An apparatus for determining the weight on a drill bit and axial forces along a drill string drilling though an earthen formation. The apparatus comprising an LVDT incorporated into a torsional bearing of a magneto-rheological damping system such that the LVDT senses the relative displacement and accelerations between a bearing mandrel portion and a bearing casing portion of the torsional damper. The LVDT is calibrated with respect to a spring in the damping system that resists relative motion between the bearing mandrel and bearing casing such that the output of the LVDT can be transformed into the force associated with the weight on the drill bit, and the same LVDT accelerations combined with the mass distribution along the drill string to determine axial stresses.