Parameter models for estimating in-situ tensile force in tie-rods

Two analytical models are presented for the identification of the actual static scheme and tensile force of metallic tie-rods included in masonry arches and vaults. The reference structural system consists of a moment-resistant tie-beam with elastic rotational springs at the extremities. Symmetrical restraint conditions are initially hypothesized, thus obtaining a two-parameter model in which the unknowns are the springs' rigidity along with the axial force. The preceding assumption is then removed by defining a more general, three-parameter model in which two different spring rigidities are considered. The mutual experimental data are the middle-section vertical displacement under a concentrated load and the fundamental vibration frequency; the second vibration frequency is adjunctively assumed for the three-parameter model. Closed-form equations are formulated in both cases. Laboratory tests show a notable agreement between analytical estimates and experimental measures. A statistical balance of the application of the proposed models to over 200 rods belonging to several Italian monumental as well as common ancient buildings is presented along with more-detailed information about a significant case study.