Bulletin of Earthquake Engineering

, Volume 17, Issue 1, pp 497–518 | Cite as

Push-over analysis of a rubble full-scale masonry wall reinforced with stainless steel ribbons

  • Nino SpinellaEmail author
Original Research


Many strengthening techniques for masonry structures were thoroughly investigated in several researches. The in plane shear behaviour of an ancient full-scale masonry wall, characterized by an opening that is strengthened by the lintel in the arch form, retrofitted with an innovative system constituted by three-dimensional pre-tensioned stainless steel ribbons, was previously tested. In this paper the double flat-jack test results were analyzed and design of the retrofitting system was detailed. The collapse mechanisms in terms of flexural bending and shear, both sliding and diagonal tension, as function of the compression stress level were taken into account. The arrangement of the ribbons was established on the base of an equivalent frame model of the masonry wall, investigating the flexural and shear strength of each element (piers and spandrel). Moreover, the numerical results of the response behaviour modelling of the unreinforced and reinforced masonry wall were presented. The analytical modelling of the wall was accomplished suitably applying the methods of the disturbed stress field model, successfully used for reinforced concrete elements. The numerical results provided a good prediction of the response behaviour of the wall, both in terms of load–displacement curve and crack pattern at failure.


Masonry wall Stainless steel Ribbons Shear Numerical analysis 

List of symbols


Total area of ribbons

B, H

Base and height of cross-section

C, T

Compression and tension forces

Em, Es

Initial modulus of elasticity of masonry and stainless steel


Slenderness factor


Effective depth of the cross-section

Em1, Em2

Secant modules of masonry along the principal directions

Em, Es

Elastic modulus of masonry and stainless steel


Length of pier or spandrel

fmm, ftm

Compressive and tensile strength of masonry

fmx fmy τmxy

Masonry stresses

fm1, fm2

Stresses of masonry along the principal directions

fsx fsy

Reinforcement stresses


Out-of-plane reinforcement stress

fv, fv0

Shear stress and shear stress strength

fys, fts

Stainless steel yield and failure strength

Ka, Km

Corrective factors between pressure in the flat-jack and the masonry stress

M, N, V

Bending moment, axial and shear force

P, Pm,

Load, maximum and failure load


Equivalent static load


Pressure applied by the flat-jack


Ribbons spacing


Vertical distribuited load


Thickness of wall


Depth of compression zone


Lever arm


Reinforcement orientation

δ, δm

Displacement, maximum and failure displacement


Strain at the peak of compressed stress of masonry

εmz, fmz

Out-of-plane masonry strain and stress

εs, εts

Strain and failure strain of stainless steel ribbon

εx εy εxy

Total strains


Vertical average strain of masonry

η, λ

Stress-block factors

μ, ν

Non-dimensionless bending moment and axial force


Mechanical percentage of reinforcement


Geometrical percentage of reinforcement


Average compression stress evaluated on the total cross-section

\(\sigma_{n} ,\sigma_{n}^{*}\)

Average compression stress evaluated on the effective depth and the compressed cross-section


Tension increase due to pre-strain


Stainless steel stress

σx σy σxy

Uniform stresses


Vertical average stress of masonry



The research was carried out within the financial support from the Sicilian Government within the research project PO. FESR 2007–2013 – Sicilia – Linea di Intervento, involving ABI S.r.l. (Italy), Chimetec S.a.s. (Italy) and Università di Messina (Italy), and the Italian Ministry of Education, University and Research (PRIN Grant 2015HZ24KH). The related financial support was greatly appreciated. The Author wishes to express his personal gratitude to these research funds and also to the PRIN Grant 2015HZ24KH, through which a research fellow scholarship was awarded.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of EngineeringUniversità di MESSINAVill. Sant’AgataItaly

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