I read a few times that a knot can reduce the strenght of a rope, but I can't understand why this happens. Can someone explain me what happens to a rope tied with a generic knot and stretched? Is there a way to calculate the reduction of resistance from the form of the knot?
A knot always requires the rope in the knot to be curved. This increases the stress on the outside of the curved bit of rope, and decreases the stress in the inside. This increase in the stress in a knot means the rope breaks at a lower overall stress than a straight rope would.
This subject gives some nice research papers! For a comparison of the effect of the different knots on the weekening of the rope see http://iopscience.iop.org/1367-2630/3/1/310/fulltext/ (and have a look at the video showing the knot breaking the spagetti!)