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

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