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Materials and Structures

, Volume 46, Issue 5, pp 765–786 | Cite as

Diagonal compressive strength of masonry samples—experimental and numerical approach

  • Rui Sousa
  • Hipólito Sousa
  • João Guedes
Original Article

Abstract

Masonry is a structural material that presents a quite complex behaviour that depends on the mechanical and geometrical characteristics of the units, the mortar and the link between these two elements. In particular, the characterization of the shear behaviour of masonry elements involves proper experimental campaigns that make these analyses particularly expensive. The main objective of this paper is to present a case study on the characterization of the shear behaviour of masonry through a methodology that merges a small number of laboratory tests with computer simulations. The methodology is applied to a new masonry system that has recently been developed in Portugal, and involves a FEM numerical approach based on micro3D modelling of masonry samples using nonlinear behaviour models that are calibrated through a small number of laboratory tests. As a result, the characterization of the masonry shear behaviour trough this methodology allowed simulating, with reasonably accuracy, a large set of expensive laboratory tests using numerical tools calibrated with small experimental resources.

Keywords

Masonry Lightweight concrete units Diagonal compression Laboratory tests Computer simulations Sensitivity analysis 

List of symbols

An

Net area of masonry sample

B

Height of the masonry sample

D

Isotropic scalar degradation variable

dc

Compressive damage variable

dmax

Maximum aggregate size

\( D_{0}^{\text{el}} \)

Initial (undamaged) elastic stiffness

dt

Tensile damage variable

e

Thickness of the mortar parallel joints

E0

Modulus of elasticity

F

Compression load

fl

Tensile flexural strength

Fmax

Maximum compression load

Fmax

Maximum compression load

Gp

Potential plastic flow

g

Full width of the mortar strips

G

Shear modulus

GF

Fracture energy

GFo

Base value of the fracture energy

H

Length of the masonry sample

hs

Depth of a sample

Kc

Ratio between the tensile and compressive stress invariants at initial yield

L

Distance between measurement points of ∆v and ∆h

N

Percentage of gross area of the unit that is solid

\( \bar{p} \)

Effective hydrostatic pressure

\( \bar{q} \)

Von Mises equivalent effective stress

R2

Coefficient of determination

sc

Weight factor to control the recovery of the compressive stiffness

st

Weight factor to control the recovery of the tensile stiffness

t

Total thickness of the wall

αi, βi, γi

Adimensional parameters

γ

Shear strain

γmax

Shear strain for the τmax

h

Horizontal extensions

v

Vertical shortening

ε

Total strain

εcu

Strain for σcu or ultimate strain

εc,limit

Limit compressive strain

εel

Elastic strain

εc

Compression strain

εmax

Strain of masonry for the F max

εpl

Plastic strain

\( \tilde{\varepsilon }^{\text{pl}} \)

Multi-axial equivalent plastic strain

\( \tilde{\varepsilon }_{\text{c}}^{\text{pl}} \)

Compressive equivalent plastic strain

\( \tilde{\varepsilon }_{\text{t}}^{\text{pl}} \)

Tensile plastic strain

εt

Tensile strain

ν

Poisson coefficient

σ

Cauchy stress

\( \bar{\sigma } \)

Effective stress

σb0

Initial equi-biaxial compressive yield stress

σc

Uniaxial compression stress

\( \bar{\sigma }_{\text{c}} \)

Compressive effective stresses

σc0

Initial uniaxial compressive yield stress

σcu

Compressive strength (maximum compression stress)

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\bar{\sigma }}_{\max } \)

Maximum principal effective stress (algebraic value)

σt

Uniaxial tensile stress

\( \bar{\sigma }_{\text{t}} \)

Tensile effective stresses

σto

Uniaxial tensile strength

τ

Shear stress

τmax

Shear strength or maximum shear stress

ψ

Dilation angle

Parameter that defines the rate at which G p approaches the asymptote

Notes

Acknowledgments

The authors gratefully acknowledged ADI-Portuguese Innovation Agency and the Company Maxit-Portugal for the help provided in the OTMAPS research project.

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Copyright information

© RILEM 2012

Authors and Affiliations

  1. 1.GEQUALTEC, Faculty of EngineeringUniversity of PortoPortoPortugal

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