Spatial Nonlinear Finite Element Analysis Of Reinforced Concrete Specially Shaped Column Frames And Their Joints

The specially shaped column structure refers to a frame structure or a frame-shear wall structure using specially shaped columns.The specially shaped column structure has the advantages of avoiding indoor corners,increasing the use area of the room and reducing the weight of the building,which brings flexibility and convenience to the design and usage of the building.As a new structural form,the concrete special-shaped column structure has not been used for a long time,and has not accumulated enough engineering experience.Concrete is made of cement,sand,stone and so on.It is a building material with complex mechanical properties.It is obviously limited to analyze the stress and deformation performance of reinforced concrete structures and members by linear elastic theory and the limit state design method.Based on the spatial nonlinear finite element method,the elastoplastic deformation and crack development of reinforced concrete specially shaped column structures and members are studied to accurately reflect the actual properties of structures and components.The main contents include:(1)Based on the elastic mechanics and virtual displacement principle,the shape function matrix,element strain matrix,element stress matrix and element stiffness matrix of four-node tetrahedral elements are derived.The node displacement array and the nodal force array of the spatial frame element in the local and global coordinate systems are analyzed,and the torsional stiffness equation,axial tensile stiffness equation and bending stiffness equation of the frame element in the local coordinate system are derived.The element stiffness matrix of the frame element in the local coordinate system is obtained.The method of integration of all stiffness matrices has been analyzed.The above contents provide a theoretical basis for the meshing and finite element calculation of specially shaped column frame joints and frame structure models.(2)The constitutive relation of concrete under uniaxial compression is studied,and the element elastic matrix and stiffness matrix of reinforced concrete integral model are given.The von Mise yield criterion,loading-unloading rule,plastic strain flow rule and strengthening rule of concrete are analyzed,and the elastoplastic matrix of the element is derived.The coupled PMM hinge applied to the frame element is studied,and the rotation-moment curve of the plastic hinge is defined.The numericalsolution of nonlinear equations is discussed,and the solution steps of nonlinear problems are summarized.These contents provide a theoretical basis for the elastoplastic analysis of the specially shaped column structure and its components.(3)The Willam-Warnke five-parameter failure model is improved and four failure surface formulas for concrete are given.The smeared fixed crack model of concrete is studied,and the four constitutive matrices of concrete with cracks are given.Four joint models in different parts of the specially shaped column frame are constructed.Their cross-section forms,mechanical properties of materials are discussed,and they are meshed by four-node tetrahedral elements.(4)Perform static loading analysis on the four frame joint models.The crack formation and development process,and the failure mode of the joint under the action of monotonic loading are obtained.Draw their beam end displacement-load curves.The crack development and the stiffness change of the four joints under low-cycle load are analyzed.Compare the bearing capacity and ductility of the four joints.The results of finite element analysis show that the beam first breaks when the specially shaped column frame joint is loaded,and the joints satisfy the design principle of "strong column weak beam".(5)Three specially shaped column frame structure models with different heights are constructed,and the calculation formulas of the section bending stiffness,tensile compression stiffness and torsional stiffness of the beam and column are given.They are analyzed and calculated by Pushover inverted triangle horizontal loading method.The inter-layer displacement and the plastic hinge situation of the three models under different earthquake intensity,and their top displacement-base shear curves are obtained.The Park-Ang two-parameter damage model is improved,and the structural damage and corresponding inter-layer damage indicators are defined.The damage indexes of each layer of the frames are calculated.The Pushover calculation results and the Park-Ang model evaluation results are compared and analyzed.The research results show that the regular concrete specially shaped column frame has its weak layer mostly in the lower part of the structure;As the floor increases,the position of the weak layer rises;The higher the structural height,the more serious the damage under the same intensity earthquake;the structural damage mode belongs to beam-hinge mechanism.