Abstract This work presents the analytical development of the stiffness matrix of a plane straight element with semi-rigid connections and its support reactions for three loading cases from the application of the Principle of Virtual Work. Semi-rigid connections are represented by translational and rotational linear elastic springs at both ends of the element, giving it six degrees of freedom. One example shows the application of this formulation using the Classical Displacement Method and the results are also obtained numerically via the Finite Element Method.
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Sousa et al. (2024) studied this question.
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