I will add my answer to the others although the results will not be much different.
The way I see it the following parameters are the most important:
The worst case scenario for the bending of the beam:
Instead of the open handle (which is a four point bending), I would go for the close handle (which is three point bending). This is a worst loading ...
You can calculate the section assuming you are as strong as the world record holder for deadlift, which I think is 500kg.
Meaning any maneuver, even acrobatic, that can cause a force imparted by the bar on your hands greater than 500kg will cause you to lose grip and let go of the bar.
Assuming a distance of 40cm between your hands on the ...
Nothing fancy. Just mild steel.
Assuming you go with at least 1"/25mm diameter for ergonomic purposes, go with a wall thickness of 3/16"/5mm which already should be overkill.
At 6ft/2m long and 1"/25mm diameter, I am skeptical if 1/8"/3mm wall thickness will be sufficient. I doubt it would break but it might flex under dynamic load.
It depends on the loading conditions.
It's important to note that the stress concentrations can be intuitively understood as created by the load's need to deviate from the hole. The larger the width of the hole, the more the load needs to move to go around it.
If it's a uniform bi-axial load (your part is under tension/compression in both the X and Y ...