These deformation variables affect each other,and constitute one measurement in space,which divide into plane and height displacement.

At first, a rotational displacement equation for geometrically nonlinear structures is derived; and then the inner forces and lateral displacements of a sway frame are calculated by the displacement equation; an example has been given for comparing the inner forces and displacements between the second-order and firs.

This paper present the accurate displacement equation of beam subject to bending distortion, the error between accurate solution and approximation solution is analyzed.

A linear acceleration integral method and the FFT frequency-domain integral method are applied to transform acceleration time history to displacement time history respectively,which will be the ground motion excitations on the bridge structure.