Torsion bars

[Burdar]

Left and right only.  The bar still twists the same direction no matter which end is front or back.

[cataclysm80]

Imagine if you put them in backwards, you would have the torsion bar unload the opposite way.

Instead of providing an upward pressure, you would have downward pressure on your suspension.

Not quite. 
The bar itself isn't installed with any preload and doesn't apply pressure.
What the bar does is resist the weight of the vehicle.
The weight of the vehicle is pressure applied to the bar, and the bar will always try to twist against this pressure in an attempt to get back to its original unsprung state.

[usraptor]

Left bar is marked "781" and right bar is marked "780".  Anyway, thanks for all the opinions/advice.   

[Cuda Cody]

781   #1857781 Left Torsion Bar 41" x .92" (426 Hemi & 440)
780   #1857780 Right Torsion Bar 41" x .92" (426 Hemi & 440)

Left bar is marked "781" and right bar is marked "780".  Anyway, thanks for all the opinions/advice.   

[screamindriver]

Left bar is marked "781" and right bar is marked "780".  Anyway, thanks for all the opinions/advice.   

A general rule with mopar part numbers :Left is  an odd part number.... Right is  an even part number...That's a quick way to ID a part that is'nt readily marked for "left or right" in an application...

   It's more important to make sure you dress {as in feather edge} any chips in the paint on a torsion bar and repaint...Supposedly even a nick in the paint can create a stress point where the bar can crack...With that being said I've never seen one fail with that being the absolute cause...
  Resto tip : Paint the bar completely nice and thick then set them horizontal on some saw horses...The factory finish had paint runs/drips from the bar and can be seen when installed..

[HP_Cuda]

What I should have said is good luck installing them on the wrong side because of the clocking.

Has anyone successfully installed a L bar on the right side?

Imagine if you put them in backwards, you would have the torsion bar unload the opposite way.

Instead of providing an upward pressure, you would have downward pressure on your suspension.

Not quite. 
The bar itself isn't installed with any preload and doesn't apply pressure.
What the bar does is resist the weight of the vehicle.
The weight of the vehicle is pressure applied to the bar, and the bar will always try to twist against this pressure in an attempt to get back to its original unsprung state.

[anlauto]

Has anyone successfully installed a L bar on the right side?

Yes...in 1993 in a Duster. Some lessons you only need to learn once.

[HP_Cuda]

I meant in an ebody but wow that must have been painful.

[HP2]

The index on the hex determines left/right, but Chrysler used part numbers as explained in earlier posts. There is no front or back, because the indexing, while different from left to right, is the same with both ends on the bar, but again, Chrysler had the part numbers on the rear so they could be identified during line inspections.

[cataclysm80]

I think bars also had colored paint marks for quick identification on the assembly line.
Build those cars fast, no time to squint at part numbers. 

[HP_Cuda]

I really don't think you can get the torsion bars to go in to the LCA swapped L to R or R to L.

Unless you took a torch and heated up the bar and physically twisted them to get them in.