Displacement-based formulations for composite beams with longitudinal slip and vertical uplift

Abstract

This paper describes three novel displacement-based formulations for the analysis of composite beams with a flexible connection which is capable of deforming along the longitudinal axis of the member as well as vertically, i.e. transverse to the interface connection. For completeness, the analytical model which forms the basis of the proposed modelling technique is presented in both its weak and strong forms. The three novel finite element formulations are derived and tested using different structural systems; their nodal freedoms include the vertical and axial displacements as well as the rotations at each element end of both layers. Curvature locking problems are observed to occur for one of these elements and the origin of this behaviour is demonstrated analytically. Two applications are then proposed adopting a bi-linear constitutive relationship for the vertical interface connection to, reflect the more realistic case in which, already in the linear-elastic range of the materials forming the cross-section and of the longitudinal interface connection, two vertical connection stiffnesses are required, i.e. one to model the event of separation between the layers and one when one bears against the other one. Copyright (c) 2005 John Wiley & Sons, Ltd

On the influence of interfacial properties to the bending rigidity of layered structures

“…Adekola (1968) took into account of both slips and uplifts in an interface to look at the deformation of a beam. Gara et al (2006) extended Adekola's model to handle a wider class of loading and boundary condition. Girhammar and Gopu (1993) and Girhammar and Pan (2007) developed an exact analysis for composite beams by the first order and second order analysis.…”

Exact static analysis of partially composite beams and beam-columns

“…by Ayoub [20,21], Ranzi et al [22] and Cas et al [23]. Gara et al [24] developed a finite element model for composite beams with both longitudinal slip and vertical uplift of the interface connection. Dall'Asta [25] developed a three-dimensional theory for composite beams with shear weak connection dealing with combinations of bending in the symmetry plane, and torsion and transverse bending in the plane parallel to the shear connector interface.…”

Nonlinear analysis of partially connected composite beams using interface elements

“…Gattesco [17] developed a numerical solution for the nonlinear analysis of composite beams by attaching springs to the element ends and with fibre integration of cross-sectional properties. More recently, this type of approach was employed by Ranzi et al [18] and Gara et al [19] on the simulation of composite beams with longitudinal as well as transverse partial interaction. The GTB element developed by Goodman et al [20] was the first zero-thickness interface element.…”