A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory

Abstract

This paper presents a new and general approach for the calculation of cross-section deformation modes in thin-walled beams, to be used in the framework of generalized beam theory (GBT). The proposed approach subdivides and hierarchizes the cross-section deformation modes by employing several kinematic hypotheses. This makes it possible to discard a priori specific types of deformation modes and consequently reduce the number of cross-section degrees-of-freedom. The approach is applicable to arbitrary (with open and closed parts) polygonal cross-sections with external and internal constraints and allows for the a posteriori inclusion of particular deformation modes (e.g., shear deformation modes in a part of the cross-section). Although only GBT applications are dealt with, the deformation modes obtained may be straightforwardly incorporated in other thinwalled beam formulations that include cross-section deformation.

A physically non-linear GBT-based finite element for steel and steel-concrete beams including shear lag effects

“…Although additional shear deformation modes in the steel web and/or concrete slab can be straightforwardly added, using e.g. sinusoidal warping functions [15,8], the examples presented in Section 3 show that there is no significant gain in considering more than the LW/QW modes.…”

“…The GBT results predict a sharp peak over the web, whereas the brick models show smoother transitions due to the contact surface between the steel flange and the concrete slab-the σ xy distributions over the web show the same effect, as the GBT results vary abruptly from one side to the other, while the brick model ones are smooth. Although not shown, GBT analyses were also carried out using sinusoidal warping (SW) modes (instead of the QW mode), with 1-4 half-waves in each concrete flange (see, e.g., [15,10] for other examples concerning SW modes), but virtually identical results were obtained.…”

“…For arbitrary flat-walled cross-sections, these displacement functions may be determined from the procedures outlined in [15,16]. The non-null small-strain components are grouped in vector ε t ¼ ½ε xx ε yy γ xy , which may be subdivided into membrane (M) and bending (B) components, viz.…”

Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams

“…However it complicates the solution of the GBT equations by introducing non negligible shear coupling terms (off diagonal) in the GBT equations as can be seen in recent GBT formulations for closed thin-walled cross-sections, e.g. [4], [5] and [6]. In this paper we will therefore adhere to the definition of the warping function given by Kollbrunner & Hajdin, [7], which adds the integral of the shear flow strains, see also [8] and [9].…”

Theoretical modelling of a beam with attached spring-mass-damper system

“…It is capable of withstanding load primarily by resisting against bending which is caused by the external loads, own weight, span and external reaction when the bending force is induced into the beam [1][2][3][4]. There are few support configuration used for beam, for example cantilever, fixed supported and a common one is simply supported [4].…”