The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches

Makris, Nicos; Alexakis, Haris

doi:10.1007/s00419-013-0763-4

Cited by 55 publications

(42 citation statements)

References 12 publications

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“…Unfortunately, Milankovitch's [24,25] seminal work remained nearly unknown until very recently (Oschendorf [28], Foce [37], Rizzi et al [38], Makris and Alexakis [29]), and we only now recognize that Couplet's intuition for not taking the resultant thrust force, − − → G K , (shown in Fig. 1) tangent to the intrados was indeed correct!…”

Section: Introductionmentioning

confidence: 90%

“…6 bottom). Recently, Makris and Alexakis [29] showed by reducing to the absurd that the catenary curve is not a physically acceptable thrust line of the semicircular arch.…”

Section: Thrust Lines Of An Arched Monolith With Zero Tensile Strengthmentioning

confidence: 99%

“…The resultant thrust T 3 at joint 3 together with its point of application is uniquely determined from force and moment equilibrium (either graphically with the force polygon or analytically by Figure 3 (top left) shows that the thrust line (line of resistance = geometrical locus of the application points of the resultant forces that develops at the joints of the arch) and the funicular polygon are two neighboring lines, and one may come to the conclusion that as we reduce the size of the voussoirs that these two lines will collapse to each other. Nevertheless, this in not always true, and the collapse of these two lines to a single curve depends on the stereotomy exercised on the arch-that is the directions of the physical joints when voussoirs with finite dimensions are used (Lamé and Clapeyron [19], Milankovitch [24,25], Foce [37], Makris and Alexakis [29], Alexakis and Makris [30]). [48] which distinguishes the line of resistance (thrust line) from the line of pressure (funicular polygon).…”

Section: Thrust Line = Line Of Resistance and Funicular Polygon = Linmentioning

confidence: 99%

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Limit equilibrium analysis of masonry arches

Alexakis

Makris

2014

Arch Appl Mech

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In this paper, we revisit the limit equilibrium analysis of masonry arches. Firstly, the major contributions during the last three centuries associated with geometric and energy formulations are discussed, and subsequently, the paper explains that the problem of determining the minimum thickness of a masonry arch capable to support its own weight has multiple solutions. The infinite many neighboring solutions for the minimum thickness of a masonry arch result from the infinite many possible directions of rupturing that an arch with finite thickness may develop when becoming a mechanism. Given this infinite number of physically admissible rupturing directions, the energy approach expressed with the principle of stationary potential energy emerges as the most powerful tool to analyze masonry arches at their limit equilibrium state. The paper concludes that vertical rupturing is the most critical rupturing direction since it results to the largest value of the minimum thickness that an elliptical arch needs to support its own weight. For the common case where there is an intrados layer of voussoirs with physical joints perpendicular to the intrados, the initial rupture has to first follow the physical joint; therefore, the broken rupture pattern reported by Lamé and Clapeyron in 1823 corresponds to the larger value of the minimum allowable thickness.

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Section: Introductionmentioning

confidence: 90%

“…6 bottom). Recently, Makris and Alexakis [29] showed by reducing to the absurd that the catenary curve is not a physically acceptable thrust line of the semicircular arch.…”

Section: Thrust Lines Of An Arched Monolith With Zero Tensile Strengthmentioning

confidence: 99%

Section: Thrust Line = Line Of Resistance and Funicular Polygon = Linmentioning

confidence: 99%

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Limit equilibrium analysis of masonry arches

Alexakis

Makris

2014

Arch Appl Mech

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“…Accordingly, the force polygon expresses graphically the equilibrium of the system; the lines of action of the resultant thrust forces generate the funicular polygon, and the lines of action of the weights of the voussoirs meet at the corners of the funicular polygon to satisfy moment equilibrium (see [7]). …”

Section: Figure 1 (A) Geometric Parameters Of Pointed Arch (B) Freementioning

confidence: 99%

“…In addition, he considered the different types of stereotomy, i.e. the direction of generic sections (joints), showing the multiplicity of limit thrust lines (see [7]). Recently, few scholars have revisited the classical issue of identifying the limit equilibrium states of the symmetrical masonry arches of different shapes and corresponding theoretical minimum thickness, when subjected to self-weight (e.g.…”

Section: Introductionmentioning

confidence: 99%

Beleška O Milankovićevoj Teoriji Potporne Linije Primenjenoj Na Gotske Masivne Lukove

Nikolić¹

2016

Zbornik GFS

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Numerical model and dynamic analysis of multi degree of freedom masonry arches

Kollár

Ther

2019

Earthq Engng Struct Dyn

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Summary A new model is presented for planar multi‐block arches subjected to earthquakes. The blocks are assumed to be rigid, and every interface between the blocks may split open and may close, ie, the blocks may impact to each other. During impact, both the classical Housner's approach and improved models with lower energy dissipation are considered. The arch model is verified by comparisons with the available results in the literature. Using the new model, it was found that the circular arch moves as a four‐hinge mechanism typically only at the beginning of excitation, and several cracks split open during motion; furthermore, that modeling a multi‐block arch by a single degree of freedom (SDOF) four‐hinge mechanism may significantly overestimate its collapse load. While, in accordance with the literature, the overturning curves of single blocks and arches with symmetrically located four hinges are similar; for multi‐block arches where several hinges may occur they can be very different.

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The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches

Cited by 55 publications

References 12 publications

Limit equilibrium analysis of masonry arches

Limit equilibrium analysis of masonry arches

Beleška O Milankovićevoj Teoriji Potporne Linije Primenjenoj Na Gotske Masivne Lukove

Numerical model and dynamic analysis of multi degree of freedom masonry arches

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