Assessing the Equivalent Spring Method for Modelling of Lightweight-concrete Encased Cold-formed Steel Elements in Compression

Using concrete for filling and bracing is one of the most crucial ways to improve cold-formed steel (CFS) elements' stability behavior and performance. An example is the novel building system made up by CFS encased in ultra-lightweight concrete. The numerical analysis of such structural members using solid finite elements is time-consuming, thus the need for an easy-to-use modelling technique has arisen. As a result, a simple time-efficient equivalent spring model (ESM) has been introduced as a viable method for properly analyzing complex structural behavior in numerous cases, replacing the concrete solid with one-directional springs applying the Winkler foundation. This study aims to examine the validity and limitations of the ESM by comparing it to 3D solid model (SMOD) results for internal plate elements. The analysis results indicate that the ESM could provide accurate results in the b/t range of 100 or less for a wide range of PAC modulus (50-250 MPa) with an error of less than 5%; hence, using spring in modelling PAC within these limits is deemed acceptable. Nevertheless, for larger b/t values up to 175, doubled the calculated spring stiffness is highly recommended. In addition, the results reveal that the applicability of ESM is limited for b/t above 175; the model fails to predict the ultimate failure load, and the failure mode. Finally, this study ends by recommending one equation for calculating equivalent foundation spring stiffness for internal components that ensure optimal performance of the ESM analysis.