Author Index - Springer978-1-4612-2994-0/1.pdf · Bresse, J.A.C., 485fn Brunelleschi, F., 313, 350...
Transcript of Author Index - Springer978-1-4612-2994-0/1.pdf · Bresse, J.A.C., 485fn Brunelleschi, F., 313, 350...
Author Index
Albenga, G., 508 Alberti, L.B., 311, 350 Aldrich, D.H., 327 d'Alembert, J. Lerond, 445-447, 452,
472, 492 Alexander of Aphrodisia, 312 Alfieri, B., 400 Amici, V., 432 Ammannati, B., 328 Antiphon, 309 Apollonius, 311 Archimedes, 322, 460 Atwood, G., 429 Audoy, 429-430
Barilari, P., 463 Barsotti, G., 457, 471, 490 Belanger, J.B., 479 Belgrado, J., 400-401 Belidor, B. Forest de, 315, 336-338,
342,372,403,431 Benedict XIV, Pope, 352 Benjamin, W., 543 Benvenuto, E., 437fn, 514fn Bernardi, 450 Bernoulli, Jakob, 329, 331, 401 Bernoulli, Johann, 326-328,358,364-
365 Bertelli, F., 463 Bertot, H., 485-486, 492, 494 Bertrand, J.L.F., 477, 490-491, 508 Betti, E., 503 Blondel, F., 311 Boistard, L.C., 399fn Bompaire, F., 471 Boncompagni, Prince of, 514 Bonnycastle, C., 461 Bordoni, A., 414, 422 Borelli, A., 358, 364 Borgnis, J.A., 332 Borra, G.B., 315, 400 Boscovich, R.G., 352, 356, 371-374,
468
Bossut, C., 344, 375-386, 407, 412, 413,426,428,447-449,451
Bouguer, P., 344-348, 360, 374, 384, 413, 420-423
Bresse, J.A.C., 485fn Brunelleschi, F., 313, 350 Bryan, G.H., 529 Buti, A., 315fn, 334fn
Caizzi, B., 472 Callot, E., 471 Capriz, G., 473 Castigliano, A., 436, 442, 447, 452,
453,469,470,473,475,476, 487,491,508,509,512,513-523, 529, 531, 542-543
Cauchy, A., 468, 469, 471, 516 Cavina, V., 451fn Cecchini, A., 350 Cerruti, V., 503, 513 Cesaro, E., 503 Charlton, T.M., 508fn Chasles, M., 526 Chezy, M., 399fn Clairaut, A., 358 Clapeyron, B.P.E., 357fn, 430, 479-
488,492,494,499,508,509, 517
Clark, E., 483 Clebsch, A., 492-498, 517 Colbert, J.B., 322 Colonnetti, G., 508, 521-523 Corradi, M., 334fn, 437fn Cosimo Medici, Grand Duke, 351 Cotterill, J.H., 508-512, 517, 542 Coulomb, C., 342, 375, 386-399, 413,
418, 428-431 Couplet, C.A., 309, 338-344, 353, 359,
398, 403, 413 Cournot, A., 447, 471-476, 478,489,
508,514 Cremona, L., 491, 526, 534, 539 Croce, F., 371
Crotti, F., 508, 523-530, 543 Culmann, K., 436, 526, 534 Curioni, G., 437fn, 515
Danyzy, A.A.H., 399fn Darbon, A., 471 Delanges, P., 406, 448-450, 455-456 Derand, F., 313-315, 336 Descartes, R., 472, 473 Donati, L., 508, 510 Dorna, A., 477-479, 489, 508 Dugas, R., 467fn, 471 Dulacq, 358
Elkana, Y., 471 Engesser, F., 508 Euler, J.A., 375 Euler, L., 388, 441-444, 447, 448,
451,455,465,475,480,529
Fabri, H., 316-320 Faguol!, G., 444, 463-466 FairbaIrn, W., 480 Faraday, M., 468 Favre, F.P.G., 357-358 Fedi, R., 471 Fermat, P. de, 460 Ferussac, Baron de, 471 Foce, F., 437fn Foggini, G.B., 350 Fontana, C., 311, 350, 352, 353 Fontana, G., 457 Fontana, M., 407-411, 453-455, 466 Fourier, J., 447 Franceschinis, F.M., 404 Frezier, A.F., 358, 399fn Frisi, P., 401-404, 413 Frost, R., 447 Fusinieri, A., 463
Galilei, G., 312, 316, 324, 358, 397, 442
Galilei, V., 312 Gaudi, A., 346 Gauthey, E.M., 399fn Gebbia, M., 503 Genocchi, A., 508, 513 Gergonne, J.D., 462, 526 Gerstner, A., 432fn, 433
Author Index 545
Gerstner, F.J., 432 Grandi, G., 313 Gratognini, G., 414, 422 Green, G., 468-470, 480, 517 Gregory, D., 326-331, 358, 401 Grioli, G., 473 Guarini, G., 311 Guerrini, G.G., 350 Gunther, R.W.T., 329fn
Hann, J., 434fn Harpe, F. de la, 471 Hartsocker, N., 357 Hegel, G.W.F., 442 Heidegger, M., 442, 543 Heppel, J .M., 483 Hertwig, A., 508 Hesse, M.B., 471 Heyman, J., 342, 343fn, 386 Hire,P. de la, 315-316,321-326,331-
336,342,353,357,358,376, 384, 403, 416, 418, 448fn
Hodgkinson, E., 483 Hooke, R., 328-329fn Huygens, C., 427
Intieri, B., 352
Jacquier, F., 352, 356fn Jammer, M.F., 471 Jourawsky, D.J., 483
Krafft, G.W., 309fn, 331
Labey, J.B., 461 Lagrange, L., 451, 457, 460, 466, 469,
474,510 Lame, G., 430, 487, 510, 511 Lana Terzi, F., 358 Landi, F., 412fn Lauricella, G., 503 Legendre, A.M., 529 Leibniz, G.W., 326, 328, 358, 472,
473 Leonardo da Vinci, 316fn, 320, 342 Lesage, M., 399fn Lorgna, A.M., 404-407, 413, 449, 452-
453
Mach, E., 471
546 Author Index
Malfatti, G.F., 457-460, 514, 527 Manfredi, G., 352 Mansart, J.H., 405 Marcolongo, R., 309fn Martinez, F., 372 Martino, P. Di, 352 Marzano, S., 473 Mascheroni, L., 344, 375, 393-394,
399, 412-425, 428, 457 Masetti, G.B., 414, 419, 457 Maupertuis, P.L. Moreau de, 460 Maxwell, J.C., 492, 499-507, 542 Mazini, G.B., 358 McLean, L., 512, 516, 529 Mead, R., 358 Mehrtens, G.C., 542 Melan, J., 542-543fn Menabrea, L.F., 434, 436, 452, 469,
471,476,477,488-491,508, 510fn, 512, 514-516, 529
Mentre, F., 471 Mersenne, M., 358 Mery, E., 428, 434 Milhaud, G., 471 Mohr, 0., 487, 530-543 Molinos, L. de, 479 Monge, G., 313 Moseley, H., 432, 434, 476, 508, 511fn Mossotti, O.F., 432, 457, 468, 469,
471,478,489,508,514 Miiller-Breslau, H.F., 542-543 Musschenbroek,P.van, 357,358,362-
364
Naderi, A., 315fn Napoleon 1,455 Nasce, V., 514fn Nava, A., 371fn Navier, L., 409, 431-432, 479, 497,
516 ' Nelli, G.B.C., 350 Nelli, G.F., 350 Newton, I., 473 Nicol, W., 499
Oersted, H.C., 474 Oravas, G.Ae., 512, 513, 516, 529 Orlandi, D.G., 352
Pagani, G.M., 477, 478, 489, 508
Paoli, P., 451-452, 455, 457, 460 Pappus, 311 Parent, A., 325fn, 331, 358 Parodi, A., 490 Pasquale, S. Di, 313fn, 457fn Pearson, K., 441, 466, 467, 470 Perrodil, J.R. de, 436 Perronet, J.R., 399fn Picard, G., 358 Piola, G., 432, 457, 466-467 Pitot, H., 342 Pliny, 312 Pluecker, J., 526 Podio Guidugli, P., 473 Poinsot, L., 461, 472 Poisson, D.S., 461, 463, 468, 469, 516 Pole, W., 483 Poleni, G., 327, 352, 358-371, 372fn Poncelet, J.V., 375, 426-429, 526 Pronnier, C., 479 Prony, R., 399fn
Regi, F. de, 372 Riccati, G., 411fn Riccati, J., 411fn Riccati, V., 411fn, 451 Richer, 358 Ritter, A., 534 Rocchi, E., 471 Romano,450 Rombaux, G.B., 515 Rondelet, J., 315 Rostand, J., 471 Ruyer, R., 471
Sabbia, E.F., 490, 508 Saint-Venant, A. Barre de, 467, 516 Salimbeni, L., 331, 342, 344, 375, 406,
425-428, 449 Santini, D.S., 357 Scamozzi, V., 312, 350 Scheffler, H., 434 Schwedler, J. W., 534 Sclopis, F., 471 Second, J., 471 Seneca, 309fn Sengher, G.F., 350 Seur, T. Ie, 352, 356fn Sganzin, M.S., 399fn
Siacci, F., 508 Signorini, A., 473fn Somigliana, C., 503 Sorel, G., 472 Souflot, J.G., 376 Staudt, G.K.C. von, 526 Stefano, R. Di, 352fn, 353fn Stephenson, R., 480, 483 Stevin, S., 442, 443 Stirling, J., 358, 359 Swedenburg, E., 358
Tate, T., 483 Taviani, P., 471 Thomson, W. (Lord Kelvin), 470, 512 Timoshenko, S.P., 375, 432, 516 Todhunter, I., 441, 466fn, 470fn Torricelli, E., 349 Truesdell, C., 328-330
Author Index 547
Vanvitelli, L., 353 Vene, A.A., 474, 476, 508, 514, 529 Venturoli, G., 344, 397, 399, 414, 420-
422, 457 Villarceau, Y., 428, 490 Viollet Ie Due, E., 315 Vitruvius, Pollio, 310 Vittone, B.A., 311, 315, 400 Viviani, V., 311-313, 349, 350
Waller, R., 328 Weingarten, J.L., 508 Weyrauch, J.J., 508, 542, 543fn William of Ockham, 460 Winkler, E., 436, 437, 443, 530 Wolff, C., 315 Wood, R., 400
Subject Index
Abutments (piers) empirical evaluation of the thrust
on-, Leonardo's intimations, 309-310; Lorgna's experiments, 404-405; ancient geometrical rules for determining the thickness of-, according to Deran, 313-315; according to medieval Arabian builders, 315fn; statical calculation of the width (or thickness of)-, de la Hire's method, 331-336; Belidor's improvement, 336-338; Bossut's contribution, 384; Mascheroni's solution, 416-420
Adherence between voussoirs de la Hire's hypothesis, 332; Cou
plet's approach, 342; Favre's remarks, 357-358; Coulomb's theory, 394-399; Mascheroni's and Venturoli's analysis, 414-420
Alberti's prejudice on the best figure of an arch, 311
Amici's general equations for a masonry structure, 432
Analogy between arch and bow according to Leonardo, 317fn, and Fabri, 315-320
Analogy between the problem of the arch
and the funicolar problem: de la Hire's theorem, 322-326; Mery's method, 434-436; between arches and catenaries: Gregory's and Jakob Bernoulli's demonstrations, 326-330; Krafft's contribution, 331; Stirling's solution, 359; Poleni's experiment, 359; Bossut's deduction, 381-382; Coulomb's
demonstration, 387-388; the case of arches of finite thickness, according to Salimbeni, 426-428; extension of the analogy to domes, according to Poleni, 360-362, and according to BOS8ut, 384; between domes and curtains: Bouguer's theory, 344-348; the case of domes of finite thickness, 420-424
Analogy between the linear equation of the elastic line, the linear equation of the funicolar curve, and the equation of equilibrium for beams, 530fn
Annular and spiral vaults, 412 Arabian rule for determining the thick
ness of the walls of an arch, 315fn
Arch Leonardo's concept of-, 309; ge
ometrical rule for the safety of an- according to Leonardo, 309, and according to Couplet, 342; the best figure of an-: Alberti's prejudice, 311; Gregory's and Jakob Bernoulli's solution for very thin arches, 327-330; Stirling's contribution, 359; Bossut's general theory, 375-383; Coulomb's demonstration, 388; Lorgna's attempt, 405-406; M. Fontana's equation, 407; Salimbeni's theory for arches of finite and uniform thickness, 426-428; of variable thickness in the hypothesis of smooth and mortarless voussoirs: de la Hire's approach, 322-326;
Arches (cont.) Couplet's variant, 339-342; Bossut's
general formulae, 379-381; Coulomb's solution, 388-390; Lorgna's approach, 406-407; G. lliccati's and M. Fontana's solution, 408-409; Salimbeni's contribution, 426; collapse mechanisms and limit analysis: de la Hire's theory, 332-336; Belidor's variant, 336-338; Couplet's contribution, 342-344; Bossut's remark, 384-385; Coulomb's method for determining the safety conditions, 394-399; Danyzy's, Gauthey's and Boistard's experiments, 399fn; Mascheroni's and Ventur-oli's limit analysis, 414-420; Audoy's contribution, 429; Lame and Clapeyron's theorem, 430-431; made of elastic material: M. Fontana's approach, 409-411; Navier's solution, 431-432; Moseley's principle of "least pressure" , 434; Mery's method, 434-436; Winkler's contribution, 436-437; Curioni's theory, 437fn
Asnieres bridge, 484
Barrel vaults, see Arch Betti's theorem of reciprocity, 503 Boscovich's studies on St. Peter's dome,
351-357, and on the Cathedral of Milan, 371-374
Bossut's theory of vaults, 375-386 Bouguer's theory of domes, 344-348,
420-424 Breaking tests: on iron bars, 364; on
models of vaults, 399fn Bridge of S. Trinita in Florence, 328 Bridges built over the Garonne, Lot
and Tarn rivers, 484 Britannia bridge, 480-484
Subject Index 549
Castigliano's demonstration of Menabrea's
"principle of elasticity" , 517-518; theorem of work derivatives, 518-519; calculation of tensions in the case of self-straining, 520-522
Cathedral of Milan, 371-374 Cathedral of S. Maria del Fiore in
Florence,312-313,349-351 Center of thrust
on the weakest joints of an arch: de la Hire hypothesis, 332; Belidor's assumption, 338; Couplet's solution, 340; M. Fontana's theory, 407-411; Mascheroni's solution, 416-420; Navier's contribution, 431; Moseley's and Gerstner's investigations, 432; Mery's principle of the middle third, 434; on the key of an arch: Couplet's assumption, 340; Coulomb's approach, 389-394; Mery's assumption, 434; Winkler's theory, 436-437
Centering building of domes without-, 313,
350-351; the problem of-, 340,425
Chapel of Santa Coloma, 346 Circular arch
Alberti's statement, 311; de la Hire's theorem, 332-334; Couplet's analysis of limit equilibrium, 342-344; Bossut's application of his general formula, 379; Coulomb's calculation of the scaling of the width, 389-390; M. Fontana's calculation of the "convex curve" (extrados), 408-409
Circular planes composed of wedges having the force of domes, 412
550 Subject Index
Clapeyron's (and Lame's) theorem on the
location of the fracture joints in an arch, 430-431; three moment equation for the continuous beam, 484-485; fundamental theorem, 487-488,499,508,517
Clebsch's solution for the continuous beam,
493-495; method of deformations, 495-498
Coefficients of influence, 539-541 Cohesion, "produced by friction" , ac
cording to Poleni, 364; due to tangential and normal stresses, according to Coulomb, 394-399; see also Adherence between voissoires
Collapse mechanisms for arches or domes; for St. Peter's dome, according to The Three Mathematicians, 353, 356; according to Poleni, 372fn; see Arch, Dome
Colonnetti's general theory of selfstraining, 522-523
Commissum denticulata, 318 Compatibility conditions, 505-507,
539-541 Complementary energy, 524-529 Composed arches and vaults, 412 Concept of force (or pressure), 442-
444, 466, 467, 473-474 Constitutive equation for elasticity,
470 Continuous beam
Clapeyron's solution, 479-485; Bertot's contribution, 485-486; Clebsch's solution, 493-495
Convex curve (extrados of an arch), see Arch of variable thickness
Conway bridge, 480-483 Corncob or pomegranate model for
the rupture of domes, 372-374
Cotterill's extension of the principle of least
action (or pressure), 508-509; discovery of the theorem of work derivatives, 509-512
Coulomb's theory of frictionless and mor
tarless vaults, 386-394; general equation of the figure of a vault acted upon any load, 388; calculation of the width of any vault under its own weight,' 388-390; the problem of the platband in masonry, 391-393; theory of vaults endowed with friction and cohesion, 394-399; collapse mechanisms, 395, 398-399; safety conditions, 396-397
Couplet's theory of arch, 338-344 Cournot's minimum principle, 475-
476 Crotti's
concept of reciprocal deformation work (or complementary energy), 524, 529; postulate of concordant movement, 526-527; seven "double theorems" for the theory of elastic systems, 525-529
D'Alembert's approach to the problem of supports, 445-447; general principle, 472
De la Hire's analogy between the problem
of the arch and the funicolar problem, 322-326; collapse mechanism of an arch, 332,336,342,353,399,416, 418; calculation of the width of the abutments of an arch, 334-336
Deflections in a frame Clebsch's approach, 495-498;
Deflections in a frame (cont.) Maxwell's method, 501-503; Cas
tigliano's solution, 518-519; Mohr's solution, 533-534
Deformation work (or energy of elastic deformation), 487-489, 508-509,514-515,517-522, 524-529, 543
Delange'S hypothesis for the problem of supports, 456
Deran's rule for determining the thickness of the walls of an arch, 314-315
Dome building of-, without using props,
scaffolds and centering, 313, 350-351; geometrical constructions for the figure of domes and the dimensions of their supports, 311, 353; the best profile of a-: Bouguer's solution for domes of minimum thickness, 344-347; Poleni's contribution, 360-362; Bossut's general equation, 384; Mascheroni's the-ory for domes of finite thickness, 420-424; -of variable thickness in the hypothe-sis of smooth and mortar-less voussoirs: Bouguer's and Mascheroni's theory, 422-424; the case of uniform thickness, 424; collapse mechanisms: according to The Three Mathematicians, 353, 356; according to Poleni's and Boscovich's model of corncob or pomegranate, 372; -with a polygonal and oval base, 412
Door hinges, the problem, 457 Dorna's minimum principle, 479 Duality, law of- in geometry, 526; in
elastomechanics, 524-529 Dynamique latente, 474
Egg, the problem, 312, 321 Elastic potential energy, 436, 469-
Subject Index 551
470, 487-488; see also Deformation work
Elastic systems, 441, 488-491, 513-522
Elasticity principle (or equation), see Menabrea's principle of elasticity
Elastoplastic analysis of structures, 520-523
Empirical evaluation of the thrust on abutment piers, 309 '
Energetical principles, see Minimum principles
Equilibrium curve in converging directions of
loads, 412; for an arch, see arch, the best figure of; for a dome, see dome, the best profile of
Ether, 468 Euler's
principle for the problem of supports, 444, 465, 477; solution of the tripod problem, 444-445,447-448,451,455, 513-514
Extrados, calculation of the- when the intrados is given, 408-409, 411fn, 426; see Arch or Dome, of variable thickness
Fabri's analogy between arches and bows, 316-320
Florentine rib-and-panel vault, 312 Flying buttresses, 315, 335, 412 Fontana's, C., geometrical rules for
domes, 311, 353 Fontana's, M., calculation of the "con
vex curve" of an arch, 408-409; discovery of ''the middle third rule", 409-411; attempts at finding a "new synthesis" for the problem of supports, 453-455
Fracture joints location of- in an arch: de la
Hire's hypothesis, 332; Belidor's assumption, 436;
552 Subject Index
Fracture joints (cant.) Couplet's theory, 342 Bossut's
remark, 384-385; Coulomb's method, 394-399; Mascheroni's and Venturoli's method, 416-420; Lame and Clapeyron's theorem, 430-431; Gerstner's remark, 432; Mery's assumption, 434; location of- in a dome: the case of St. Peter's, according to the three mathematicians, 353-356; Boscovich's remark, 374
Friction, Cohesion de la Hire's remark, 326; Cou
plet's remark, 342; Poleni's law, 364; Boscovich's remark, 372; Coulomb's laws of- and their application to the analysis of vaults, 390, 394-397; Venturoli's contribution, 414-420; Amici's treatment, 432; Moseley's and Gerstner's remarks, 432; coefficient (or angle) of friction, 396, 414, 432, 520; in elastic structures, 520; see also Adherence between voussoirs
Frictionless (or smooth) and mortarless voussoirs (or joints), see Arch, Dome
Funicular equilibrium, 322-324, 342 Funicular polygon of forces, 435
Galileo's explanation of the strength of the egg, 312
Geometrical rules for determining the width of the
abutments of a vault, 314-315; for the figure of domes, 311, 353; for the safety of an arch, 309, 342
Geometrie der Lage (geometry of position), 526
Green's approach to the theory of elasticity, 468-470, 517
Horror vacui, 312
Impact between two rigid bodies, 472-473
Joints direction of-, when both the in
trados and the extrados of a vault are given, 391-394; see also Fracture joints
Key of an arch, see Center Of thrust on the-
Lagrangean methods, 451, 460, 466-467,469,510-511,517-518
Law of weights (or forces), given the figure of a vault, see Arch, Dome, of variable thickness
Leonardo's empirical evaluation of the thrust of an arch, 309; rule for the safety of an arch, 309, 342
Limit analysis of arches, see Arch Line of influence, 530-531 Line of pressure, 432, 435 Line of resistance, 432, 435 Lorgna's approach to the theory of
arch, 404-407; postulate for the problem of supports, 452-453
Malfatti's "physical axiom" for the problem of supports, 458; teleonomic principle, 460
Mascheroni's contribution to the theory of vaults, 412-425
Maxwell's concept of frame, 492, 507; cal
culation of deflections in a simply stiff framework, 501-502; theorem of reciprocity, 503; calculations of tensions in statically indeterminate frame- works, 504-507
Mechanisms of collapse for arches and domes, see Arch, Dome
Menabrea's principle of elasticity, 433, 436,476,479,488-491,512, 513-518, 520
Method of deformations, 492-498, 517-518
Method offorces, 499, 504-507, 537-542
Method of Lagrange multipliers, see Lagrangean methods
Method (or rules) of maxima and minima, 374, 386-387, 396-398,433,436-437
Middle third, rule of the-, 409-411, 431, 434
Minimum principles Vene's memoir, 474; Cournot's
solution, 475-476; Moseley's new principle of least pressure, 434, 476; Pagani's and Mossotti's contribution, 477-478; Dorna's solution, 478-479; Menabrea's principle of elasticity, 489-490; Bertrand's demonstration, 491; Cotterill's extension of Mose-ley's principle, 508-509; Castigliano's demonstration of Menabrea's principle, 517-518; Colonnetti's contribu-tion, 522-524; Crotti's "double theorem No. two", 525, and "double theorem No. seven" , 529
Model of smooth spheres for determining the best figure of an arch or of a dome, 359-362
Mohr's analogy between the linear equa
tion of elastic line, the linear equation of the funicolar curve, and the equation of equilibrium for beams, 530fn; solution for deflections in statically determinate trusses, 530-534;
. solution for non-canonical trusses, 534-537; solution
Subject Index 553
for statically indeterminate trusses, 537-542
Molecular theory of elasticity, 432, 467-469, 516-517
Moseley's principle of least pressure (or action), 434, 436, 476, 508-509
Mossotti's minimum principle, 477-478
Muscles Borelli's interpretation of their
action, 364; Johann Bernoulli's improvement of Borelli's mechanical model, 364-368; Poleni's experiments on Bernoulli's results, 368
Natural state of a frame, 522-523 Naval architecture, 344, 375 Non-canonical trusses, 534-537 Notched joints, 318
Pagani's minimum principle, 477 Paradox of statics, 461-462 Piesimetro, 463 Planes composed of wedges having
the force of arches, 412 Platbands in masonry, 391-394, 412-
413 Poleni's studies on St. Peter's dome,
358-371 Polygonal roofs
Leonardo's model of two bars, 309; Fabri's treatment, 316-320; Borra's approach, 400; Belgrado's solution, 400-401; Lorgna's investigation, 405; Mascheroni's analysis of the quadrangular and pentagonal roof, 414-416
Principle of elasticity, see Menabrea's
Principle of least pressure (or action), see Moseley's -
Principle of virtual work (or of virtual velocities), 356-357, 451, 456,466,475,478,488,491, 523, 531-541, 542
554 Subject Index
Pyrometer, 364
R,eciprocal deformation work, 524, 529
Reinforced beam, 318 Relative elasticity coefficients, 490 Retaining wall, 339, 405 Rigid bodies, 407, 433-434, 443-444,
461, 463-466, 472-473 Roman hull-shaped vault, 312 Roof, see Polygonal roofs Round dome of variable or constant
thickness, 424-425 Rupture joints, see Fracture joints
Safety conditions for a vault, see Arch, Dome
Scale of voussoir sizes, see Arch, Dome, of variable thickness
Second fundamental law of the dynamical theory of heat, 470
Semicircular arch, see Circular arch Smooth, frictionless voussoirs, see Arch,
Dome Stability of equilibrium, 480, 512, 520,
529 Statically determinate systems, cal
culation of deflections in-, see Deflections in a frame
Statically indeterminate systems, 407, 428,433-434,443,445,448, 451,455,457,458,460,463, 465,466-467,489,504-507, 537-542
Supports problem, 441-460, 461-466, 474-476,477-479,487,492
Tetrapod problem, according to M. Fontana, 454-455; according to Malfatti, 458-459
Theorem of minimum work, 489-491, 509,512,514-515,517-518, 529
Theorem of reciprocity, 503, 525-526, 541
Theorem of work derivatives, 442, 470, 509-512, 515-516,
518-519, 524-525, 542 Thermal effects on elastic structures,
521, 532-533, 538-539 Three Mathematicians'
studies on St. Peter's dome, 351-357; theorem on the strength of a ring, 356-357; Poleni's experiment on- theorem, 364-368
Three moment equation, 479, 484-487
Thrust of earth, 339, 405 Thrust of the arch on its abutments,
see Abutments, Center of thrust
Trabs armata, 318 Tripod problem, 444-445, 447-448,
459, 514 Tubular bridges for the London-Chester
Holyhead railway, 480-484
Underwater arch, 382-383 Unilateral constraints, 445-447, 452-
453, 456, 463
Vaults, see Arch, Dome VEme's minimum or maximum prin
ciple,474 Viviani's rules for squaring vaulted
ceilings, 311-312 Voussoirs, see Arch, Dome, of vari
able thickness in the hypothesis of smooth and mortarless voussoirs; see also Adherence between voussoirs
Walls of an arch, see Abutments Wedge (and lever) models for the
static behavior of an arch, 325-326,332,339-340,353-356
Winker's minimum principle, 436-437