(Originally posted on 2016-11-19)
A barrel roll is a 1g maneuver. If done right, there's no stress on the airplane, or more accurately, the stress is identical to that of not doing any aerobatics at all.
It's so gentle that that late Bob Hoover doesn't even spill his drink while pouring it:
Here's Tex Johnston's famous Boeing 707 Dash-80 Prototype Roll:

By Boeing Dreamscape (Flickr: Dash80TaxiTestK62712-5) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons