Matrix equations models for nonlinear dynamic analysis of two-dimensional and three-dimensional RC structures with lateral load resisting cantilever elements

• Published in: Nonlinear dynamics Vol. 111; no. 1; pp. 493 - 528
• Main Author: Shmerling, Assaf
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2023; Springer Nature B.V
• Subjects: Automotive Engineering; Bending moments; Boundary conditions; Cantilever members; Classical Mechanics; Concrete construction; Control; Cyclic loads; Dynamical Systems; Elastic properties; Engineering; Equations of motion; Flexibility; Lateral loads; Mechanical Engineering; Modal analysis; Nonlinear dynamics; Original Paper; Reinforced concrete; Seismic analysis; Seismic response; Shear walls; State space models; Stiffness matrix; Structural analysis; Three dimensional analysis; Two dimensional analysis; Vibration; Cyclic loading; Vibration and dynamics; Structural mechanics; Reinforced concrete structures; Nonlinear dynamic analysis
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-022-07852-2

In control engineering and structural dynamics, mathematical models such as the state-space representation, equation of motion, and the phase plane are matrix equations describing the system equilibrium. This paper develops novel matrix equations models for linear/nonlinear dynamic analysis of reinforced concrete (RC) buildings with cantilever elements lateral load resisting systems (e.g., RC shear wall, RC core). The models offer a new approach for introducing two-dimensional and three-dimensional cantilever structures to control the theory’s state-space representation and structural dynamics’ equation of motion. The development primarily addresses the stiffness and mass matrices. The proposed displacement-related stiffness matrix of cantilever elements satisfies the necessary conditions of symmetricity and elemental boundary conditions. The nonlinear matrix structural analysis employs a smooth hysteretic model for deteriorating inelastic structures, referring to the relation between the bending moment and the bending curvature through the bending stiffness. The parameters controlling the cyclic behavior regard a composite RC cross section subject to gravitational load and bending simultaneously. The paper includes four examples that exemplify the practical utilization of the matrix equations models in analyzing two-dimensional and three-dimensional structures of linearly elastic and inelastic properties. The four examples demonstrated the idealized applicability of the matrix equations models for modal analysis, pushover analysis, and inelastic earthquake response analysis.