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Review Articles

An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part II: Load Singularities, Numerical Implementation and Applications

[+] Author and Article Information
Alessandro Baratta

Department of Structural Engineering, University of Naples Federico II, Via Claudio 21 Napoli, Napoli 80125, Italyalessandro.baratta@unina.it

Ottavia Corbi

Department of Structural Engineering, University of Naples Federico II, Via Claudio 21 Napoli, Napoli 80125, Italyottavia.corbi@unina.it

Appl. Mech. Rev 63(4), 040803 (Jan 13, 2011) (21 pages) doi:10.1115/1.4002791 History: Received September 22, 2010; Revised October 14, 2010; Published January 13, 2011; Online January 13, 2011

The present note follows the previous one, part I, where theoretical tools for analyzing structures made by no-tension (NT) material are presented in extensive form. Some significant results are presented in this part II of the note, ranging from the highlight of problems related to the treatment of singularities possibly occurring in the modeling of loads that burden on NT structures, and the development of tools for their treatment, to the specialization of general problems to planar and spatial structures, with the related ad hoc conceived analytical set up, original numerical tools, and noncommercial software. The implementation of the problems, deriving from the set up of the constrained optimization presented in part I of the note, is developed together with a number of applications, also providing, in some cases, the comparison of numerical, experimental, and/or field evidence referred to masonry structures, which finally validates the applicability of the adopted approach for the analysis of masonry constructions.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The panel subject to counterposed surface loads: (a) the load function with a discontinuity of first type and (b) the approximated load function tending to the load condition in Fig. 1

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Figure 2

Sample plots of the mk(x) function: k=1, k=2, and k=5

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Figure 3

Sample plots of functions mk(x) and ψk(x) for: (a) k=1 and (b) k=5

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Figure 4

Sample plots of εfx(x,y∣k) for k=1 and y=h, 0.5h, and 0

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Figure 5

(a) Scanning mesh and load condition and (b) deformed configuration k=1

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Figure 6

(a) Scanning mesh and load condition and (b) deformed configuration k=5

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Figure 7

(a) Scanning mesh and load condition and (b) deformed configuration k=20

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Figure 8

(a) Function Bk(x) for k→∞ and (b) function Bk(x)−Hk(x) for k→∞

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Figure 9

Function ηk(x) for k→∞

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Figure 10

Discontinuous load pattern: (a) the deformed and fractured panel and (b) a picture of fractures in real walls

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Figure 11

The panel subject to counterposed surface loads tending to lumped forces: the panel subject to α-type surface loads pk(x) distributed on a length with radius bk=1/k and tending to infinity for bk=1/k tending to zero

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Figure 12

Comparison between ψk(x), mk(x), and Foαk″/((2E)); β=5 and k=1

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Figure 13

(a) Scanning mesh and load condition and (b) deformed configuration k=1

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Figure 14

(a) Scanning mesh and load condition and (b) deformed configuration k=2

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Figure 15

(a) Scanning mesh and load condition and (b) deformed configuration k=3

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Figure 16

The deformation and fracture pattern of the panel under lumped force

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Figure 17

Domains identified by conditions (i)–(iv) in step 1

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Figure 18

Flow graph of the MPE implementation on a NT panel loaded by in-plane forces

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Figure 19

The panel subject to distributed surface loads: (a) calculated elastic deformed configuration, (b) calculated NT deformed configuration, (c) calculated compressive stresses (bulbs) for the elastic panel, and (d) calculated NT compressive stresses for the NT panel

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Figure 20

The NT block subject to compression (see also Fig. 14(b) of Part I): (a) The FEM model simulating the lateral containment by the loading platens and (b) the calculated NT potential cracks

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Figure 21

The NT panel loaded by in-plane forces: (a) finite element model of a masonry panel with storey fasciae, openings and architraves and (b) deformed configuration

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Figure 22

The NT panel loaded by in-plane forces: (a) compressive stress distribution, (b) potential fractures distribution and orientation (c=+0.3), and (c) expected fractures after “engineering” elaboration of the computer’s picture

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Figure 23

Tensile stress convergence with procedure reiteration

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Figure 24

The single span portal arch model: (a) the geometric dimensions and (b) the load pattern

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Figure 25

The isostatic equivalent structure

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Figure 26

Superposition scheme for managing equilibrium stress fields. (a) The disconnected structure subject only to active loads, (b) the effects of the redundant force X1=1, (c) the effects of the redundant force X2=1, and (d) the effects of the redundant force X3=1.

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Figure 27

(a) Bilinear stress pattern σ at the generic cross section s (dependence on the abscissa s in the picture is implicit): N represents the normal stress resultant acting on the solicitation center C, G is the barycenter, ⟨f⟩ is the deflection axis, ⟨n⟩ is the neutral axis, Ar is the resistant part, Af is the fractured (and not resistant) part of the cross section, Gr is the barycenter of the resistant part Ar, er is the distance of N from Gr (representing the eccentricity of N with respect to the resistant part), dGr is the distance of Gr from the neutral axis, e is the eccentricity of N from the barycenter, and h′ and h″ are the distances of the extrados and intrados fibers from the barycenter. (b) The arch element of original length ds and its deformation pattern (dependence on the abscissa s in the picture is implicit).

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Figure 28

Admissible resultants line

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Figure 29

The portal arch under seismic coefficient c=0.1 in solution (σmax=3.5 N/mm2): (a) pressure curve, (b) bending moments, (c) rotations, (d) curvatures, (e) stresses, and (f) deformed configuration amplified in the plot by the factor η=50

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Figure 30

Sketches captured from the calculus code of the numerical implementation of the NT portal arch: (a) admissible funicular captured at an intermediate step of the running of the code and (b) final collapse mechanism

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Figure 31

The prototype for experimental testing with monitoring equipment: (a) at the start of the loading process and (b) at an intermediate step of the loading process, when some fractures have already occurred

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Figure 32

Distance variation between the abutments Δu (mm) versus the horizontal load F (N): comparison between numerical results and experimental data

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Figure 33

Typical force-displacement F−δ diagrams in masonry panels subject to a horizontal action

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Figure 34

(a) Reference 3D masonry model and (b) plant of the 3D masonry model with the static load components monotonically increasing according to the parameter t

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Figure 35

Barycenter displacement (cm) versus force increment parameter t: (a) u-component and (b) v-component along the coordinate axes

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Figure 36

(a) Floor rotation (deg) versus force increment parameter t and (b) phase plots of barycenter displacement components

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Figure 37

Forcing action components (kg) versus displacement (cm) components: (a) x-components and (b) y-components

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Figure 38

The first and second piles’ shear components in the phase plane

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Figure 39

The third and fourth piles’ shear components in the phase plane

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Figure 40

The fifth pile’s shear components in the phase plane

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