal analysis of the spans. Usually this will result in loading the support (bent) with one axle and the other two axles are in the span at 14' increments from one another. You looking for a single wheel line reaction so this value must take into account the live load distribution (s/5.5). Also you must use the multiple lane load reduction factors which are 100% for up to two lanes loaded at one time and 90% for three lanes and 75% for four or more lanes loaded.

Once you are done with the product of the "P"s for each load case and reaction and lane reduction the sum of those for a single load case must equal the number of "P" loads originally placed for that load case. So that there is a check in this procedure.

I hope this helps. If not write and we'll discuss it some more!

 

QShake,
Thank you very much for your response. What you wrote is very helpful. Now, I have some direction to start. I am wondering...do you have an example of a multiple column pier (one that breaks down the steps you depicted above), preferably a 3 or 4 concrete colum pier bridge, you've worked out or from some reference I maybe able to obtain? Thank you again.

 

[yakpol]

vbridge,

Here's some guidlines for Live Load analysis of Crossbeams from Washington State DOT Bridge Design Manual. It applies to column loads as well.


For concrete box girders, prestressed giders with hinged or fixed diaphragms, the superstructure dead load shall be considered as uniformly distributed over the crossbeam.

For prestressed girders or other type of girders sitting on the bearings, the superstructure dead load shall be considered as concentrated loads to the crossbeam at girder on web locations.

For concrete box girders, prestressed girders with hinged or fixed diaphragms, the live load shall be considered as the truck load directly to the crossbeam from the wheel axles. Truck axles shall be moved transversely over the crossbeam to obtain the maximum design forces for the crossbeam and supporting colums.

For prestressed girders or other type of girders sitting on the bearings, the live load shall be considered as concentrated loads to the crossbeam at girder locations.

The last paragraph refers to the method Qshake described.

Hope it helps!

 

[aun]

Qshake
Yr post is very helpful. But I still have a few questions to ask.
I have seen some examples using a uniform load, 0.64 kips(lane load ) with 6' width at right a top of capbeam instead of using a wheel line load. Also, the end of capbeam is not the constant depth,let say 3'-6" middle of beam to 2'-9" at the end, how would you design the reinforcement?
I used to calculate a 3 columns bent to compare with the Dot standard by taking a cap as a continuous beam with overhang and then determine the columns, resisting axial load and moment at top. I mean I did not do the frame analysis. and I found out that I used the same rebars as shown in the standard. Please comment my calculation.
Thank you.

 

[Qshake]

AUN,

Variable depth does nothing for the method as noted above. The cantilever section (usually tapered) from the last column to the end, simply meets the moment demand on it. Afterall, if it is a cantilever then it has no moment at then end and needs only meet minimum requirements of the particular DOT as well as allowing anchorage of the reinforcing. In most cases, the beams are constant depth. Even those that are not horizontal but have beam steps.

As for the uniform live load, this may be treated the same way, except that you can apply the uniform load across the 10' lane width for how many ever lanes you have or what load you're interested in. However, most engineers still employ the method above with the wheel lines as the lane live load is just a train of trucks bumber to bumber. The only difference is the reaction from the longitudinal analysis. Once you have this reaction you may go the computations noted above and multiply this reaction with the "P" values.

Either or it is still better than guesstimating from standards. Should you be asked to turn in the calculations your client may frown on this analysis.

 

[aun]

Qshake
it is what I was told. " if a column bent is not so tall that the wind load produces a large moment at top, you can determine it as a continuous beam." It is clearly not a good calculation but it's time saving. ( much simpler than the frame analysis)
Please comment

Thank you.

 

[Qshake]

Yes, I agree that it gives a good preliminary approximation and that from there many things can be determined based on overall geometry. But what about minimum and maximum dead and live load to columns to be used in conjunction with the noted lateral forces? How do you design columns?

 

Qshake and all,
I am trying to follow the steps you've outlined above. But, it is a little difficult to do unless you follow an example. The only example I could find and I am trying to follow is in "Bridge Substructure and Foundation Design" by Petros Xanthakos :

http://www.buildabout.com/forum.php?action=display&&item_id=51

I do not understand the load distribution and the process in the example. Please explain to me how to arrive at the numbers in the example. Thank you.