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Diagonal cracking shear strength of unreinforced masonry panels: a correction proposal of the b shape factor

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Abstract

After summarising the failure criteria adopted by the new Italian Seismic Code (NTC 2008) for the seismic assessment of unreinforced masonry panels (URM), the paper presents a numerical study aimed at investigating the b shape factor. This factor is a coefficient, function of the panels’ slenderness, employed to evaluate the ultimate shear strength of URM for the failure mechanism with diagonal cracking. The results herein presented show that the actual values of the coefficient b are higher than those proposed by the NTC (2008); consequently, the shear strength obtained by applying the Italian Seismic Code is not conservative. An amendment is proposed for the b shape factor, and its effects are evaluated through the analysis of three plane-URM walls with regular openings and different slenderness of the masonry beams. Pushover analyses were performed to estimate their seismic capacity and their collapse modes. The walls were modelled by both the finite element method (FEM) and the equivalent frame approach (EFM). In the EFM approach the b shape factor was selected both according to the NTC (2008) and as proposed in the paper. The seismic capacity curves show that the EFM approach significantly overestimate the ultimate shear strength of the walls with respect to the results obtained by the FEM, and this effect is amplified when the b shape factor is evaluated as recommended by the NTC (2008).

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Abbreviations

b :

Shape factor associated to the shear stress distribution in the central horizontal section of the masonry panel

c :

Cohesion

d cu :

Maximum displacement of the control point

e :

Axial load eccentricity

η :

Dilatancy angle

E :

Longitudinal modulus of elasticity

φ :

Friction angle

f d :

Design compressive strength of the masonry

f td :

Design tensile strength of the masonry

f vd :

Design shear strength of the masonry for sliding

f vd0 :

Ultimate design shear strength of masonry without compression

f hd :

Ultimate design compressive strength of the masonry in the horizontal direction

f vk0 :

Characteristic shear strength for sliding without axial force on the panel section

f t :

Tensile strength of the masonry

G :

Shear modulus of elasticity

γ M :

Partial safety factor

h :

Height of vertical section of the spandrel or height of the pier

K e :

Initial stiffness

l :

Panel width

l′:

Length of the compressive portion of the transversal section of the masonry panel

λ :

Slenderness of masonry panels (λ = h/l)

M :

Acting bending moment

M u :

Ultimate bending moment

ν :

Poisson’s ratio

P :

Actual compressive axial load

σ 0 :

Average normal stress acting on the whole masonry panel section [σ 0 = P/(lt)]

σ n :

The same as σ 0 calculated as σ n  = P/(l′t), being l′ less than l

t :

Wall thickness

τ 0d :

The same as f vk0 considering the shear failure with diagonal cracking

τ k :

Characteristic shear strength of the masonry

τ u :

Ultimate average shear stress

V t :

Ultimate shear strength

V p :

Shear strength required for the equilibrium of a beam subject to M u

V b :

Base shear

V bu :

Maximum base shear

w :

Weight per unit volume

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering (DICeA), University of Florence, Via di Santa Marta, 3, 50139, Florence, Italy

    Michele Betti, Luciano Galano & Andrea Vignoli

  2. Viale Palmiro Togliatti, 143, 50019, Sesto Fiorentino, FI, Italy

    Michele Petracchi

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  1. Michele Betti
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  2. Luciano Galano
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  3. Michele Petracchi
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  4. Andrea Vignoli
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Correspondence to Michele Betti.

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Betti, M., Galano, L., Petracchi, M. et al. Diagonal cracking shear strength of unreinforced masonry panels: a correction proposal of the b shape factor. Bull Earthquake Eng 13, 3151–3186 (2015). https://doi.org/10.1007/s10518-015-9756-8

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