In this paper, the so-called Couplet–Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general opening angle, subjected only to its own weight is reexamined. Classical analytical solutions provided by J. Heyman are first rederived and explored in details. Such derivations make obviously use of equilibrium relations. These are complemented by a tangency condition of the resultant thrust force at the haunches' intrados. Later, given the same basic equilibrium conditions, the tangency condition is more correctly restated explicitly in terms of the true line of thrust, i.e., the locus of the centers of pressure of the resultant internal forces at each theoretical joint of the arch. Explicit solutions are obtained for the unknown position of the intrados hinge at the haunches, the minimum thickness to radius ratio and the nondimensional horizontal thrust. As expected from quoted Coulomb's observations, only the first of these three characteristics is perceptibly influenced, in engineering terms, by the analysis. This occurs more evidently at increasing opening angle of the arch, especially for over-complete arches. On the other hand, the systematic treatment presented here reveals the implications of an important conceptual difference, which appears to be relevant in the statics of masonry arches. Finally, similar trends are confirmed as well for a Milankovitch-type solution that accounts for the true self-weight distribution along the arch.

References

References
1.
Heyman
,
J.
,
1977
,
Equilibrium of Shell Structures
,
Oxford University Press
,
Oxford, UK
.
2.
Heyman
,
J.
,
1982
,
The Masonry Arch
,
Ellis Horwood Ltd.
,
Chichester, UK
.
3.
Heyman
,
J.
,
1966
, “
The Stone Skeleton
,”
Int. J. Solids Struct.
,
2
(
2
), pp.
249
279
.10.1016/0020-7683(66)90018-7
4.
Heyman
,
J.
,
1967
, “
On Shell Solutions for Masonry Domes
,”
Int. J. Solids Struct.
,
3
(
2
), pp.
227
241
.10.1016/0020-7683(67)90072-8
5.
Heyman
,
J.
,
1969
, “
The Safety of Masonry Arches
,”
Int. J. Mech. Sci.
,
11
(
4
), pp.
363
385
.10.1016/0020-7403(69)90070-8
6.
Heyman
,
J.
,
1995
,
The Stone Skeleton—Structural Engineering of Masonry Architecture
,
Cambridge University Press
,
Cambridge, UK
.
7.
Irvine
,
H. M.
,
1979
, “
The Stability of the Roman Arch
,”
Int. J. Mech. Sci.
,
21
(
8
), pp.
467
475
.10.1016/0020-7403(79)90009-2
8.
Benvenuto
,
E.
,
1981
,
La Scienza delle Costruzioni e il suo Sviluppo Storico
,
Sansoni
,
Firenze, Italy
.
9.
Sinopoli
,
A.
,
Corradi
,
M.
, and
Foce
,
F.
,
1997
, “
Modern Formulation for Preelastic Theories on Masonry Arches
,”
J. Eng. Mech.
, ASCE,
123
(
3
), pp.
204
213
.10.1061/(ASCE)0733-9399(1997)123:3(204)
10.
Sinopoli
,
A.
,
2003
, “
The Role of Geometry in the Theories on Vaulted Structures by Lorenzo Mascheroni (1785)
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
, ed., Madrid, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_175, pp.
1865
1873
.
11.
Huerta
,
S.
,
2001
, “
Mechanics of Masonry Vaults: The Equilibrium Approach
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P.B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2003, pp.
47
70
.
12.
Huerta
,
S.
,
2004
,
Arcos, Bóvedas y Cúpulas. Geometría y Equilibrio en el Cálculo Tradicional de Estructuras de Fábrica
,
Instituto Juan de Herrera
,
Madrid, Spain
.
13.
Huerta
,
S.
,
2006
, “
Galileo was Wrong: The Geometrical Design of Masonry Arches
,”
Nexus Network J.
,
8
(
2
), pp.
25
52
.10.1007/s00004-006-0016-8
14.
Albuerne
,
A.
, and
Huerta
S.
,
2010
, “
Coulomb's Theory of Arches in Spain ca. 1800: The Manuscript of Joaquín Monasterio
,” Proceedings of 6th International Conference on Arch Bridges (ARCH’10),
B.
Chen
and
J.
Wei
, eds., Fuzhou, China, Oct. 11–13, 2010,
College of Civil Engineering, Fuzhou University
,
P. R. C.
, Paper No. 46, pp.
354
362
.
15.
Aita
,
D.
,
Barsotti
,
R.
, and
Bennati
,
S.
,
2003
, “
Some Explicit Solutions for Flat and Depressed Masonry Arches
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
ed., Madrid, Spain, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_018, pp.
171
183
.
16.
Becchi
,
A.
,
2003
, “
The Statics of Arches Between France and Italy
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
ed., Madrid, Spain, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_034, pp.
353
364
.
17.
Foce
,
F.
, and
Aita
,
D.
,
2003
, “
The Masonry Arch Between «Limit» and «Elastic» Analysis. A Critical Re-Examination of Durand-Claye's Method
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
, ed., Madrid, Spain, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_088, pp.
895
908
.
18.
Foce
,
F.
,
2005
, “
On the Safety of the Masonry Arch. Different Formulations From the History of Structural Mechanics
,”
Essays in the History of the Theory of Structures
,
S.
Huerta
, ed.,
Instituto Juan de Herrera
,
Madrid, Spain
, pp.
117
142
.
19.
Foce
,
F.
,
2007
, “
Milankovitch's Theorie der Druckkurven: Good Mechanics for Masonry Architecture
,”
Nexus Network J.
,
9
(
2
), pp.
185
210
.10.1007/s00004-007-0039-9
20.
Aita
,
D.
,
2003
, “
Between Geometry and Mechanics: A Re-Examination of the Principles of Stereotomy From a Statical Point of View
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
ed., Madrid, Spain, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_017, pp.
161
170
.
21.
Sakarovitch
,
J.
,
2003
, “
Stereotomy, a Multifaceted Technique
,” Proceedings of the 1st International Congress on Construction History,
S.
Huerta
ed., Madrid, Jan. 20–24, 2003,
Madrid Instituto Juan de Herrera
, Vol. 1, Paper No. CIHC1_008, pp.
69
79
.
22.
Heyman
,
J.
,
2009
, “
La Coupe Des Pierres
,” Proceedings of the Third International Congress on Construction History,
Brandenburg University of Technology
,
Cottbus, Germany
, May 20–24, 2009, Vol. 2, pp.
807
812
.
23.
Bičanič
,
N.
,
Stirling
,
C.
, and
Pearce
,
C. J.
,
2003
, “
Discontinuous Modelling of Masonry Bridges
,”
Comput. Mech.
,
31
(
1–2
), pp.
60
68
.10.1007/s00466-002-0393-0
24.
Thavalingam
,
A.
,
Bičanič
,
N.
,
Robinson
,
J. I.
, and
Ponniah
,
D. A.
,
2001
, “
Computational Framework for Discontinuous Modelling of Masonry Arch Bridges
,”
Comput. Struct.
,
79
(
19
), pp.
1821
1830
.10.1016/S0045-7949(01)00102-X
25.
MacLaughlin
,
M. M.
, and
Doolin
,
D. M.
,
2006
, “
Review of Validation of the Discontinuous Deformation Analysis (DDA) Method
,”
Int. J. Numer. Anal Methods Geomech.
,
30
(
4
), pp.
271
305
.10.1002/nag.427
26.
Tóth
,
A. R.
,
Orbán
,
Z.
, and
Bagi
,
K.
,
2009
, “
Discrete Element Analysis of a Stone Masonry Arch
,”
Mech. Res. Commun.
,
36
(
4
), pp.
469
480
.10.1016/j.mechrescom.2009.01.001
27.
Lucchesi
,
M.
,
Padovani
,
C.
,
Pasquinelli
,
G.
, and
Zani
,
N.
,
1997
, “
On the Collapse of Masonry Arches
,”
Meccanica
,
32
(
4
), pp.
327
346
.10.1023/A:1004275223879
28.
Blasi
,
C.
, and
Foraboschi
,
P.
,
1994
, “
Analytical Approach to Collapse Mechanisms of Circular Masonry Arch
,”
J. Struct. Eng., ASCE
,
120
(
8
), pp.
2288
2309
.10.1061/(ASCE)0733-9445(1994)120:8(2288)
29.
Boothby
,
T. E.
,
1996
, “
Discussion: Analytical Approach to Collapse Mechanisms of Circular Masonry Arch
,”
J Struct. Eng.
,
122
(
8
), pp.
978
980
.10.1061/(ASCE)0733-9445(1996)122:8(978)
30.
Ochsendorf
,
J.
,
2006
, “
The Masonry Arch on Spreading Supports
,”
Struct. Eng.
,
84
(
2
), pp.
29
36
. Available at http://www.istructe.org/journal/volumes/volume-84-%28published-in-2006%29/issues/issue-2/articles/the-masonry-arch-on-spreading-supports
31.
Block
,
P.
,
DeJong
,
M.
, and
Ochsendorf
,
J.
,
2006
, “
As Hangs the Flexible Line: Equilibrium of Masonry Arches
,”
Nexus Network J.
,
8
(
2
), pp.
13
24
.10.1007/s00004-006-0015-9
32.
Ochsendorf
,
J.
,
2002
, “
Collapse of Masonry Structures
,” Ph.D. thesis,
University of Cambridge, King's College
,
UK
.
33.
Milankovitch
,
M.
,
1904
, “
Beitrag zur Theorie der Druckkurven
,” Ph.D. thesis,
K. K. Technische Hochschule
,
Vienna, Austria
.
34.
Milankovitch
,
M.
,
1907
, “
Theorie der Druckkurven
,”
Z. Math. Phys.
,
55
, pp.
1
27
.
35.
Romano
,
A.
, and
Ochsendorf
,
J.
,
2009
, “
The Mechanics of Gothic Masonry Arches
,”
Int. J. Archit. Heritage
,
4
(
1
), pp.
59
82
.10.1080/15583050902914660
36.
Martinez Martinez
,
J. A.
,
Moreno Revilla
,
J.
, and
Aragon Torre
,
A.
,
2001
, “
Critical Thickness Criteria on Stone Arch Bridges With Low Rise/Span Ratio and Current Traffic Loads
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães
,
Portugal, University of Minho
, Nov. 7–9, 2001, pp.
609
616
.
37.
Block
,
P.
,
2005
, “
Equilibrium System. Studies in Masonry Structures
,” M.S. thesis,
Massachusetts Institute of Technology, Department of Architecture
,
Cambridge, MA
.
38.
Block
,
P.
,
Ciblac
,
T.
, and
Ochsendorf
,
J.
,
2006
, “
Real-Time Limit Analysis of Vaulted Masonry Buildings
,”
Comput. Struct.
,
84
(
29–30
), pp.
1841
1852
.10.1016/j.compstruc.2006.08.002
39.
DeJong
,
M.
, and
Ochsendorf
,
J. A.
,
2006
, “
Analysis of Vaulted Masonry Structures Subjected to Horizontal Ground Motion
,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06),
P. B.
Lourenço
,
P.
Roca
,
C.
Modena
, and
S.
Agrawal
, eds., New Delhi, India, Nov. 6–8, 2006,
Macmillan Advanced Research Series
, pp.
973
980
.
40.
O'Dwyer
,
D.
,
1999
, “
Funicular Analysis of Masonry Vaults
,”
Comput. Struct.
,
73
(
1–5
), pp.
187
197
.10.1016/S0045-7949(98)00279-X
41.
Andreu
,
A.
,
Gil
,
L.
, and
Roca
,
P.
,
2007
, “
Computational Analysis of Masonry Structures With a Funicular Model
,”
J. Eng. Mech., ASCE
,
133
(
4
), pp.
473
480
.10.1061/(ASCE)0733-9399(2007)133:4(473)
42.
Gilbert
,
M.
,
2007
, “
Limit Analysis Applied to Masonry Arch Bridges: State-of-the-Art and Recent Developments
,” Proceedings of 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira, Portugal
, pp.
13
28
.
43.
Oikonomopoulou
,
A.
,
Ciblac
,
T.
, and
Guéna
,
F.
,
2009
, “
Modelling Tools for the Mechanical Behaviour of Historic Masonry Structures
,” Proceedings of the 3rd International Congress on Construction History,
Brandenburg University of Technology
,
Cottbus, Germany
, May 20–24, 2009, Vol. 3, pp.
1097
1104
.
44.
Varma
,
M.
,
Jangid
,
R. S.
, and
Ghosh
,
S.
,
2010
, “
Thrust Line Using Linear Elastic Finite Element Analysis for Masonry Structures
,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010,
Advanced Materials Research, Trans Tech Publications
, Vols. 133–134, pp.
503
508
.
45.
Antunes
,
G. J. J.
,
2010
, “
Comportamento Estrutural de Edifícios Antigos. Estruturas Arqueadas Planas
,” M.S. thesis,
Instituto Superior Técnico, Universidade Técnica de Lisboa
.
46.
Gago
,
A. S.
,
Alfaiate
,
J.
, and
Lamas
,
A.
,
2011
, “
The Effect of the Infill in Arched Structures: Analytical and Numerical Modelling
,”
Eng. Struct.
,
33
(
5
), pp.
1450
1458
.10.1016/j.engstruct.2010.12.037
47.
Gago
,
A. S.
,
2004
, “
Análise Estrutural de Arcos, Abóbadas e Cúpulas—Contributo para o Estudo do Património Construído
,” Ph.D. thesis,
Universidade Técnica de Lisboa, Instituto Superior Técnico, IST-UTL
.
48.
Colasante
,
G.
,
2007
, “
Sui Meccanismi di Collasso degli Archi in Muratura Secondo l'Analisi Limite
,” B.S. thesis,
Università di Bergamo
,
Italy
.
49.
Rusconi
,
F.
,
2008
, “
Analisi Numerica per Elementi Discreti dei Meccanismi di Collasso degli Archi in Muratura
,” B.S. thesis,
Università di Bergamo
,
Italy
.
50.
Rizzi
,
E.
,
Cocchetti
,
G.
,
Colasante
,
G.
, and
Rusconi
,
F.
,
2010
, “
Analytical and Numerical Analysis on the Collapse Mode of Circular Masonry Arches
,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010,
Advanced Materials Research, Trans Tech Publications
, Vols. 133–134, pp.
467
472
.
51.
Rizzi
,
E.
,
Rusconi
,
F.
, and
Cocchetti
,
G.
,
2011
, “
Numerical DEM (DDA) Analysis on the Collapse Mode of Circular Masonry Arches
,”
University of Bergamo
, Technical Report No. SdC2011/02.
52.
Kooharian
,
A.
,
1952
, “
Limit Analysis of Voussoir (Segmental) and Concrete Arches
,”
J. Proc. Am. Concr. Inst.
,
49
(
12
), pp.
317
328
. Available at http://www.concrete.org/PUBS/JOURNALS/OLJDetails.asp?Home=JP&ID=11822
53.
Livesley
,
R. K.
,
1978
, “
Limit Analysis of Structures Formed From Rigid Blocks
,”
Int. J. Numer. Anal. Methods Eng.
,
12
(
12
), pp.
1853
1871
.10.1002/nme.1620121207
54.
Livesley
,
R. K.
,
1992
, “
A Computational Model for the Limit Analysis of Three-Dimensional Masonry Structures
,”
Meccanica
,
27
(
3
), pp.
161
172
.10.1007/BF00430042
55.
Boothby
,
T. E.
, and
Brown
,
C. B.
,
1992
, “
Stability of Masonry Piers and Arches
,”
J. Eng. Mech., ASCE
,
118
(
2
), pp.
367
383
.10.1061/(ASCE)0733-9399(1992)118:2(367)
56.
Boothby
,
T. E.
,
1994
, “
Stability of Masonry Piers and Arches Including Sliding
,”
J. Eng. Mech., ASCE
,
120
(
2
), pp.
304
319
.10.1061/(ASCE)0733-9399(1994)120:2(304)
57.
Boothby
,
T. E.
,
1995
, “
Collapse Modes of Masonry Arch Bridges
,”
Masonry Int.
,
9
(
2
), pp.
62
69
. Available at http://www.masonry.org.uk/masonry/publications/masonry_international/masonry_international_papers/volume_09/collapse_modes_of_masonry_arch_bridges
58.
Boothby
,
T. E.
,
2001
, “
Analysis of Masonry Arches and Vaults
,”
Prog. Struct. Eng. Mater.
,
3
(
3
), pp.
246
256
.10.1002/pse.84
59.
Como
,
M.
,
1992
, “
Equilibrium and Collapse Analysis of Masonry Bodies
,”
Meccanica
,
27
(
3
), pp.
185
194
.10.1007/BF00430044
60.
Clemente
,
P.
,
Occhiuzzi
,
A.
, and
Raihtel
,
A.
,
1995
, “
Limit Behaviour of Stone Arch Bridges
,”
J. Struct. Eng., ASCE
,
121
(
7
), pp.
1045
1050
.10.1061/(ASCE)0733-9445(1995)121:7(1045)
61.
Del
Piero
,
G.
,
1998
, “
Limit Analysis and No-Tension Materials
,”
Int. J. Plast.
,
14
(
1–3
), pp.
259
271
.10.1016/S0749-6419(97)00055-7
62.
Gilbert
,
M.
,
Casapulla
,
C.
, and
Ahmed
,
H. M.
,
2006
, “
Limit Analysis of Masonry Block Structures With Non-Associative Frictional Joints Using Linear Programming
,”
Comput. Struct.
,
84
(
13–14
), pp.
873
887
.10.1016/j.compstruc.2006.02.005
63.
Cavicchi
,
A.
, and
Gambarotta
,
L.
,
2006
, “
Two-Dimensional Finite Element Upper Bound Limit Analysis of Masonry Bridges
,”
Comput. Struct.
,
84
(
31–32
), pp.
2316
2328
.10.1016/j.compstruc.2006.08.048
64.
Cavicchi
,
A.
, and
Gambarotta
,
L.
,
2007
, “
Lower Bound Limit Analysis of Masonry Bridges Including Arch–Fill Interaction
,”
Eng. Struct.
,
29
(
11
), pp.
3002
3014
.10.1016/j.engstruct.2007.01.028
65.
Chen
,
Y.
,
Ashour
,
A. F.
, and
Garrity
,
S. W.
,
2007
, “
Modified Four-Hinge Mechanism Analysis for Masonry Arches Strengthened With Near-Surface Reinforcement
,”
Eng. Struct.
,
29
(
8
), pp.
1864
1871
.10.1016/j.engstruct.2006.09.023
66.
Smars
,
P.
,
2000
, “
Etudes sur la Stabilité des Arcs et Voûtes, Confrontation des Méthodes de l'Analyse Limite aux Voûtes Gothiques en Brabant
,” Ph.D. thesis,
Catholic University of Leuven, Belgium
.
67.
Smars
,
P.
,
2008
, “
Influence of Friction and Tensile Resistance on the Stability of Masonry Arches
,” Proceedings of the 6th International Conference on Structural Analysis of Historic Construction,
D.
D'Ayala
and
E.
Fodde
, eds., Bath (UK), July 2–4, 2008,
Taylor & Francis Group
,
London
, pp.
1199
1206
.
68.
Smars
,
P.
,
2010
, “
Kinematic Stability of Masonry Arches
,” Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China, Oct. 6–8, 2010,
Advanced Materials Research, Trans Tech Publications
, Vols. 133–134, pp.
429
434
.
69.
Lucchesi
,
M.
,
Šilhavý
,
M.
, and
Zani
,
N.
,
2012
, “
Equilibrium Problems and Limit Analysis of Masonry Beams
,”
J. Elast.
,
106
(
2
), pp.
165
188
.10.1007/s10659-011-9318-5
70.
Baratta
,
A.
, and
Corbi
,
O.
,
2010
, “
An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part I: Material Modeling, Theoretical Setup, and Closed Form Solutions
,”
Appl. Mech. Rev.
,
63
(
4
), p.
040802
.10.1115/1.4002790
71.
Baratta
,
A.
, and
Corbi
,
O.
,
2010
, “
An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part II: Load Singularities, Numerical Implementation and Applications
,”
Appl. Mech. Rev.
,
63
(
4
), p.
040803
.10.1115/1.4002791
72.
Bednarz
,
L.
,
Górski
,
A.
,
Jasienko
,
J.
, and
Rusinski
,
E.
,
2011
, “
Simulations and Analyses of Arched Brick Structures
,”
Autom. Constr.
,
20
(
7
), pp.
741
754
.10.1016/j.autcon.2011.01.005
73.
Fanning
,
P. J.
, and
Boothby
,
T. E.
,
2001
, “
Three-Dimensional Modelling and Full-Scale Testing of Stone Arch Bridges
,”
Comput. Struct.
,
79
(
29–30
), pp.
2645
2662
.10.1016/S0045-7949(01)00109-2
74.
Vermeltfoort
,
A. T.
,
2001
, “
Analysis and Experiments of Masonry Arches
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, pp.
489
498
.
75.
Brencich
,
A.
, and
Morbiducci
,
R.
,
2007
, “
Masonry Arches: Historical Rules and Modern Mechanics
,”
Int. J. Archit. Heritage
,
1
(
2
), pp.
165
189
.10.1080/15583050701312926
76.
de Arteaga
,
I.
, and
Morer
,
P.
,
2012
, “
The Effect of Geometry on the Structural Capacity of Masonry Arch Bridges
,”
Constr. Build. Mater.
,
34
, pp.
97
106
.10.1016/j.conbuildmat.2012.02.037
77.
Armesto
,
J.
,
Roca-Pardiñas
,
J.
,
Lorenzo
,
H.
, and
Arias
,
P.
,
2010
, “
Modelling Masonry Arches Shape Using Terrestrial Laser Scanning Data and Nonparametric Methods
,”
Eng. Struct.
,
32
(
2
), pp.
607
615
.10.1016/j.engstruct.2009.11.007
78.
Morer
,
P.
,
de Arteaga
,
I.
,
Armesto
,
J.
, and
Arias
,
P.
,
2011
, “
Comparative Structural Analyses of Masonry Bridges: An Application to the Cernadela Bridge
,”
J. Cult. Heritage
,
12
(
3
), pp.
300
309
.10.1016/j.culher.2011.01.006
79.
Riveiro
,
B.
,
Morer
,
P.
,
Arias
,
P.
, and
de Arteaga
,
I.
,
2011
, “
Terrestrial Laser Scanning and Limit Analysis of Masonry Arch Bridges
,”
Constr. Build. Mater.
,
25
(
4
), pp.
1726
1735
.10.1016/j.conbuildmat.2010.11.094
80.
Riveiro
,
B.
,
Caamaño
,
J. C.
,
Arias
,
P.
, and
Sanz
,
E.
,
2011
, “
Photogrammetric 3D Modelling and Mechanical Analysis of Masonry Arches: An Approach Based on a Discontinuous Model of Voussoirs
,”
Autom. Constr.
,
20
(
4
), pp.
380
388
.10.1016/j.autcon.2010.11.008
81.
Solla
,
M.
,
Caamaño
,
J. C.
,
Riveiro
,
B.
, and
Arias
,
P.
,
2012
, “
A Novel Methodology for the Structural Assessment of Stone Arches Based on Geometric Data by Integration of Photogrammetry and Ground-Penetrating Radar
,”
Eng. Struct.
,
35
, pp.
296
306
.10.1016/j.engstruct.2011.11.004
82.
Solla
,
M.
,
Lorenzo
,
H.
,
Rial
,
F. I.
, and
Novo
,
A.
,
2012
, “
Ground-Penetrating Radar for the Structural Evaluation of Masonry Bridges: Results and Interpretational Tools
,”
Constr. Build. Mater.
,
29
, pp.
458
465
.10.1016/j.conbuildmat.2011.10.001
83.
Oliveira
,
D.V.
,
Lourenço
,
P. B.
, and
Lemos
,
C.
,
2010
, “
Geometric Issues and Ultimate Load Capacity of Masonry Arch Bridges From the Northwest Iberian Peninsula
,”
Eng. Struct.
,
32
(
12
), pp.
3955
3965
.10.1016/j.engstruct.2010.09.006
84.
Roca
,
P.
,
Cervera
,
M.
,
Gariup
,
G.
, and
Pelá
,
L.
,
2010
, “
Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches
,”
Arch. Comput. Methods Eng.
,
17
(
3
), pp.
299
325
.10.1007/s11831-010-9046-1
85.
Atamturktur
,
S.
, and
Laman
,
J. A.
,
2012
, “
Finite Element Model Correlation and Calibration of Historic Masonry Monuments: Review
,”
Struct. Des. Tall Build.
,
21
(
2
), pp.
96
113
.10.1002/tal.577
86.
Lourenço
,
P. B.
,
2001
, “
Analysis of Historical Constructions: From Thrust-Lines to Advanced Simulations
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd Internaional Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, pp.
91
116
.
87.
Dede
,
T.
, and
Ural
,
A.
,
2007
, “
A Finite Element Program for Historical Stone Arch Bridges
,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira, Portugal
, pp.
533
541
.
88.
Melbourne
,
C.
,
Wang
,
J.
, and
Tomor
,
A.
,
2007
, “
A New Masonry Arch Bridge Assessment Strategy (SMART)
,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira, Portugal
, pp.
227
236
.
89.
Gibbons
,
N.
, and
Fanning
,
P. J.
,
2010
, “
Ten Stone Masonry Arch Bridges and Five Different Assessment Approaches
,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10),
B.
Chen
and
J.
Wei
, eds., Fuzhou, China, Oct. 11–13, 2010,
College of Civil Engineering, Fuzhou University
, Paper No. 63, pp.
482
489
.
90.
Kumar
,
P.
,
2010
, “
Performance Assessment and Maintenance of Masonry Arch Bridges
,”
34th IABSE Symposium on Large Structures and Infrastructures for Environmentally Constrained and Urbanised Areas
, Venice, Sept. 22–24, 2010,
International Association for Bridge and Structural Engineering
, pp.
818
826
.
91.
Casas
,
J. R.
,
2011
, “
Reliability-Based Assessment of Masonry Arch Bridges
,”
Constr. Build. Mater.
,
25
(
4
), pp.
1621
1631
.10.1016/j.conbuildmat.2010.10.011
92.
Harvey
,
W. J.
,
1988
, “
Application of the Mechanism Analysis to Masonry Arches
,”
Struct. Eng.
,
66
(
5
), pp.
77
84
. Available at http://www.istructe.org/Journal/Volumes/Volume-66-%28Published-in-1988%29/Issues/Issue-5/Articles/Application-of-the-Mechanism-Analysis-to-Masonry-A
93.
Smith
,
F. W.
,
Harvey
,
W. J.
, and
Vardy
,
A. E.
,
1990
, “
Three-Hinge Analysis of Masonry Arches
,”
Struct. Eng.
,
68
(
11
), pp.
203
213
. Available at http://www.istructe.org/Journal/Volumes/Volume-68-%28Published-in-1990%29/Issues/Issue-11/Articles/Three-Hinge-Analysis-of-Masonry-Arches
94.
Harvey
,
B.
, and
Maunder
,
E.
,
2001
, “
Thrust Line Analysis of Complex Masonry Structures Using Spreadsheets
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, pp.
521
528
.
95.
Harvey
,
B.
,
2009
, “
Interactive Analysis of Arching Masonry Structures
,” Proceedings of the 3rd Australasian Engineering Heritage Conference, Engineering in the Development of a Region—Heritage and History,
Salmond College, University of Otago
,
Dunedin, New Zealand
, Nov. 22–25, 2009.
96.
Hughes
,
T. G.
, and
Blackler
,
M.
,
1997
, “
A Review of the UK Masonry Arch Assessment Methods
,”
Proceedings of the Institution of Civil Engineers—Structures and Buildings
,
122
(
3
), Paper No.11302, pp.
305
315
.10.1680/istbu.1997.29801
97.
Hughes
,
T. G.
,
Hee
,
S. C.
, and
Soms
,
E.
,
2002
, “
Mechanism Analysis of Single Span Masonry Arch Bridges Using a Spreadsheet
,”
Proceedings of the Institution of Civil Engineers—Structures and Buildings
,
152
(
4
), Paper No. 12710, pp.
341
350
.10.1680/stbu.2002.152.4.341
98.
Miri
,
M.
, and
Hughes
,
T. G.
,
2006
, “
The Physical and Numerical Modelling of a Repaired Masonry Arch Bridge
,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06),
P. B.
Lourenço
,
P.
Roca
,
C.
Modena
, and
S.
Agrawal
, eds., New Delhi, India, Nov. 6–8, 2006,
Macmillan Advanced Research Series
, pp.
1255
1262
.
99.
Molins
,
C.
, and
Roca
,
P.
,
1998
, “
Capacity of Masonry Arches and Spatial Frames
,”
J. Struct. Eng., ASCE
,
124
(
6
), pp.
653
663
.10.1061/(ASCE)0733-9445(1998)124:6(653)
100.
Ponterosso
,
P.
,
Fishwick
,
R. J.
,
Fox
,
D.
St.
J.
,
Liu
,
X. L.
, and
Begg
,
D. W.
,
2000
, “
Masonry Arch Collapse Loads and Mechanisms by Heuristically Seeded Genetic Algorithm
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
8–10
), pp.
1233
1243
.10.1016/S0045-7825(99)00477-6
101.
Alfaiate
,
J.
, and
Gallardo
,
A.
,
2001
, “
Numerical Simulations of a Full Scale Load Test on a Stone Masonry Arch Bridge
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, pp.
739
748
.
102.
Roeder-Carbo
,
G. M.
, and
Ayala
,
A. G.
,
2001
, “
An Evaluation of Methods for the Determination of the Structural Stability of Historic Masonry Arches
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, pp.
557
566
.
103.
Giordano
,
A.
,
Mele
,
E.
, and
De Luca
,
A.
,
2002
, “
Modelling of Historical Masonry Structures: Comparison of Different Approaches Through a Case Study
,”
Eng. Struct.
,
24
(
8
), pp.
1057
1069
.10.1016/S0141-0296(02)00033-0
104.
Giordano
,
A.
,
De Luca
,
A.
,
Mele
,
E.
, and
Romano
,
A.
,
2006
, “
Simplified Evaluation of the Horizontal Capacity of Masonry Arches
,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06),
P. B.
Lourenço
,
P.
Roca
,
C.
Modena
, and
S.
Agrawal
, eds., New Delhi, India, Nov. 6–8, 2006,
Macmillan Advanced Research Series
, pp.
1221
1229
.
105.
Ford
,
T. E.
,
Augarde
,
C. E.
, and
Tuxford
,
S. S.
,
2003
, “
Modelling Masonry Arch Bridges Using Commercial Finite Element Software
,” Proceedings of the 9th International Conference on Civil and Structural Engineering Computing,
B. H. V.
Topping
, ed., The Netherlands, Sept. 2–4, 2003,
Civil-Comp Press
,
Stirlingshire, UK
, Paper No. 101.
106.
Ng
,
K.-H.
, and
Fairfield
,
C. A.
,
2004
, “
Modifying the Mechanism Method of Masonry Arch Bridge Analysis
,”
Constr. Build. Mater.
,
18
(
2
), pp.
91
97
.10.1016/j.conbuildmat.2003.08.015
107.
Toker
,
S.
, and
Ünay
,
A.
,
2004
, “
Mathematical Modeling and Finite Element Analysis of Masonry Arch Bridges
,”
GU J. Sci.
,
17
(
2
), pp.
129
139
. Available at http://194.27.18.47/dergi/ojs/index.php/GUJS/article/viewFile/414/212
108.
Kumar
,
P.
, and
Bhandari
,
N. M.
,
2005
, “
Non-Linear Finite Element Analysis of Masonry Arches for Prediction of Collapse Load
,”
Struct. Eng. Int.
(IABSE, Zurich, Switzerland),
15
(
3
), pp.
166
174
.10.2749/101686605777963026
109.
Kumar
,
P.
, and
Bhandari
,
N. M.
,
2006
, “
Mechanism Based Assessment of Masonry Arch Bridges
,”
Struct. Eng. Int.
(IABSE, Zurich, Switzerland),
16
(
3
), pp.
226
234
.10.2749/101686606778026484
110.
Migliore
,
M. R.
,
Letizia
,
F. S.
, and
Ruocco
,
E.
,
2006
, “
On the Stability of Masonry Arches
,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06),
P. B.
Lourenço
,
P.
Roca
,
C.
Modena
, and
S.
Agrawal
, eds., New Delhi, India, Nov. 6–8, 2006,
Macmillan Advanced Research Series
, pp.
965
972
.
111.
Audenaert
,
A.
,
Peremans
,
H.
, and
Reniers
,
G.
,
2007
, “
An Analytical Model to Determine the Ultimate Load on Masonry Arch Bridges
,”
J. Eng. Math.
,
59
(
3
), pp.
323
336
.10.1007/s10665-006-9129-z
112.
Audenaert
,
A.
,
Fanning
,
P.
,
Sobczak
,
L.
, and
Peremans
,
H.
,
2008
, “
2-D Analysis of Arch Bridges Using an Elasto-Plastic Material Model
,”
Eng. Struct.
,
30
(
3
), pp.
845
855
.10.1016/j.engstruct.2007.05.018
113.
Betti
,
M.
,
Drosopoulos
,
G. A.
, and
Stavroulakis
,
G. E.
,
2007
, “
On the Collapse Analysis of Single Span Masonry/Stone Arch Bridges With Fill Interaction
,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira
, pp.
617
624
.
114.
Campo
,
M.
,
Drosopoulos
,
G. A.
,
Fernández
,
J. R.
, and
Stavroulakis
,
G. E.
,
2007
, “
Unilateral Contact and Damage Analysis in Masonry Arches
,”
IUTAM Symposium on Computational Contact Mechanics
,
P.
Wriggers
and
U.
Nackenhorst
, eds.,
Springer
,
New York
, pp.
357
363
10.1007/978-1-4020-6405-0_22.
115.
Drosopoulos
,
G. A.
,
Stavroulakis
,
G. E.
, and
Massalas
,
C. V.
,
2006
, “
Limit Analysis of a Single Span Masonry Bridge With Unilateral Frictional Contact Interfaces
,”
Eng. Struct.
,
28
(
13
), pp.
1864
1873
.10.1016/j.engstruct.2006.03.016
116.
Drosopoulos
,
G. A.
,
Stavroulakis
,
G. E.
, and
Massalas
,
C. V.
,
2008
, “
Influence of the Geometry and the Abutments Movement on the Collapse of Stone Arch Bridges
,”
Constr. Build. Mater.
,
22
(
3
), pp.
200
210
.10.1016/j.conbuildmat.2006.09.001
117.
Ainsworth
,
M.
, and
Mihai
,
L. A.
,
2007
, “
Modeling and Numerical Analysis of Masonry Structures
,”
Numer. Methods Partial Differ. Equ.
,
23
(
4
), pp.
798
816
.10.1002/num.20253
118.
Mihai
,
L. A.
, and
Ainsworth
,
M.
,
2009
, “
An Adaptive Multi-Scale Computational Modelling of Clare College Bridge
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
21–26
), pp.
1839
1847
.10.1016/j.cma.2008.12.030
119.
Viola
,
E.
,
Panzacchi
,
L.
, and
Tornabene
,
F.
,
2007
, “
General Analysis and Application to Redundant Arches Under Static Loading
,”
Constr. Build. Mater.
,
21
(
5
), pp.
1129
1143
.10.1016/j.conbuildmat.2005.10.001
120.
Oikonomopoulou
,
A.
,
2009
, “
Approches Numériques pour l’Étude du Comportement des Structures Maçonnées Anciennes: un Outil Basé sur le Calcul à la Rupture et la Visualisation Graphique
,” Ph.D. thesis,
Université Paris Est et de l'Ecole Nationale Supérieure d'Architecture de Paris la Villette
,
Paris, France
.
121.
Pintucchi
,
B.
, and
Zani
,
N.
,
2009
, “
Effects of Material and Geometric Non-Linearities on the Collapse Load of Masonry Arches
,”
Eur. J. Mech. A/Solids
,
28
(
1
), pp.
45
61
.10.1016/j.euromechsol.2008.02.007
122.
Vares
,
R. J.
,
2009
, “
Avaliação de Segurança de Pontes Existentes de Alvenaria de Pedra com Recurso a Métodos Simplificados
,” M.S. thesis,
Universidade do Porto
.
123.
Grandjean
,
A.
,
2010
, “
Capacité Portante de Ponts en Arc en Maçonnerie de Pierre Naturelle—Modèle d’Évaluation Intégrant le Niveau d'Endommagement
,” Ph.D. thesis,
École Polytechnique Fédérale de Lausanne (EPFL)
,
Suisse, Février
.
124.
Peng
,
D. M.
,
Chen
,
Y. Y.
,
Jiang
,
R. J.
, and
Fairfield
,
C. A.
,
2010
, “
Optimal Design of Masonry Arch Bridges
,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10),
B.
Chen
and
J.
Wei
, eds., Fuzhou, China, Oct. 11–13, 2010,
College of Civil Engineering, Fuzhou University
, Paper No. 87, pp.
674
682
.
125.
Tsutsui
,
M.
,
Mizuta
,
Y.
, and
Sakata
,
T.
,
2010
, “
Line of Thrust and Theoretical Load of Masonry Arch Bridge
,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10),
B.
Chen
and
J.
Wei
, eds., Fuzhou, China, Oct. 11–13, 2010,
College of Civil Engineering, Fuzhou University
, Paper No. 43, pp.
332
337
.
126.
Yamao
,
T.
,
Yamamoto
,
K.
,
Kudo
,
T.
,
Ogami
,
K.
, and
Nakamura
,
H.
,
2010
, “
Development of Static Analytical Method for Mechanical Behavior of Stone Arch Bridges
,” Proceedings of the 6th International Conference on Arch Bridges (ARCH’10),
B.
Chen
and
J.
Wei
, eds., Fuzhou, China, Oct. 11–13, 2010,
College of Civil Engineering, Fuzhou University
, Paper No. 48, pp.
370
378
.
127.
Manrique Hoyos
,
C.
,
2010
, “
Limit Analysis: Collection of Examples of Applications
,” M.S. thesis,
UPC Barcelona
,
Spain
.
128.
Cai
,
Y.
,
2011
, “
Detailed Numerical Simulation of Experiments on Masonry Arch Bridges by Using 3D FE
,” M.S. thesis,
UPC Barcelona, Spain
.
129.
Koltsida Spyridoula
,
I.
,
2011
, “
Detailed Numerical Simulation of Experiments on Masonry Arch Bridges by Using 3D FE
,” M.S. thesis,
UPC Barcelona
,
Spain
.
130.
Sinopoli
,
A.
,
Aita
,
D.
, and
Foce
,
F.
,
2007
, “
Further Remarks on the Collapse Mode of Masonry Arches With Coulomb Friction
,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira, Portugal
, pp.
649
657
.
131.
Casapulla
,
C.
, and
Lauro
,
F.
,
2000
, “
A Simple Computation Tool for the Limit-State Analysis of Masonry Arches
,”
Proceedings of the 5th International Congress on Restoration of Architectural Heritage (Firenze 2000
),
Università di Firenze
, Sept. 17–24, 2000, pp.
2056
2064
(CDROM).
132.
Casapulla
,
C.
, and
D'Ayala
,
D.
,
2001
, “
Lower Bound Approach to the Limit Analysis of 3D Vaulted Block Masonry Structures
,”
Proceedings of the 5th International Symposium on Computer Methods in Structural Masonry
(
STRUMAS V
),
Roma, Italy
, p.
28
36
.
133.
D'Ayala
,
D.
, and
Casapulla
,
C.
,
2001
, “
Limit State Analysis of Hemisferical Domes with Finite Friction
,” Historical Constructions 2001—Possibilities of Numerical and Experimental Techniques, Proceedings of the 3rd International Seminar,
P. B.
Lourenço
and
P.
Roca
, eds.,
Guimarães, Portugal
,
University of Minho
, Nov. 7–9, 2001, Paper No. 056, pp.
617
626
.
134.
D'Ayala
,
D.
, and
Tomasoni
,
E.
,
2011
, “
Three-Dimensional Analysis of Masonry Vaults Using Limit State Analysis With Finite Friction
,”
Int. J. Archit. Heritage
,
5
(
2
), pp.
140
171
.10.1080/15583050903367595
135.
Frigerio
,
A.
,
2010
, “
Sul Meccanismo di Collasso Misto negli Archi Semicircolari in Muratura
,” B.S. thesis,
Università di Bergamo
,
Italy
.
136.
Colasante
,
G.
,
2010
, “
Sul Ruolo dell'Attrito nei Meccanismi di Collasso degli Archi Circolari in Muratura
,” M.S. thesis,
Università di Bergamo
,
Italy
.
137.
Rizzi
,
E.
,
Colasante
,
G.
,
Frigerio
,
A.
, and
Cocchetti
,
G.
,
2012
, “
On the Mixed Collapse Mechanism of Semi-Circular Masonry Arches
,”
Proceedings of the 8th International Conference on Structural Analysis of Historical Constructions
(
SAHC
2012), J. Jasiénko, ed., Wroclaw, Poland, Oct. 15–17, DWE, Vol. 1, pp. 541–549.
138.
Aita
,
D.
,
Barsotti
,
R.
, and
Bennati
,
S.
,
2012
, “
Equilibrium of Pointed, Circular and Elliptical Masonry Arches Bearing Vertical Walls
,”
J. Struct. Eng. ASCE
,
138
(
7
), pp.
880
888
.10.1061/(ASCE)ST.1943-541X.0000522
139.
Romano
,
A.
,
2005
, “
Modelling, Analysis and Testing of Masonry Structures
,” Ph.D. thesis,
Università degli Studi di Napoli Federico II
,
Italy
.
140.
Romano
,
A.
, and
Ochsendorf
,
J.
,
2006
, “
Circular, Pointed and Basket-Handle Arches: A Comparison of Structural Behavior of Masonry Spans
,” Proceedings of the 5th International Conference on Structural Analysis of Historical Constructions—Possibilities of Numerical and Experimental Techniques (SAHC06),
P. B.
Lourenço
,
P.
Roca
,
C.
Modena
, and
S.
Agrawal
, eds., New Delhi, India, Nov. 6–8, 2006,
Macmillan Advanced Research Series
, pp.
1205
1212
.
141.
De Rosa
,
E.
, and
Galizia
,
F.
,
2007
, “
Evaluation of Safety of Pointed Masonry Arches Through the Static Theorem of Limit Analysis
,” Proceedings of 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Portugal
, pp.
659
668
.
142.
Hejazi
,
M.
, and
Jafari
,
F.
,
2010
, “
Structural Effects of Brick Arrangement and Span Length on Mid-Pointed Arches
,”
Proceedings of the 7th International Conference (SAHC 2010), Shanghai, China
, Oct. 6–8, 2010,
Advanced Materials Research, Trans Tech Publications
, Vols. 133–134, pp.
411
416
.
143.
Aita
,
D.
,
Foce
,
F.
,
Barsotti
,
R.
, and
Bennati
,
S.
,
2007
, “
Collapse of Masonry Arches in Romanesque and Gothic Constructions
,” Proceedings of the 5th International Conference on Arch Bridges (ARCH’07),
P. B.
Lourenço
,
D. B.
Oliveira
, and
A.
Portela
, eds., Funchal, Madeira, Portugal, Sept. 12–14, 2007,
Multicomp, Lda Publishers
,
Madeira, Portugal
, pp.
625
632
.
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