Gough Thomas, who was a highly qualified engineer once wrote that the strain on the pin is about 1/3 of a ton, but did not elaborate on how he calculated it.
Calculating the strain would involve taking into account the Poisson effect of thick walled tubes contraction and expansion of the chambers, the force exerted by the recovery of the action body as well as the forward thrust of the charge going through the forcing cone etc.
The action body flexes back on firing, according to accepted theory. If it flexes back then it must recover and that recovery must by definition involve a rather powerful push on the barrels and through them on the cross pin.
More than calculations I would love to see a high speed film sequence of a double shotgun action during firing. That would give visual proof of what actually happens and not what is commonly thought happens.
