Moving Load Lane Question

Thank you for the email.  Let me explain what I need to do first and see if you have better suggestions.

First of all, the model consists of 2 spans, and these 2 spans are supported by the abutment as shown.  The abutment consists of backwall, stem, and footing at the bottom.  I’d like to find the stress at the footing calculating from the concurrent vertical reaction FZ, longitudinal moment MY, and transverse moment MX.    

Per design criteria, we have to consider train longitudinal acceleration & deceleration load (call it LF) along with the live loads.  If there’s no live load, LF = 0; if there’s one lane loaded, there will be a constant value LF1; if there’re two lanes loaded, there will be a constant value LF2.  Values 0, LF1, and LF2 differ by quite a bit and thus affect the longitudinal moment MY. 

From modeling standpoint for the best compliant with the code, in the load combination I would define 0track (no moving load, no LF), 1track (1 lane moving load + LF1), 2tracks (2 lanes moving load + LF2).  

Below shows the result at the bottom of the footing from 2 loaded lanes.  In this model in the lane definition, I defined the max. and min. lane number as 2.  And I used the load combination as 2tracks (2 lanes moving load + LF2).  

From max. MX standpoint, 1 lane loaded creates max. torsion as shown, even I defined max. and min. as 2.  If strictly following the code, this max. MX from 1 lane loaded would only need to add LF1 for the footing design, instead of LF2 as defined in the load combination.    

Your second question brings up a very interesting point.  Consider max. MX case specifically:

1)      In my opinion. two lanes loaded: 

a.      MX + LF2

b.      MX is a bit smaller than max. MX from one lane loaded

c.       MX combined with LF2 may still control the stress at footing

2)      One lane loaded:  Max. MX + LF1

a.       This case can be obtained from one lane loaded only

This is the reason I am trying to separate the # of lanes into 0 loaded, 1 loaded, and 2 loaded cases, so that I can combine them with the corresponding LFs.  From what I have now I think it is conservative but acceptable. But I'd like to hear your thoughts on this - any better way to do this?

Thanks,

First of all, in your model, the whole span consists of just one long element. If we divide it into 10 elements and view the vehicle position for the span center, we can see that two lanes are loaded as shown below and the positions of the two vehicles will cause the maximum torsion.

This is the case for all elements except for the start/end point of the span for which one vehicle is located inside the span and the other vehicle is located outside the span so that maximum torsion can be found. We cannot say that this algorithm is incorrect. Rather, it is the widely accepted algorithm among a lot of practical engineers for a very long time. 

Secondly, we thought about your comment that two lanes must be loaded because the user entered 2 for both maximum and minimum number of lanes. Then, the following question arises. How should two vehicles be positioned on the two lanes inside the span? Is it case 1 or case 2 or case 3 and on what basis? We have not found the appropriate answer between ourselves.

Please understand that we cannot change the current rule of the program. If you let us know why you need to do this, we will try to find any workaround for you or we can consider this for the future development if there is no workaround.

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