A corotational finite element for large-displacement elastic analysis of semi-rigid planar steel frames is proposed in this paper. Two zero-length rotational springs are attached to the ends of the Euler-Bernoulli element formulated in corotational context to simulate the flexibility of the beam-to-column connections and then the equilibrium equations of the hybrid element, including the stiffness matrix which contains the stiffness terms of the rotational springs, are established based on the static condensation procedure. The linear and Kishi-Chen three-parameter power models are applied in modelling the moment-rotation relation of beam-column connections. The arc-length nonlinear algorithm combined with the sign of displacement internal product are used to predict the equilibrium paths of the system under static load. The analysis results are compared to previous studies to verify the accuracy and effectiveness of the proposed element and the applied nonlinear procedure.
Keywords: corotational context; Euler-Bernoulli element; large displacement; semi-rigid connection; steel frame; static analysis.
This paper presents the elastic large-displacement analysis of planar steel frames with flexible connections under static loads. A corotational beam-column element is established to derive the element stiffness matrix considering the effects of axial force on bending moment (P-∆ effect), the additional axial strain caused by end rotations and the nonlinear moment -rotation relationship of beam-to-column connections. A structural nonlinear analysis program is developed by MATLAB programming language based on the modified spherical arc-length algorithm in combination with the sign of displacement internal product to automate the analysis process. The obtained numerical results are compared with those from previous studies to prove the effectiveness and reliability of the proposed element and program.
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