The use of Fibre Reinforced Polymer composites (FRPs) [1] is becoming increasingly widespread in the rehabilitation of masonry structures [2]. The reasons of such increasing use can be found in the high FRP tensile strength and in the resins-based perfect bond between FRPs and masonry structures. Other important factors determining the increasing designers' interest are: the low invasive nature of masonry strengthening with FRP materials; the reinforcement reversibility due to the possibility of removing FRPs without damaging underlying material; the FRPs adaptability to curved surfaces as well as their small additional mass contribution, which enables strength increases of structures without modifying dynamic load distribution.

It is known that cloister vaults are generated by the intersection of barrel vaults placed on the opposite sides of a polygonal springing line. The cylindrical sectors intersect along lines lying in vertical planes and called groins. The stresses induced by external loads in the cloister vaults may be more complex than those generated in other kinds of vaults, as barrel-vaults or cross-vaults [3]. In fact, the geometrical discontinuities represented by the groins cause stresses which can not be reduced to plain state distributions, specially in the case of four-sided cloister vaults.

On the basis of previous considerations, a non-linear finite element model of a brick masonry four-sided cloister vault has been developed and calibrated on the results of specific experimental tests carried out at University of Venice [4]. In the experimental phase the vault specimen was previously loaded up to the collapse state with no FRPs and successively with two different configurations of FRP reinforcements: in the first case FRPs were positioned round the top and along the groins and in the second one a strengthening ring was added near to the base of the structure.

The performed tests demonstrated that the FRP strengthening placement can increase the vault strength up to three times the case without any reinforcement.

Numerical analyses have been performed using the FEM code ANSYS. The masonry vault has been simulated using brick elements with non-linear Drucker- Prager material model, while the FRP modeling has been done by using linear elastic shell elements.

The numerical results have allowed the actual collapse mechanism occurred during the tests to be interpreted and have suggested the optimal FRP reinforcement position.

The failure mode has been interpreted through a double three-hinges arch system formed along generators and profiles of cylindrical sectors. Cracks observed on the prototype were consistent with the mechanism predicted by FE analyses.

It has been demonstrated that the placement of FRP reinforcements along the groins and round the top of the vault is not optimal. In fact the plastic limit load calculated through the FE model is only 1% greater than the collapse load obtained for the cloister vault without FRPs.

On the basis of experimental and numerical results, a damage index for masonry has been implemented considering the maximum dissipated plastic work. The damage index has been formulated by computing the plastic work in the numerical models for different strengthening settlements with the applied vertical load equal to the collapse one measured during the tests.

Being a function of FRP surface to vault surface ratios, this criterion allows to calculate the dispersible plastic energy for similar structures with different strengthening.

Compared with the vault without FRPs, the top vertical load increase of 40 occurred in experimental tests with reinforcement placed along the groins and round the top of the specimen can be interpreted through the damage index as a consequence of ductility enhancement of the structure provided by strengthening application.

The proposed damage index together with FRP stresses monitoring can be used to evaluate the strength of four-sided cloister vaults.

Assuming that maximum plastic work per unit volume is the same even for different load conditions and for cyclic actions, the calculated values can be used in estimating the limit strength for seismic accelerations. The evaluation of earthquake- induced effects on four-sided cloister vaults represent the further development of the current research.

1

J.G. Teng, "FRP Composites in Civil Engineering", Elsevier Science, 2001.

2

W. Hendry, "Structural Masonry", Macmillan Press, 1998.

3

J. Heyman, "The Stone Skeleton", Cambridge University Press, 1995.

4

F. Portioli, P. Foraboschi, R. Landolfo, "Numerical and experimental study on the structural behaviour of cloister vaults reinforced with FRPs" (in Italian) Costruire in Laterizio, Faenza Editrice, November 2003 (submitted for publication).

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £123 +P&P)