Force–displacement response of in-plane loaded unreinforced brick masonry walls: the Critical Diagonal Crack model

Wilding, Bastian Valentin; Beyer, Katrin

doi:10.1007/s10518-016-0049-7

Cited by 22 publications

(33 citation statements)

References 14 publications

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“…If one substituted

\overset{M}{true} false(x false)

by M ( x ) in the above equations, the effect of large deflections would be annihilated. One would obtain the equations that have been the basis of models for the in‐plane behaviour of unreinforced masonry walls, for which P −Δ effects do not play a significant role . When analysing the out‐of‐plane behaviour of these walls, large deflections are, on the contrary, essential .…”

Section: Model Formulationmentioning

confidence: 99%

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Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

Godio

Beyer

2017

Earthq Engng Struct Dyn

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SummaryAn analytical model describing the flexural response of vertically spanning out-of-plane loaded unreinforced masonry walls is presented in this paper. The model is based on the second-order Euler-Bernoulli beam theory and captures important characteristics of the out-of-plane response of masonry walls that have been observed in experimental tests and from numerical studies but for which an analytical solution was still lacking: the onset and the evolution of cracking, the peak strength of the out-of-plane loaded walls, and the softening of the response due to P−Δ effects. The model is validated against experimental results, and the comparison shows that the model captures both the prepeak and postpeak response of the walls. From the analytical model of the force-displacement curve, a formula for the maximum out-of-plane strength of the walls is derived, which can be directly applied in engineering practice. KEYWORDSanalytical model, out-of-plane behaviour, pushover analysis, unreinforced masonry

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“…If one substituted

\overset{M}{true} false(x false)

Section: Model Formulationmentioning

confidence: 99%

“…For the in‐plane behaviour, it is, nevertheless, essential to account for shear deformability. In that case, the Euler‐Bernoulli beam model has to be replaced by a Timoshenko beam model …”

Section: Model Formulationmentioning

confidence: 99%

Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

Godio

Beyer

2017

Earthq Engng Struct Dyn

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“…where N is the normal force on the wall. The compressed length L c (x) of a cross section undergoing only flexural decompression but no shear cracking (flexure controlled walls) can be determined as follows

L_{c} ((), x) = 3 ((), \frac{L}{2} - \frac{V ((), H_{0} - x)}{N})

…”

Section: An Analytical Model For the Effective‐to‐initial Stiffness Rmentioning

confidence: 99%

“…Corresponding to the assumptions in Wilding and Beyer, diagonal cracking in the pre‐peak regime at 0.7 V P (70% of the peak shear capacity) is supposed to expand over the whole wall apart from the first and last course of bricks respectively due to the confinement effect of the rather stiff foundation and ceiling slabs (see Figure 10C). Figure 10A shows the resulting assumed linearized profile of reduced‐to‐full moment of inertia ( I sc ( x ) / I ) based on a diagonal crack separating 2 wall halves (and therefore splitting the subjected cross sections in two) as illustrated in Figure 10C.…”

Section: An Analytical Model For the Effective‐to‐initial Stiffness Rmentioning

confidence: 99%

The effective stiffness of modern unreinforced masonry walls

Wilding

Beyer

2018

Earthq Engng Struct Dyn

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Summary Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Eurocode estimates the effective stiffness as 50% of the gross sectional elastic stiffness, but comparisons with experimental results have shown that this may not yield accurate predictions. In this paper, 79 shear‐compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective‐to‐initial stiffness ratios are approximately 75% rather than the stipulated 50%. An empirical relationship that estimates the E‐modulus as a function of the axial load and the masonry compressive strength is proposed, yielding better estimates of the elastic modulus than the provision in Eurocode 6, which calculates the E‐modulus as a multiple of the compressive strength. For computing the ratio of the effective to initial stiffness, a mechanics‐based formulation is built on a recently developed analytical model for the force‐displacement response of URM walls. The model attributes the loss in stiffness to diagonal cracking and brick crushing, both of which are taken into account using mechanical considerations. The obtained results of the effective‐to‐initial stiffness ratio agree well with the test data. A sensitivity analysis using the validated model shows that the ratio of effective‐to‐initial stiffness is for most axial load ratios and wall geometries around 75%. Therefore, a modification of the fixed ratio of effective‐to‐initial stiffness from 50% to 75% is suggested.

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“…The CdC model is briefly summarised within this paper and will be outlined in more detail in the yet to be submitted paper by Wilding & Beyer (2016). It is based on Timoshenko beam theory to describe the nonlinear force-displacement behaviour of URM walls loaded in-plane.…”

Section: The Force-displacement Response Of Urm Wallsmentioning

confidence: 99%

Influence of eco-friendly ductile cementitious composites (EDCC) on in-plane behaviour of hollow concrete masonry walls

Kaheh¹,

Shrive²,

Soleimani-Dashtaki³

et al. 2016

Brick and Block Masonry

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Code design of Unreinforced Masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Current approaches estimate the effective stiffness as fixed ratio of the gross sectional stiffness but comparisons with experimental results have shown that this does not yield satisfactory predictions. In this paper, a recently developed analytical model for the force-displacement response of URM walls is used to investigate the effective stiffness. First, the key features of this model are summarised. In further course, the model is used to predict the effective stiffness of full-scale tests on modern unreinforced clay brick masonry walls and the results are compared to the provisions of Eurocode 8. Concluding, the model is used to investigate the sensitivity of the effective stiffness to the wall geometry and axial loading. strongly non-linear load-displacement histories by means of bi-linear curves (Fig.

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Force–displacement response of in-plane loaded unreinforced brick masonry walls: the Critical Diagonal Crack model

Cited by 22 publications

References 14 publications

Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

The effective stiffness of modern unreinforced masonry walls

Influence of eco-friendly ductile cementitious composites (EDCC) on in-plane behaviour of hollow concrete masonry walls

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