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AREMA Rocking Effect Question

AREMA Rocking Effect Question

AREMA Rocking Effect Question

(OP)
Hi all,

I just had a general question about the calculation of the AREMA rocking component of impact in beam spans, particularly as shown in an example of John Unsworth's "Design and Construction of Modern Steel Railway Bridges." As shown in the attachment (hopefully), the cross-section in question shows 5 beams spaced at 2'8", and the rocking overturning couple is resolved to the center of the outer two beams on either side (8' between resisting beam groups), which results in a (0.2W)*(5')/(8') = 0.125W resisting couple. Unsworth then says this is translated into a rocking impact of 12.5% -- but isn't it the case in this example that as far as vertical effects, each of the 5 beams would be assumed to take (2W)/5 = 0.4W. So now, if you have a 0.125W force resisted by 2 beams (0.0625W/beam), the percentage of this effect would be 0.0625W/0.4W ~ 15.6% rather than 12.5% (unless we were neglecting the center beam's participation in the vertical resistance as well for some reason such that each of the outer beams is taking 0.5W instead of 0.4W)?

Usually in my office we calculate these effects using a pile analogy/rigid cross-section analogy where the overturning couple is resolved as a function of the distance of the beam from the CL track and the "inertia" of all beams in the cross-section (which in this case would result in about 0.075W due to rocking compared to 0.4W of vertical effects in the outer beam ~ 18.75%), but I came across Unsworth's method and thought it was also reasonable, except maybe the final result he found.

Thanks!

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