Closed-form solution of Timoshenko frames with semi-rigid connections

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−θr) 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.