Dynamical Assessment of the Work Conditions of Reinforcement Tie-Rods in Historical Masonry Structures

ABSTRACT

Tie-rods are essential structural elements, which have been employed for centuries in masonry historical buildings, either during the construction or in successive strengthening interventions, with the aim of containing dangerous horizontal actions. The actual work conditions of these tie-rods, which are strongly influenced by their load history, are difficult to be quantified theoretically, and an effective method for their measure is of great importance in order to ensure the efficiency of these elements during the time and the stability of the entire building. Common measurements are often carried out adopting models based upon significant simplifications, like, for example, hinges at the extremities. These assumptions, rarely represent the real work conditions for anchorages. In this work, a non-destructive testing method is presented, based upon sophisticated dynamical models that can take into consideration many of the circumstances neglected by the simplified models. Four case studies are extensively described, trying to embrace the most common situations in term of peculiar features of the building, structural configuration, and load history. The discussion of the results yields the safety margin of the rod with respect to the material failure and provides important indications about the overall stability of the whole building.

KEYWORDS:

• Architectural restoration
• historical buildings
• masonry structures
• structural health monitoring
• tie-rods
• vibration measurement

Nomenclature

A	=	Local net cross-section area of the tie-rod
B1, B2	=	coefficients in the time function of the solution for tie-rod deflection
C	=	coefficient of the general solution for the form function
c2	=	constant equal to the ratio $EI/\rho A$
E	=	elastic modulus of the tie-rod material
F	=	axial load acting on the tie-rod
$f_k^{exp}$	=	natural frequency number k determined experimentally
$f_k^{mdl}$	=	natural frequency number k determined from the numerical modelling
H(x)	=	Heaviside function
I	=	moment ofinertia of the cross-section if the tie-rod
Kf	=	distributed stiffness of the elastic bed
L	=	total length of the tie-rod
lf	=	length of the tie-rod portions inserted into the wall
l	=	free length of the tie-rod
pk	=	weight coefficient of a frequency number k
q(x,t)	=	external forces system
R	=	residual error between two sets of frequencies
ρ	=	density of the tie-rod material
ω	=	natural frequency in rad/s
w(x,t)	=	tie-rod deflection function

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Fondazione Cariparma; Fondazione Cassa di Risparmio di Pistoia e Pescia; Comune di Fontanellato; Soprintendenza per i Beni Architettonici e Paesaggistici per le Province di Ravenna Ferrara Forlì-Cesena e Rimini.