Modelling of steel frames using advanced beam and joint elements with interfaces governed by beam modes

Abstract

For decades, engineers have assessed and analysed steel frames using simple joints between beams and columns. These joints are often based on oversimplified assumptions using hinges or a direct transfer of beam displacements without any relative displacements. More seldom is the use of spring models that allow relative beam and column displacements at the joints. This despite the standardised component method approach, which can be used to determine the rotational spring stiffness of the relative rotation in a joint. This paper gives a background overview of essential developments in joint modelling and generalised thin-walled beam modelling, including torsional, distortional and related warping effects. For particular situations, some recent proposals for joint models can be applied to joints between thin-walled beams. On this basis, this paper presents a novel idea and a generic methodology that allows the interface between an extended number of generalised beam displacement modes and joints that are modelled using shell elements. The main novelty is the idea to transform from standard degrees of freedom of the interface into a reduced number of beam displacement mode related degrees of freedom. Thus, the number of degrees of freedom of the joint can be reduced to the corresponding total sum of beam modes that have been chosen for the modelling of each of the connected beam elements. The total number of degrees of freedom used for modelling the complete framework will depend on the selected number of modes in each beam element and on the number of extra internal modes chosen in the joint models. For enhanced structural analysis with advanced beam elements and joints that allow relevant distortions and built-in refined connection components, it is believed that this methodology will enable the full detailed analysis of large steel frameworks with a reasonable number of degrees of freedom.

Steel frames analyzed by use of advanced displacement mode‐based beam and joint elements

“…Using this as a one-way transformation it is not required that 𝒖 𝑏 and 𝝋 contain the same number of degrees of freedom. In fact, by an intelligent reduction of the number of cross-sectional modal displacement fields in the matrix 𝑽 it is possible to reduce the number of modal degrees of freedom included in the final analysis and assessments of the frame structure hopefully without introducing noteworthy errors, [13].…”

“…The assessment of thin-walled steel structures has been a topic receiving an intense awareness in the academic societies through decades [1]. Especially topics such as in-plane distortion and out-of-plane warping of a thin-walled cross-section have led to a considerable amount of research.…”

“…However, this joint formulation requires a detailed assessment prior to the analysis in order to specify constraint equations that will make sure the detailed displacement patterns from a beam-end will be transmitted from the one beam element through the joint and into the other beam element, which is essential when assessing thin-walled frames. Recently, Hansen & Jönsson [1] overcame these problems by introducing a novel idea on how to analyze thinwalled frames by joining advanced beam elements and joint elements using modal displacement formulations in the interfaces between beams and joints.…”