131:
400:
424:
79:
20:
358:
326:
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480:
354:
parallels to DO through the points of division a, b, c. The points where these parallels intersect the horizontal axis AB and the extended vertical axis CO give the centers we need to trace various curves with 3 centers on AB, as shown in the figure. These curves are what we usually call the ancient oval.
881:
Finally, at the point of intersection n'' of these two lines, a parallel is drawn to the radius Oc, and the points m3, m4 where it intersects the extension of the radius n'm2 and the extension of the vertical axis give the third and fourth centers. The last three centers m5, m6 and m7 are symmetrical
558:
The following table refers to the drawing of the basket-handle arch with equality of the angles subtended by the parts of the arcs of which it is composed. The proportional values it gives for the first radii are calculated using the half-opening as the unit. The overhang is the ratio of the arrow to
414:
The intersection of AM and Em determines the boundary m of the first arc. By drawing the line mP parallel to MO through this point m, the points n and P are the two centers we're looking for. The third center n is located at a distance n'O from the axis OE equal to nO. It's enough to study the figure
385:
This ratio may be one-third, one-quarter, one-fifth, or less, but as soon as it falls below one-fifth, the circular arc should generally be preferred to the basket-handle arch or ellipse. With a larger slope, it's a good idea to have at least five centers, and we've sometimes allowed up to eleven, as
373:
Sometimes, for example, it was accepted that the various arcs of a circle, of which the curve is composed, must correspond to equal angles at the center; sometimes, these partial arcs were assumed to be of equal length, or again, either the amplitude of the angles or the length of the successive rays
872:
On the AB axis, starting from point A, we take a length equal to 1.590 m and have the first center m1. A parallel of radius Oa is drawn through this point, and the point n where it meets the chord Aa is the limit of the first arc. From point n, we take a length nm2 equal to 2.514 m, and point m2 is
410:
Given AB as the opening and OE as the arrow of the vault, from the center O, with OA as the radius, we describe the arc AMF, from which we take the arc AM, equal to one sixth of the circumference, and whose chord is therefore equal to the radius OA. Draw this chord AM and the chord MF, then draw Em
438:
AB and OE are again the opening and the arrow of the vault, i.e., the long and the short axis of the curve to be traced. We join AE and from point E we take EF' to be equal to OA-OE, then we draw a perpendicular through the middle m of AF' and the points n and P, where this perpendicular meets the
292:
curve are fixed, without the architect being able to change anything at will. On the other hand, the multi-center curve can be more or less rounded at the base and more or less flattened at the top, depending on the arrangement of the centers, leaving a certain amount to the architect's taste.
353:
mn, on which we take the lengths Cm and Cn equal to half the radius. By joining mO and nO, we determine points D and E, through which we trace the isosceles triangle DOE, whose base is equal to the height. Once this has been done, we take the line DA, divide it into four equal parts, and draw
365:
Since the basket-handle arch has been widely used in bridge construction, the procedures proposed for tracing it have multiplied, and the number of centers has increased. The following is a brief description of the most widely used of these procedures.
369:
The goal was to create perfectly continuous curves with an elegant contour. Due to the indeterminate nature of the problem, certain conditions were arbitrarily imposed on the assumption that they would lead more reliably to the desired result.
877:
Ob, from point n a parallel to the chord ab, and the point of intersection n' of these two parallels is the limit of the second arc. Then, through point n', we draw a parallel to the chord bc, and through point E, a parallel to the chord cd.
377:
Moreover, it has always been accepted that a certain ratio should be maintained between the lowering of the arch and the number of centers used to trace the intrados curve, thus lowering being measured, for the basket-handle arch as for the
853:
It's easy to see how you can use this table to draw a basket-handle arch with any opening at five, seven, or nine centers without doing any research. The only requirement is that the drop is exactly one of those predicted by Mr. Michal.
857:
For example, we need to draw a curve with seven centers, a 12-meter opening, and a 3-meter slope corresponding to a quarter or twenty-five-hundredth drop. The first and second radii are 6 x 0.265 and 6 x 0.419, or 1.594 and 2.514.
537:
In a paper published in 1831, Mr. Michal dealt with the question more scientifically and prepared tables containing the data necessary to draw curves with 5, 7, and 9 centers without trial and error and with perfect accuracy.
390:
Bridge or even up to nineteen for the Signac Bridge. Since one of the centers must always be on the vertical axis, and the others symmetrically arranged in equal numbers to the right and left, the total number is always odd.
889:
with AB and OE as the major and minor axes, the arcs of this semi-ellipse, contained within the same angles as the arcs of the circle, would have a radius of curvature in their center equal to the radius of the latter.
465:
Tracing a first approximate curve according to arbitrary data, whose elements were then rectified, using more or less certain formulas, so that they passed exactly through the extremities of the major and minor axes.
301:
The advantages in terms of layout were undeniable: the layout of full-scale grooves was considered easier and more precise, and the layout of the normals, and thus the segment joints, was immediately on site.
348:
If AB is the width of the vault to be built, its height (or rise, or spire) being indeterminate, we describe a half-circumference on AB, and through the point C of this, taken on the vertical OC, we draw the
277:
The ancient architects attached a certain importance to the processes that were used to define the outline of the basket-handle arch. It's easy to understand that these processes can vary
415:
to see that the three arcs of the circle Am, mEm', m'B that make up the curve correspond to angles at the centers Anm, mPm,' and m'n'B that are equal to each other and all three of 60°.
407:
For curves with three centers, the following procedure, according to
Huyghens, consists in tracing them by making arcs of different radii correspond to equal angles, i.e., angles of 60.
190:(1766–1774) with eleven centers in the second half of the 18th century. There were also eleven centers in Tours (1764–1777). The others were reduced to 1/3 or a little more, except for
548:
subtending equal angles, sometimes of arcs of equal length. Since this is not sufficient to determine all the radii, he also assumes that the radii of each arc are equal to the
544:
Since the conditions that must be met for the problem to cease to be indefinite are partly arbitrary, Mr. Michal proposes that the curves be composed sometimes of arcs of a
1363:
Les Ponts, Monuments historiques : inventaire, description, histoire des ponts et ponts-aqueducs de France protégés au titre des monuments historiques
885:
As the figure shows, the arcs An, nn', n'n'', etc. correspond to equal center angles and da 51° 34' 17" 14. What's more, if we were to construct a semi-
312:
However, the discontinuity of the layout led to the appearance of unsightly voussoirs, which could not always be removed during restoration work.
1435:
1123:
288:
In the case of an ellipse, given the opening of a vault and the height at the center, i.e., the major and minor axes, all the points of the
130:
498:
490:
552:
of curvature of the ellipse described in the center of these arcs, with the opening as the major axis and the ascent as the minor axis.
1498:
1389:
1370:
309:
shapes was limited to the number of different radii, whereas for the ellipse, it was equal to half the number of voussoirs plus one.
1408:
516:
62:
variation from its origin to its apex, i.e. from the extremities of the long axis to the apex of the short axis. Also known as a
345:(who wrote his mathematical treatises more than a century before our era) had already defined a simple method for tracing it.
869:, dividing it into seven equal parts and tracing the chords Aa, ab, bc, cd, the latter corresponding to a half-division.
555:
As the number of centers increases, the curve becomes closer and closer to the ellipse with the same opening and slope.
382:, by the ratio of the rise to the opening, i.e. by the ratio b/2a, where b is the rise and 2a is the width of the arch.
1296:
Annales des ponts et chaussées. Mémoires et documents relatifs à l'art des constructions et au service de l'ingénieur
1271:
Annales des ponts et chaussées. Mémoires et documents relatifs à l'art des constructions et au service de l'ingénieur
165:
82:
1348:
1310:
1285:
285:, architects have often preferred the curve thus traced to the ellipse, whose contour is determined geometrically.
123:, offering an undeniable aesthetic advantage over the segmental vault: the fact that its end arches are vertically
105:, an incomplete half-circumference, was used to build vaults that were less than half the height of their opening.
914:
increase according to an arithmetic progression, regardless of the equality of the angles they form between them.
54:. The basket-handle arch is used in architecture, especially bridges. Its shape is similar to that of a semi-
451:
175:
161:
152:
In the 18th century, the use of basket handle arches was common, often with three centers: the bridges of
1508:
1493:
442:
With the same opening and rise, the curve drawn in this way differs very little from the previous one.
282:
90:
1294:
329:
Trace of a three-center cove using the method of Heron of
Alexandria (without construction circles)
227:
A few basket-handle arches remained in the second half of the 19th century and early 20th century:
142:
1269:
1304:
1279:
907:, who also drew up tables for tracing curves with three, five, seven, and up to fifteen centers.
342:
261:
1427:
455:
361:
Trace of a three-center cove using the method of Heron of
Alexandria (with construction circles)
46:
to each other (smoothly transitioning), and the end ones tangent with supports. For example, a
1465:
1446:
1431:
1404:
1385:
1366:
1119:
1116:
The Great Road: The
Building of the Baltimore and Ohio, the Nation's First Railroad, 1828–1853
459:
387:
191:
187:
116:
is greater than half the opening), was not used in bridge construction until the Middle Ages.
94:
1319:
1503:
1423:
183:
338:
264:
and is still in use today, making it one of the oldest railroad bridges still in service.
221:
179:
893:
This method can construct curves with five, seven, and nine centers with the same ease.
439:
major axis and the extension of the minor axis, are the two centers we're looking for.
432:
399:
253:
198:
102:
78:
23:
19:
423:
1487:
1268:"Notice sur les courbes en anse de panier employées dans la construction des ponts".
901:
After Mr. Michal, the topic was taken up again by Mr. Lerouge, chief engineer of the
217:
202:
157:
1299:(in French). Pierre-Jacques Lerouge. Paris: Carilian-Goeury. 1839. pp. 335–362.
541:
His method of calculation can also be applied to curves with any number of centers.
112:, which, instead of reducing the excess height of vaults, accentuates it (since the
379:
278:
109:
42:(inner surface) formed by a sequence of circular arcs with neighboring ones being
1112:, The Maryland Surveyor, September 2000,pp 20-28, , accessed 6 April 2024 citing
120:
113:
98:
357:
325:
213:
146:
134:
238:
With five centers: Annibal Bridge (1868–1870) and Devil's Bridge (1870–1872).
50:
contains three arc segments with different centers; the other common type is
529:
232:
206:
59:
1274:(in French). Zoroastre Alexis Michal. Paris: Carilian-Goeury. 1831. 49-61.
450:
For curves with more than three centers, the methods indicated by BĂ©rard,
910:
However, his calculations are based on the condition that the successive
866:
306:
39:
26:
of the
Baltimore and Ohio railroad as an example of a basket handle arch.
1342:(in French). Vol. 3. Bourges: Imprimerie Vve Tardy-Pigelet et fils.
1333:(in French). Vol. 1. Bourges: Imprimerie Vve Tardy-Pigelet et fils.
886:
350:
257:
153:
124:
55:
43:
911:
874:
549:
545:
334:
242:
169:
865:
is to be inscribed, we describe a half-circumference on AB as the
862:
528:
422:
398:
356:
324:
149:
in the following century are the earliest applications in France.
129:
77:
873:
the second center. From this point m2, we draw a parallel to the
341:, it was sometimes used in the construction of other vaults. And
201:
bridges were basket-handle arches: Cinq-Mars bridge (1846–1847),
289:
252:
One basket-handle arch railway bridge in the United States, the
35:
473:
411:
through point E, the end of the minor axis, parallel to MF.
929:
119:
The basket-handle arch appeared at the beginning of the
97:, forming a complete half-circumference. From the early
1347:
Ministère des
Transports, Direction des routes (1982).
374:
was allowed to vary according to certain proportions.
224:
in London (1816–1818) was still basket-handle arches.
1418:
Woodman, Francis; Bloom, Jonathan M. (2003). "Arch".
1401:
533:
Trace of a seven-center cove using the Michal method.
427:
Trace of a three-center cove using the Bossut method.
403:
Trace of a three-center cove using the
Huygens method
1331:
Grandes Voûtes : Partie 1 – voûtes inarticulées
16:
Plane curve drawn by an odd number of circular arcs.
1340:Grandes Voûtes : voûtes inarticulées (suite)
333:Although the basket-handle arch was not used for
268:Comparison between basket handle arch and ellipse
248:With nineteen centers: Signac Bridge (1871–1872).
435:for tracing the same 3-center curve is faster.
241:With seven centers: Emperor Francis Bridge in
231:With three centers: Edmonson Avenue Bridge in
8:
1293:"Mémoire sur les voûtes en anse de panier".
1252:
1240:
1228:
1213:
1201:
1186:
1174:
1142:
1118:. Palo Alto, CA: Stanford University Press.
982:
965:
953:
902:
209:(1843–1845), Plessis-les-Tours (1855–1857).
197:In the 19th century, the first major French
85:in Orléans - Three-center basket-handle arch
882:concerning the first three m1, m2, and m3.
462:bridge, in proceeding by trial and error.
137:in Paris - Three-center basket-handle arch
1428:10.1093/gao/9781884446054.article.t003657
1097:
1085:
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1013:
1001:
517:Learn how and when to remove this message
1324:(in French). Vol. 2. Paris: Baudry.
561:
281:, but precisely because of this kind of
205:bridge (1846–1848), Morandière bridges:
145:in Toulouse in the 16th century and the
18:
1110:BENJAMIN LATROBE and the THOMAS VIADUCT
922:
1302:
1277:
861:If ABCD is the rectangle in which the
178:designed the arches of the bridges of
1318:Degrand, Eugène; Resal, Jean (1887).
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1222:
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256:, was constructed in 1833-1835. The
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997:
995:
993:
991:
978:
976:
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1445:American Technical Society (1920).
458:, and others consisted, as for the
446:Curves with more than three centers
1470:A Treatise on Masonry Construction
932:, p. 395, Basket-Handle Arch.
489:tone or style may not reflect the
168:(1750–1760), Moulins (1756–1764),
14:
316:Tracing curves with three centers
220:(1824–1831) were elliptical, the
499:guide to writing better articles
478:
386:in the case of the curve of the
1451:Cyclopedia of Civil Engineering
1382:Ponts et Viaducs au xixe siècle
930:American Technical Society 1920
1:
260:is now owned and operated by
297:Advantages and disadvantages
194:, which was reduced to 1/4.
1422:. Oxford University Press.
1356:(PDF) (in French). Bagneux.
216:Bridge (1826–1827) and the
89:Since Roman times, bridges
1525:
1499:Piecewise-circular curves
1253:Degrand & Resal (1887
1241:Degrand & Resal (1887
1229:Degrand & Resal (1887
1214:Degrand & Resal (1887
1202:Degrand & Resal (1887
1187:Degrand & Resal (1887
1175:Degrand & Resal (1887
1143:Degrand & Resal (1887
983:Degrand & Resal (1887
572:
569:
566:
58:, which has a continuous
1114:Dilts, James D. (1996).
966:Woodman & Bloom 2003
954:Woodman & Bloom 2003
431:The following method by
38:with the profile of its
1403:(in French). Brissaud.
1384:(in French). Brissaud.
1365:(in French). Brissaud.
1350:Les ponts en maçonnerie
1338:Séjourné, Paul (1913).
1329:Séjourné, Paul (1913).
1016:, pp. 93, 97, 103)
493:used on Knowledge (XXG)
1399:Prade, Marcel (1990).
1380:Prade, Marcel (1988).
1361:Prade, Marcel (1986).
1309:: CS1 maint: others (
1284:: CS1 maint: others (
903:
534:
497:See Knowledge (XXG)'s
452:Jean-Rodolphe Perronet
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362:
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212:In England, while the
176:Jean-Rodolphe Perronet
138:
86:
27:
1472:. J. Wiley & sons
532:
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360:
328:
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93:have been built with
81:
22:
1466:"Basket-Handle Arch"
1464:Baker, I.O. (1889).
1447:"Basket-Handle Arch"
1321:Ponts en maçonnerie
563:
559:the whole opening.
343:Heron of Alexandria
95:semicircular arches
48:three-centered arch
904:Ponts et Chaussées
897:The Lerouge method
562:
535:
429:
405:
395:The Huygens method
363:
331:
262:CSX Transportation
139:
87:
32:basket-handle arch
28:
1437:978-1-884446-05-4
1420:Oxford Art Online
1125:978-0-8047-2629-0
851:
850:
527:
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491:encyclopedic tone
470:The Michal method
419:The Bossut method
127:to the supports.
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501:for suggestions.
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321:The ancient oval
186:(1766–1769) and
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1074:Séjourné (1913a
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1062:Séjourné (1913a
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1038:Séjourné (1913a
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222:Waterloo Bridge
83:George V bridge
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1255:, p. 371)
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103:segmental arch
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24:Thomas Viaduct
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339:ancient times
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218:London Bridge
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203:Port-de-Piles
200:
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182:(1757–1765),
181:
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172:(1756-1770).
171:
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164:(1716–1724),
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101:onwards, the
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52:five-centered
49:
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25:
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1509:Arch bridges
1494:Architecture
1474:. Retrieved
1469:
1454:. Retrieved
1450:
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1262:Bibliography
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956:, Depressed.
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380:circular arc
376:
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279:ad infinitum
276:
251:
245:(1898–1901).
235:(1908–1909).
226:
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151:
140:
118:
110:pointed arch
107:
88:
67:
63:
51:
47:
31:
29:
1160:Prade (1986
602:3nd radius
599:2nd radius
596:1st radius
590:2nd radius
587:1st radius
581:1st radius
121:Renaissance
99:Middle Ages
68:basket arch
1488:Categories
1476:2024-04-05
1456:2024-04-05
1130:page 162.
942:Baker 1889
918:References
573:9 centers
570:7 centers
567:5 centers
507:March 2024
337:vaults in
283:elasticity
273:Aesthetics
214:Gloucester
156:, Lavaur,
147:Pont Royal
135:Pont Royal
125:tangential
1305:cite book
1280:cite book
968:, Basket.
233:Baltimore
207:Montlouis
143:Pont-Neuf
60:curvature
867:diameter
307:voussoir
290:intrados
199:railroad
40:intrados
1504:Bridges
887:ellipse
460:Neuilly
388:Neuilly
351:tangent
258:viaduct
192:Neuilly
188:Neuilly
166:Orléans
154:Vizille
74:History
56:ellipse
44:tangent
1434:
1407:
1388:
1369:
1122:
875:radius
839:0,419
836:0,265
816:0,445
813:0,289
793:0,472
790:0,312
784:0,396
776:0,443
773:0,228
770:0,166
764:0,498
761:0,346
755:0,423
747:0,474
744:0,251
741:0,185
735:0,525
732:0,359
718:0,504
715:0,276
712:0,203
706:0,551
703:0,383
697:0,477
689:0,535
686:0,296
683:0,222
677:0,578
674:0,406
668:0,504
660:0,556
657:0,318
648:0,604
645:0,431
631:0,597
628:0,341
625:0,259
616:0,455
610:0,556
546:circle
335:bridge
243:Prague
184:Nogent
180:Mantes
170:Saumur
158:Gignac
91:vaults
34:is an
1354:(PDF)
912:radii
863:curve
833:0,25
810:0,26
787:0,27
758:0,28
752:0,31
738:0,21
729:0,29
726:0,45
723:0,32
709:0,22
694:0,33
680:0,23
671:0,31
665:0,34
654:0,24
651:0,24
642:0,32
639:0,53
636:0,35
622:0,25
619:0,63
613:0,33
607:0,36
593:Drop
584:Drop
578:Drop
550:radii
162:Blois
1432:ISBN
1405:ISBN
1386:ISBN
1367:ISBN
1311:link
1286:link
1120:ISBN
781:0,3
767:0,2
700:0,3
141:The
114:rise
108:The
36:arch
1424:doi
1490::
1468:.
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1307:}}
1303:{{
1282:}}
1278:{{
1221:^
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1167:^
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454:,
160:,
70:.
66:,
30:A
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1288:)
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520:)
514:(
509:)
505:(
495:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
