In order to consider the effect of non-coincidence of torsion center and gravity center,the rectangular variable-curvature-box girder with vertical symmetrical axis is studied. Considering the influence of shear deflection and non-coincidence of torsion center and gravity center, the elastic equilibrium formulas are established. Based on deformation equations of the girder and the relations of inner forces and deformations,the flexure-torsion differential equations are developed. The equilibrium differential equations and Galerkin methods formulas for clothoid curved box girder are presented.