Numerical Analysis and Parametric Study on Multiple Degrees-of-Freedom Frames

The design of multiple degrees-of-freedom frames is critical in civil engineering, as these structures are commonly used in various applications such as buildings, bridges, and industrial structures. In this study, a six-degrees-of-freedom beam-column element stiffness matrix was formulated by superposition of beam and truss elements stiffness matrices and was adapted to statically analyze indeterminate frame structures. The development of a numerical model for the frame structures was achieved using the finite element method in the current study. Also, the investigation of the effects of various parameters such as frame geometries, material properties, and loading conditions was conducted on the internal forces developed in the frame structures. Three different parametric study cases that presented the frame structures with varying geometries and loading conditions were analyzed utilizing this matrix approach for the sake of emphasis and to evaluate the flexibility and adequacy of this formula to analyze the indeterminate frames using the MATLAB software. The analysis method comprised the derivation of the system displacements employing the relationships between the stiffness matrix and fixed end forces as the force vector and taking the attained displacements, which would be transformed to the local coordinates to obtain the member forces. The computed results from the element stiffness matrix approach were further statistically compared with the results achieved from the finite element software (SAP2000) applying the analysis of variance (ANOVA). The statistical results showed a P-value > 0.05, which indicated a good correlation between the compared results and adequate performance for the derived beam-column element matrix formula method.