GBT-Based buckling analysis of cold-formed steel purlin-sheeting systems using restrained deformation modes

Resumo

In Generalized Beam Theory (GBT), which incorporates genuine plate theory concepts, the cross-
section displacement field is expressed as a linear combination of deformation modes, making it possible to write

the equilibrium equations in a very convenient format. In practical applications, thin-walled steel members are
often continuously braced along their lengths - e.g., cold-formed steel purlins restrained by sheeting. In order to
incorporate such bracing in a GBT analysis, two approaches can be followed: (i) incorporate the restraints only at
the member analysis stage, which means that the deformation modes are obtained for the unrestrained cross-section
(conventional approach) or (ii) incorporate the restraints at the cross-section analysis stage, which means that the
deformation modes already take them into account (restrained cross-section analysis approach - proposed in this
work).This paper reports the results of an investigation on improving the GBT buckling analysis of continuously
braced cold-formed steel purlins by including the displacement/rotation restraints at the cross-section analysis
stage, i.e., during the determination of the cross-section deformation modes and calculation of the associated modal
properties - the end product of this procedure are “restrained deformation modes”. After describing, the procedures
involved in the determination of such restrained deformation modes, the paper illustrates the advantages of their
use in the GBT-based buckling analysis of cold-formed steel purlins restrained by sheeting. For validation and
assessment purposes, some GBT-based results are compared with values provided by the codes GBTUL2.0

(conventional GBT approach) and Finite Strip Method (FSM) analyses. It is still worth noting that restrained cross-
section analysis makes it possible to obtain semi-analytical solutions to determine critical buckling loadings in

purlins restrained by sheeting - such solutions are based on one or two restrained deformation modes.