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 system (e.g., RC shear wall, RC core). The matrix equations models offer a reliable and idealized tool for introducing two-dimensional and three-dimensional cantilever structures to control engineering and structural dynamics' equation-of-motion. The displacement-related stiffness matrix of cantilever elements is determined using the Left Riemann Sums (LRS) numerical integration method that yields transformation matrices that cater to the element's boundary conditions. The three-dimensional structure's mass and stiffness matrices are determined using the Direct Stiffness Method (DSM) and local-to-global-coordinates transformation matrices. 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 that suit state-space, equation-of-motion, and phase plane analyses.

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Posted 10 Jun, 2021

###### No community comments so far

###### Reviewers invited

Invitations sent on 06 Jun, 2021

###### Editor assigned

On 26 May, 2021

###### First submitted

On 25 May, 2021

Posted 10 Jun, 2021

###### No community comments so far

###### Reviewers invited

Invitations sent on 06 Jun, 2021

###### Editor assigned

On 26 May, 2021

###### First submitted

On 25 May, 2021

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 system (e.g., RC shear wall, RC core). The matrix equations models offer a reliable and idealized tool for introducing two-dimensional and three-dimensional cantilever structures to control engineering and structural dynamics' equation-of-motion. The displacement-related stiffness matrix of cantilever elements is determined using the Left Riemann Sums (LRS) numerical integration method that yields transformation matrices that cater to the element's boundary conditions. The three-dimensional structure's mass and stiffness matrices are determined using the Direct Stiffness Method (DSM) and local-to-global-coordinates transformation matrices. 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 that suit state-space, equation-of-motion, and phase plane analyses.

Figure 1

Figure 2

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Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

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Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

This preprint is available for download as a PDF.

This is a list of supplementary files associated with this preprint. Click to download.

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