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The influence of regular openings and pre-compression loading on the in-plane strength parameters of unreinforced masonry shear walls

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Abstract

This study presents a comprehensive investigation of the in-plane response of unreinforced masonry shear walls with regular openings, under the action of monotonic lateral displacement. Walls are considered with several pre-compression loads as well as different window and door openings configurations. To this end, a group of masonry shear walls built with clay bricks and hydraulic lime-sand mortar was selected featuring regular opening layouts. The micro-modeling approach was utilized by considering complex constitutive laws for materials' nonlinear behavior for capturing damages in elements. Results from the nonlinear analysis of the walls were obtained, including the lateral load capacity of shear walls at different performance points, their lateral displacement, stiffness, ductility capacity, normalized absorbed energy, and the overstrength, force reduction, and response modification factors. Moreover, a full discussion is presented regarding the estimating equations from the ASCE 41–17 code on the maximum shear capacity of the walls including their accuracy to predict the shear capacity of URM walls with openings. It is observed that opening reduces the shear strength of the unreinforced masonry shear wall between 5 and 60% as well as a reduction of 10–85% in its effective stiffness, depending on the intensity of the pre-compression load. Moreover, the code’s estimation equations for shear strength of unreinforced masonry shear walls lead to an underestimation. For walls with two or more openings of window or door, the average strength from the upper and lower bound of the code-based strength seems appropriate, considering an intense pre-compression load on the wall.

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Abbreviations

2D:

Two dimensional

A curve :

The area below the analytical backbone curve

A n :

The area of the mortared section

d − :

The compression damage indices for the inelastic part of the effective stress tensor

d + :

The tension damage indices for the inelastic part of the effective stress tensor

E :

The young modulus

E N :

The normalized absorbed energy

f’ dt :

The lower bound masonry diagonal tension strength

f’ m :

The lower bound compressive strength per area of masonry

f a :

The axial compressive stress from gravity loads

f c 0 :

Compression elastic limit

f cp :

The compressive peak stress of the material

f cr :

Compressive residual strength

f t :

The tensile peak stress of the material

F u :

Force capacity

G f :

The tensile fracture energy per unit area

g f :

The specific fracture energy per unit volume

G t :

The compression fracture energy per unit area

H(x) :

The Heaviside function

h eff :

The height to resultant lateral force

H sid :

The discrete softening parameter

\(\overline{I}_{1}\) :

The first invariant of the effective tensor of stress

\(\overline{J}_{2}\) :

The second invariant of the effective deviatoric tensor of stress

k 1 :

A constant factor between 0 and 1, controls the shear behavior of the model on the compressive surface

k b :

The ratio of bi-axial to uniaxial compressive strength

K e :

The effective stiffness of the wall

KN:

Kilonewton

l dis :

The size of the damage zone

mm:

Millimeter

MPa:

Mega Pascal

N:

Newton

OpenSees:

Open system of earthquake engineering simulation

P D :

Dead load at the top of the wall

P w :

Self-weight of the wall

R :

The response modification factor

R μ :

The force reduction factor

STKO:

Scientific ToolKit for OpenSees

URM:

Unreinforced masonry

V :

Shear force

V bjs :

The masonry wall's bed joint sliding capacity

V cr :

The shear resistance of the wall at the formation of the first significant crack

V dt :

The diagonal tension capacity of the wall

V eq :

The equivalent elastic base shear

V max :

The maximum resistance of the wall

v me :

The lower bound masonry shear strength

V r :

The wall rocking capacity

V tc :

The wall-toe-crushing capacity of the wall

v te :

The average of the bed-joint shear strength from the test value

V Δmax :

The ultimate capacity of the walls at the maximum displacement point

W 0 :

Wall without any opening

W R-1D :

Wall with a regular distribution of 1 door opening in the middle

W R-1W :

Wall with a regular distribution of 1 window opening in the middle

W R-1W2D :

Wall with a regular distribution of 2 doors on the sides and 1 window opening in the middle

W R-2D :

Wall with a regular distribution of 2 door openings on the sides

W R-2W :

Wall with a regular distribution of 2 window openings on the sides

W R-2W1D :

Wall with a regular distribution of 2 windows on the sides and 1 door opening in the middle

W R-3D :

Wall with a regular distribution of 3 door openings, one in the middle and two on the sides

W R-3W :

Wall with a regular distribution of 3 window openings, one in the middle and two on the sides

Δ:

The average displacement at the top of the wall

Δ (@ Fu):

The second-floor displacement at the force capacity point

Δcr :

The average displacement of the wall at the formation of the first significant crack

Δe :

The elastic limit of displacement on the bilinear relationship

Δmax :

The maximum displacement

Δu :

The ultimate idealized displacement of the wall

ε p :

Compressive strain at peak strength

μ u :

The ultimate ductility factor

ν:

Poison’s ratio

\(\overline{\sigma }^{ - }\) :

The negative components of the elastic part of the effective stress tensor

\(\overline{\sigma }^{ + }\) :

The positive components of the elastic part of the effective stress tensor

σ eff :

The effective tensor of stress

\(\overline{\sigma }_{\max }\) :

The maximum effective principal stress

σ v :

Pre-compression stress

τ − :

The equivalent stress scalar measure in compression

τ + :

The equivalent stress scalar measure in tension

Ω:

The overstrength factor

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Acknowledgements

This research has been supported by the Graduate University of Advanced Technology (Kerman-Iran) under grant number of 02.912.

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Graduate University of Advanced Technology (Kerman-Iran), 02.912, Farshad Homaei.

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  1. Faculty of Civil and Surveying Engineering, Department of Earthquake and Geotechnical Engineering, Graduate University of Advanced Technology, Kerman, Iran

    Farshad Homaei

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Homaei, F. The influence of regular openings and pre-compression loading on the in-plane strength parameters of unreinforced masonry shear walls. Archiv.Civ.Mech.Eng 24, 6 (2024). https://doi.org/10.1007/s43452-023-00816-2

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