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I'm no engineer but it seems to me that the above would be true for a stationary train but not for one in motion.

For a train going up the grade the loco drivers will apply force to the rails pushing the rail down the grade with a force equal to the force of the driver pulling the train up the grade. On the downhill trip the brakes, if used, will transfer some of the train's momentum to the rail and therefore to the bridge.

Not sure whether these forces are significant enough to require the downhill support to be stronger.

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