Out-of-Plane Retrofit of Masonry with Fiber-Reinforced Polymer and Fiber-Reinforced Cementitious Matrix Systems: Normalized Interaction Diagrams and Effects on Mechanisms Activation
Publication: Journal of Composites for Construction
Volume 25, Issue 1
Abstract
Nowadays retrofitting and strengthening of masonry buildings are important challenges for structural engineering to ensure the structural safety under seismic or exceptional loads. This paper aims to clarify the effects of strengthening systems on out-of-plane mechanisms activation, such as horizontal and vertical bending mechanisms, by analyzing P-M interaction diagrams according to available international design guidelines. They enable the assessment of structural behavior of strengthened masonry walls under different external loads. Dimensionless equations of maximum bending moment capacity of masonry cross sections retrofitted with composite strengthening systems are derived, assuming different failure modes such as crushing of masonry and rupture of the strengthening system. Parametric analyses are performed to assess the impact of the mechanical parameters of the strengthening systems in terms of strength. The results show that the strengthening systems play a fundamental role in terms of cross section capacity and, if not well designed, the strengthening systems may be ineffective or deleterious in cultural heritage.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Notation
The following symbols are used in this paper:
- b
- depth of masonry cross section;
- Ef
- elastic modulus of composite;
- Em
- elastic modulus of masonry;
- ffu
- tensile strength of composite;
- fm
- compression strength of masonry;
- i
- imaginary unit;
- k
- coefficient of cubic equation solution;
- L
- length of masonry wall;
- Mi
- ultimate bending moment function related to failure mode i (i = 1–4);
- mR
- ultimate bending moment of masonry cross section;
- mi
- dimensionless ultimate bending moment function related to failure mode i (i = 1–4);
- first derivative of dimensionless ultimate bending moment function related to failure mode i (i = 1–3);
- m0
- ultimate bending moment of unreinforced cross section;
- second derivative of dimensionless ultimate bending moment function related to failure mode 3;
- mω
- ultimate bending moment of strengthened cross section;
- Ni
- axial load function related to failure mode i (i = 1–4);
- ni
- dimensionless axial load function related to failure mode i (i = 1–4);
- q
- uniform load;
- s
- thickness of masonry cross section;
- tf
- thickness of composite;
- x
- neutral axis depth;
- ɛ
- strain;
- ɛf
- composite strain;
- ɛfu
- ultimate composite strain;
- ɛfu,2
- ultimate composite strain equal to 2‰;
- ɛfu,3
- ultimate composite strain equal to 2.323‰;
- ɛm
- most compressed masonry fiber strain;
- ɛmf
- masonry strain at composite depth;
- ɛmu
- ultimate masonry strain;
- ɛm0
- strain corresponding to masonry peak stress;
- λ
- dimensionless factor that correlates the real distance of centroid of nonlinear stress distribution with the neutral axis depth;
- λi
- dimensionless factor that correlates the real distance of centroid of nonlinear stress distribution with the neutral axis depth depending on stress–strain constitutive relationship of masonry (i = 1–2);
- η
- conventional masonry compressive strength coefficient;
- σ
- stress;
- σ1
- parabolic stress function of stress–strain constitutive relationship of masonry;
- σ2
- constant stress function of stress–strain constitutive relationship of masonry;
- ω
- composite mechanical percentage;
- ω3
- critical composite mechanical percentage;
- ξ
- normalized neutral axis depth with wall thickness;
- ξbal,1
- normalized neutral axis depth due to balanced condition 1;
- ξbal,2
- normalized neutral axis depth depending on balanced condition 2;
- ξN0
- normalized neutral axis minimum value that guarantees positive axial loads;
- ξi
- solution of cubic equation (i = 1–3);
- ξ2,0
- critical normalized neutral axis depth;
- ψ
- effective height of the compressed masonry cross section; and
- ψi
- effective height of the compressed masonry cross section depending on stress–strain constitutive relationship of masonry (i = 1–2).
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Journal of Composites for Construction
Volume 25 • Issue 1 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Nov 27, 2019
Accepted: Aug 25, 2020
Published online: Nov 20, 2020
Published in print: Feb 1, 2021
Discussion open until: Apr 20, 2021
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