Calculation Live load with Cooper E80

[Tran Anh]

Hi, I'm new student in university. I'm checking truss steel bridge railway (It was built 1900s). Before, i just did simple concrete bridge. So this is my first time i do truss bridge. When I read the live load, I don't understand how to apply live load cooper E80 on the bridge.

Are we must apply this train on all the bridge ?
Assumption: the span of bridge is 160 ft. So what should I do with Cooper E80 ?

If you have a example for this calculate, it's so nice. Thank for your help.
o----------------------160ft--------------------------o

[steve14]

There are two references you can use to answer your question. The first is the primary source for this calculation. American Railway Engineering and Maintenance of Way Association (AREMA) Manual for Railway Engineering Chapter 15, Steel Structures. 

This is the industry's manual of recommended practices for design and rating of steel structures. 

The other source is "Design and Construction of Modern Steel Railway Bridges" by John Unsworth, published in 2018 by CRC Press. John is the retired Chief Engineer of Bridges for Canadian Pacific and was chairman of AREMA Committee 15 which is responsible for creating and maintaining Chapter 15 noted above and was also president of AREMA.

I worked with John for many years at CP. He designed them and I built them.

[timz]

Think the general idea is...

A bridge with an E-80 rating is supposed to be good for a train of two (?) 2-8-0 locomotives pulling many four-axle cars, where each driving axle of each 2-8-0 weighs 80000 lb and each of the other axles (engine and train) weighs some percentage of 80000 lb. The axle spacings (engine and train) are specified -- same? spacings for any Cooper rating.

[Randy Stahl]

I think live load refers to moment , shear and floor in cooper equivilant ratings. As stated before AREMA has the charts and graphs. I almost always use examples from existing charts and graphs. 

[Overmod]

I was taught that it's 'inherent' in the idea of Cooper rating that it's like the cantilever analogue of ruling grade: the imposition of the complex test load at the least favorable point on the bridge structure for resultant stresses on the members and supports.  Personally I would also include a factor for dynamic loading which might in some cases represent a significant proportion of effective live load.

[Paul_D_North_Jr]

"+1" to steve14's comment above. 

The factor for dynamic loading varies with the length of the bridge. 

For E-80 loading, after the 2 ea. 2-8-0 locomotives and their tenders is a "continuous" live load of 8000 lbs./ ft. 

An 'influence line" is used to determine where to places the train loads for maximum structural load / usually maximum stress on a particular member. 

The whole subject needs about 2 - 3 semester long university level courses plus a seminar in AREMA loadings to be covered comprehensively.

- PSN.

[Paul_D_North_Jr]

A search for "Cooper E loading" will find a lot.

An illustration and some comments on the loading conditions can be found here: 

http://www.dot.ca.gov/des/techpubs/manuals/bridge-memo-to-designer/page/section-17/17-130.pdf 

The 2nd page has formulas for adding a percentage of the live load for impact for concrete structues only.  It refers to the AREA (now AREMA) specificaions for steel structures, which are similar in concept.  

Here's another diagram and a brief explanantion:

http://armytransportation.tpub.com/TI-850-02/Figure-7-19-Cooper-Load-Configuration-For-Bridges-112.htm 

- PDN 

[Tran Anh]

Thank you so much.

On the deck we have 2 rails, so Cooper E80 will divide 2 each rail. It is ok or not ?

For influence line, I will calculate at 1/4L, 3/8 L, 1/2L. But in here it have many loads, I don't understand how to calculate it. We must change cooper E80 to only one load or just push it on the line ?
Sorry the first time is always difficult for me.

[Tran Anh]

Thank you. I will find this book to learn more. I'm quite don't know this live load. Do you think cooper E80 like lane load in design normal bridge ?

[Tran Anh]

Do you have example for calculate by hand or word ?

[Overmod]

Tran Anh

On the deck we have 2 rails, so Cooper E80 will divide 2 each rail. It is ok or not

I think you are reading too much into this.  The AREA ratings are plainly longitudinal only (no allowance for transverse moments) and in that respect ought to be like lane ratings. 

Once you are done with the basic structure, you can go back and calculate peak transverse moments (e.g. resulting from the effective near-point loading on the two rails) or any effect of multiple-track structure.  I suspect these are relatively slight compared to effect of longitudinal loads and would be considered part of the factor of safety rather than explicitly included. 

It might be interesting to model an example bridge, using Cooper E rating assumptions, on a computer via FEM and see exactly how the effect of shock affects the validity of the 'rating'.

[Tran Anh]

Yes Overmod, That's exactly what I'm doing. I will model FEM and I will apply load in this. So I don't know exactly Cooper E80 working. For section transverse I have 4 I-beam so I will distribute this live load (Cooper E80) on this beam like this: I I I I 20% 35% 30% 15% I don't know It's wrong or not... So I must ask expert like you, Paul, Steve....

[Tran Anh]

@Overmod
That's exactly I will do. I have model 3D, so I will distribute live load on the beam like this:
1st I-beam: 20%
2nd I-beam: 35%
3rd I-beam: 30%
4th I-beam: 15%

In my case, I remove deck and apply load directly on the beam.
I don't know it's bad or good. So I want to ask experts like you, Paul, Steve...

[Tran Anh]

Thank Overmod, I want to model FEM to do it. Now I'm try to distribute live load on each beam. I have 4 beam so, 20% for 1st - 35% for 2nd - 30% for 3rd - 15% for 4th. I don't know it's wrong or can accept, so i wanna to ask expert like you, Paul, Steve...