We present in this paper a theory for a continuum mechanics based beams and associated mixed finite element formulation for geometric nonlinear analysis. The kinematic description is directly derived by degenerating from the assemblage of the 3-D solid finite elements. The exact material position vector is given by enriching the torsional warping deformation with the corresponding warping direction. Thus, the Wagner strain is automatically and appropriately accounted. MITC formulation is adopted in order to circumvent shear locking and to improve nonlinear performance. We evaluate the remarkable nonlinear performance and the excellent modeling capabilities of the derived formulation through the means of several numerical examples.