Plane straight element with semi-rigid connections: formulation from an energetic approach

Discrete connectors, such as screws, nails, and others, are commonly used to fasten various structural elements. The established hypothesis regarding the behavior of joints conceived with discrete connectors directly impacts the distribution of forces. For example, in the design of truss structures, the resisting moments that arise due to the arrangement of the connectors are often disregarded, as considering the semi-rigid behavior of the joints introduces greater complexities in the modeling required to determine displacements and internal forces. This work presents 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 (PVW). 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 (FEM)This work presents 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 (PVW). 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 (FEM).