Rotations

[caroengr]

I am designing the bearings for a railway bridge according to AREMA. I have been following AREMA Ch 15 but I am getting stuck on calculating the rotations. These are the variables I need to solve for but I am new at this so any help would be appreciated!
aL = Relative rotation of top and bottom surfaces of bearing about an axis perpendicular to the longitudinal
axis of the bridge—radians
aW = Relative rotation of top and bottom surfaces of bearing about an axis parallel to the longitudinal axis
of the bridge—radians

 

[BridgeSmith]

aL would be the rotation of the girders due to bending under load (change in slope of the bottom flange).

aW would be any torsional rotation of the girders at the bearing locations.

 

[caroengr]

Could you provide some more information on how I can calculate these? Thank you!

 

[caroengr]

Or if you know of any examples that would help me understand that would be greatly appreciated!

 

[BridgeSmith]

Are you doing the girder analysis by hand, or with beam analysis software?

If it's a simple span, aL can be calculated using the appropriate equation from this table:

aW will be determined by the lateral/torsional restraint conditions.

 

[caroengr]

Hi! I am doing the girder analysis by hand. Thank you I calculated the aL. Could you elaborate on determining aW by lateral/torsional restraint conditions? Thanks![pre][/pre]

 

[BridgeSmith]

You would need to account for any rotation due to twisting of the girders allowed by the diaphragms or cross frames (which is typically near zero if slip-critical connections are used).

You will also need to account for the out-of-level tolerance for the seat or masonry plate on the bottom. If the seat is allowed to be out of level by, say, 1/8" per foot, then you'll need to add 0.6 degrees of 'rotation' to account for the potential lack of parallelism between the bottom flange of the girder and the seat.