Deflections and AREMA Design 2

[anominal]

I'm stepping into the world of Rail Bridge Design and the daunting AREMA manual.

The Cooper E-80 loads that we design the bridges for are irregular. AREMA has done us designers a favor and tabulated the maximum moment that your primary members would see for most simple spans:

HOWEVER, most design in the rail world is deflection controlled instead of strength.

While envisioning the moving Cooper E-80 load, my brain comes to a screeching halt:

1. Does maximum deflection and maximum moment occur at the same engine position on the bridge?

AND

2. Without using STAAD is there a less than rigorous way of calculating the deflection?

I ask because my superiors are questioning whether I know what I'm doing in STAAD and want to see some hand calculations. Not only that, some here are asserting there is a simple way to do it using the maximum moment given in AREMA and I just don't believe them.

 

[IJR]

ustationchump

Think about the following:

If AREMA shows where wheel loads are for maximum span moment, then that wheel load configuration is likely to give you max live load deflection.

I would treat that load as if it is uniformly distributed and use statics to determine deflection. If you have negative moments too, then treat the span as simple, find deflection delta1, then treat the span as loaded only by the negative moment, find delta2. Algebraic differences should give you a close estimate.

Dont know what load factors are used in Arema for deflection. Have a look at that.

respects
ijr

 

[Stillerz]

sounds like a good problem for STAAD's moving loads facility.

 

[cntw1953]

Refresh your memory on influence line due to moving load may help you to clear the air.

 

[anominal]

I cheated... found the location of the Engine to produce the maximum moment using STAAD and then calculated deflection using super-position and some AISC beam formulas, hopefully this is sufficient.

IJR:
AREMA does not show the location of the Axle Loads, only gives Maximum Moment.

Stillerz:
It's was a great problem for that however I'm working with a few senior employees for the first time... and they're lacking confidence in STAAD and myself (I'm the new kid on the block).

cntw1953:
Plan B.

Thanks everyone

 

[graybeach]

Since you have simple spans, you could just do a few iterations and get a good answer. I have made spreadsheets for this very problem and just kept copying and pasting the load pattern at different positions. Good for your senior employees to as these questions. Personally, I like using STAAD for simpler problems because you can easily print out the entire input and output. This makes it easy for someone else to check your work. This may not be so easy when using the moving load feature because you will get a lot of output, but you should check STAAD carefully. I got some really weird behavior some years back using their moving load feature.

 

[Stillerz]

One thing that might convince them is showing them the moves moving along the beam in Post-processing and graphically showing the moment diagram as you cursor down thru the load cases STAAD has porduced.

STAADS moving load facility works very nice for this...I use it for crane runway analysis quite often.

 

[Stillerz]

Also, Pg 3-226 of AISC 13th (as well as AISC ASD 9th pg 2-310), last paragraph explains where to place moving loads for max moment on simple spans.
This might be an over-simplification of what you are doing; I dont know.
For me, it helps to sketch out the loads ...helps in understanding what the text is saying.

 

[cntw1953]

Another topic to review is how to find location of "Absolute Maximum Live-Load Moment'. A very simple, yet helpful method by hand.

 

[Stillerz]

indeed, cntw1953, would you please refresh us?

 

[BAretired]

If you just want an approximate value for deflection, knowing only the maximum moment, you can narrow it down pretty easily for a simple span.

For a uniform load, [Δ] = ML²/9.6EI

For a concentrated load at midspan, [Δ] = ML²/10EI

For constant moment across the entire span, [Δ] = ML²/8EI (it can't be more than that).

My best guess would be half way between uniform and point load, i.e. [Δ] = ML²/9.8EI

BA

 

[desertfox]

Hi uStationChump

Look at page 53 of this link it might help:-

http://books.google.co.uk/books?id=...k_result&ct=result&resnum=10&ved=0CDoQ6AEwCQ#

desertfox

 

[cntw1953]

1. Find resultant force (RF) of the wheel loads.
- Use the wheel loads on each side of the RF to position the wheel load pattern that will yield max M:
2. Position the wheels so centerline of the simple span fall in the MIDDLE of one of the wheel load and the RF, calculate moment under this wheel.
3. Repeat step 2 for another wheel (ie: re-position the wheel, and get moment under that wheel), and compare the two results.

Now you got the max moment and location of the wheels (pattern) that produce it.

Hope this is clear. Best reviewed in elementary "Structural Analysis" textbook with graphical expressions.

 

[desertfox]

Hi uStationChump

Try this link its better than the last one I posted:-

http://books.google.co.uk/books?id=...zgK#v=onepage&q=moving loads on beams&f=false

desertfox

 

[desertfox]

Hi uStationChump

If you have two wheel loads a fixed distance apart, workout the resultant load of the two and the position it would take up between the wheels.
Position this resultant line of action of the two loads at the centre of your beam, this will give you the position of the train for the maximum bending moment, then revert back to taking moments on the beam using the individual wheel loads this will yield the maximum bending moment on the beam.
Then use superposition or Macaulay's method to obtain deflection.

desertfox