Analytical solutions of horizontal displacement for the dual structure consisting of flexural-shear substructures and flexural substructures

A calculation method of horizontal displacement was studied for the dual structure consisting of flexural-shear substructures and flexural substructures.The flexural substructures are regarded as flexural cantilever walls which exhibit a predominantly flexural behavior,and the flexural-shear substructures are regarded as Timoshenko cantilever walls which exhibit a mixed flexural/shear behavior.On the basis of the above assumptions,a differential equation was established for calculating the displacement of the dual structure.With boundary conditions,the analytical solutions of the displacement,including the flexural deformation,the shear deformation and the total horizontal displacement,were derived when the dual structure was subjected to uniform loads.The relation between the dual structure consisting of flexural-shear substructures flexural substructures and that consisting of shear substructures flexural substructures was discussed,and the result shows that the later can be viewed as a special form of the former where the flexural stiffness of the flexural-shear substructures tends to infinity.