New Φ method in EN1996 for the verification of second-order effects in load-bearing masonry walls

The Eurocode 6 (EC6) revision work carried out in recent years within the “CEN/TC 250/SC 6 – Masonry Structure” was an opportunity to reconsider verification methods for unreinforced masonry (URM) walls when subjected to combined vertical and out-of-plane loading and with significant second-order effects. The method proposed in the previous version of EC6 was based on an axial load capacity reduction factor (ϕm), the values of which were derived from an approximate model, fairly conservative for a wide range of wall stiffnesses. In addition, the previous version of EC6 did not require explicit verification in terms of lateral flexural capacity for URM walls subjected to significant lateral loads (e.g., seismic actions), when it would be appropriate and rational. For the latter verification, which should also take into account second-order effects, a reduction factor similar to ϕm can be defined for bending capacity reduction (ϕM). Therefore, this paper aims to show the scientific derivation of the new criteria adopted in the current version of EC6 (EN1996-1-1:2022) for the verification of second-order effects in URM walls. In particular, the numerical procedure for quantifying the ϕ factors is presented, which has improved the estimates previously available in the literature. Based on these numerical results, prediction models of these ϕ factors are proposed, which are also used to demonstrate the one-to-one correspondence between ϕm and ϕM. Then, validation comparisons are shown between the predicted values of the reduction factors and the relevant experimental and numerical values previously available in the literature. Finally, the calibration of the models proposed in the new version of EC6 is shown for both ϕm and ϕM.