Unified approach for structural analysis of curved elements under vertical loads and various settlements

Existing masonry buildings and infrastructures are often characterized by curved elements like arches, where the settlements could induce damages up to compromising their stability. Curved elements are very sensitive to settlements due to the modification of the lateral thrust. The effects of settlements could be very critical on heritage buildings, where the intrados of curved elements are often characterized by decorated plasters. These issues caused by settlements are very important also in the infrastructures, where the displacement of the foundations could affect the main structural elements. When dealing with existing heritage buildings the analysis cannot be focused on the ultimate state only. In order to preserve the heritage value, it is important to refer to elastic behaviour to minimize the damages at serviceability limit state (e.g., newly defined artistic limit state). In this work, an existing theory has been used to obtain the closed-form solution for a specific curved system (i.e., Standard arch). The behaviour of semi-circular and parabolic curved elements is investigated under several load conditions of vertical loads and settlements. The solutions were numerically estimated according to the Principle of Virtual Works and are dimensionless in order to obtain generalizable results. A parametrical analysis was performed, providing several useful design charts to assess the impact of settlements and vertical loads on the behaviour of curved elements. The closed-form solution derived for standard arch if applied to different cases yields to approximated solutions and the scatter was estimated by comparing them with refined numerical evaluations. The outcomes of this work are useful tools to assess the sensitivity to structural damage of curved elements under settlements.