I'm not familiar with the formula... you have a Mf = Ff*(l1+l2/2) and this is resisted by lw * Vw *l2 (Vw is the unit capacity of the weld) and you have to resist the horizontal component due to the force itself and this is included in the force from the moment. You calculate the forces on the bolts by simple statics... you also should include for prying action... likely, for small loads, your plate will be approx 12mm (1/2") thick. Also, the moment on your handrail will be increased by the increased length l1 and often normal handrail sizes get 'bumped' up by a size or two.
Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?
-Dik