Analytical Study Of Damaged Continuous Beams

Continuous beams are widely used structures in daily engineering.Due to perennial work or other reasons continuous beams may be damaged in some places.With the accumulation of damage,it is likely that the structure will be destroyed suddenly,resulting in major engineering accidents and loss of life and property.Therefore,the study of damaged continuous beams,including how to accurately determine the location and extent of damage,has become the goal of scholars.At present,the research on damaged continuous beams are mainly focused on the identification and detection of damages,but there are few reports on the theoretical research of their mechanical response.Analytical study on them can accurately grasp various mechanical responses of damaged continuous beams.In this paper,the static and dynamic problems of continuous beams with stiffness damage are studied by analytic method.Firstly,the static and dynamic problems of simply supported beam with damage are analyzed.The simply supported beam is evenly divided into periodic structure with n substructures,an equivalent periodic structure system is constructed,and the governing equation is established.Then,the U-transform method is used to decouple the governing equation and the nodal deflection expressions of damage elements and other elements of simply supported beam are derived.The influence of damage degree and location on the deformation of simply supported beam are discussed,and the analytical expression of natural frequency of simply supported beam is deduced.Next,the research is extended to the analysis of continuous beams with damage,and the influence of damage degree and location on the deflection of continuous beams are studied.Finally,the analytical expressions of deflection under three different end restraints are analyzed,taking the damage of middle span as an example.The convergence law of solutions under different conditions is also discussed.At the same time,ABAQUS,a finite element analysis software,is used to simulate the above problems,and the numerical results are compared with the analytical results.