How to calculate the magnitude of force when some force is applied at far away distan

The concept of "static equilibrium" or "dynamic equilibrium" applies to finding forces and moments in a body. Basically, to find the resultant forces and/or moments at a location far from where they are applied, you add all forces and moments up in the directions they are applied.

For example, a force applied perpendicular to a line that runs from the point of interest to the point where the force intercepts that radial line, creates a moment around that point equal to the length of the perpendicular line times the force. The force also produces a direct force on that point in the same direction and the same magnitude as the force.

Here's a few web sites that goes over some of this stuff.
http://www.uvi.edu/Physics/SCI3xxWeb/Structure/StaticEq.html
http://www.bsu.edu/web/jkshim/bm/kinetics/externalforce/externalforce.htm
http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l3c.html

Or just google "static equilibrium" or "dynamic equilibrium"