Fragility analysis is of important in the evaluation of seismic safety of building structures under earthquake excitation.Such analysis usually involve a large number of dynamic time history analyses which indicate that the computational process is inefficient. This study focus on developing highly efficient dynamic nonlinearity analysis and collapse fragility analysis methods for frame structure. To this end， this study firstly use the fiber beam column element to establish the numerical model of the frame and use the inelasticity separated theory to model local material nonlinear behavior. The P-Δ effect is simulated by decomposing the corresponding geometric stiffness and formulating the decomposed stiffness as perturbation expansion form. Thus， a novel governing equation of fiber beam column element that can uniformly depict the material nonlinear behavior and P-Δ effect using a separated way is developed and it can be solve by adopting the Woodbury formula directly. Because the proposed method can avoid the repeatedly updating of global stiffness matrix in tradition method， the computational efficient is improved greatly. Then， to overcome the limitation of the dynamic Woodbury formula in the selection of time interval， a preconditioning mechanism and an adaptive scheduling mechanism for the coefficient matrices relating the implementation of Woodbury formula corresponding to various time intervals are established. Based on the above investigation， an adaptive Woodbury solution method for highly efficient dynamic nonlinear analysis of frame structure is presented. Furthermore， by incorporating the multiple-stripe method， a fast collapse fragility analysis method of frame structure can be developed. Finally， the proposed method is verified by a nine-story frame structure.