Closed-form solution of Timoshenko frames with semi-rigid connections. (February 2023) - Molina-Villegas, Juan Camilo; Ballesteros Ortega, Jorge Eliecer
Abstract: The response of steel frame structures is highly influenced by the degree of rotational stiffness of the connections between beams and columns, which are characterized by nonlinear moment–rotation ( M − θ r ) curves. Design codes such as the ANSI/AISC 360-16 and the Eurocode 3 specify that the effect of the joints rotational stiffness should be included in the linear and/or nonlinear structural models used in the steel design process. To model the effect of the degree of rigidity between structural elements, it is a common practice to use zero-length semi-rigid connections. This paper presents the static formulation of the Green's Functions Stiffness Method (GFSM) for prismatic Timoshenko frames with zero-length elastic semi-rigid connections subjected to arbitrary external loads and bending moments. The GFSM is a novel analytical method based on the classical Stiffness Method (SM), and the Green's Functions (GFs), for the computation of closed-form solutions of the response of structures. This method is formulated from the decomposition of the structural response into two complementary parts: a homogeneous response (related to the stiffness matrix and the shape functions) and a particular or fixed response (associated with the load vector and the fixed displacement field), the latter computed using GFs of fixed elements. An example of a one-bay one-storey two-dimensional frame is presented.