142:
411:
435:
90:
31:
369:
337:
541:
491:
365:
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.
892:
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
569:
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
425:
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
396:
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
384:
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
883:
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
421:
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
449:
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
303:
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.
364:
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
376:
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.
380:
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.
888:
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.
388:
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
864:
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.
868:
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.
548:
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.
401:
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.
900:
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.
476:
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.
312:
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.
359:
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
288:
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
426:
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°.
418:
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.
201:(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
559:
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
555:
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
1374:
Les Ponts, Monuments historiques : inventaire, description, histoire des ponts et ponts-aqueducs de France protégés au titre des monuments historiques
896:
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-
323:
However, the discontinuity of the layout led to the appearance of unsightly voussoirs, which could not always be removed during restoration work.
299:
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
563:
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.
320:
shapes was limited to the number of different radii, whereas for the ellipse, it was equal to half the number of voussoirs plus one.
73:
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
356:(who wrote his mathematical treatises more than a century before our era) had already defined a simple method for tracing it.
1446:
1134:
509:
501:
880:, dividing it into seven equal parts and tracing the chords Aa, ab, bc, cd, the latter corresponding to a half-division.
566:
As the number of centers increases, the curve becomes closer and closer to the ellipse with the same opening and slope.
393:, 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.
1509:
1400:
1381:
1419:
1307:
Annales des ponts et chaussées. Mémoires et documents relatifs à l'art des constructions et au service de l'ingénieur
1282:
Annales des ponts et chaussées. Mémoires et documents relatifs à l'art des constructions et au service de l'ingénieur
527:
1359:
296:, architects have often preferred the curve thus traced to the ellipse, whose contour is determined geometrically.
134:, offering an undeniable aesthetic advantage over the segmental vault: the fact that its end arches are vertically
116:, an incomplete half-circumference, was used to build vaults that were less than half the height of their opening.
925:
increase according to an arithmetic progression, regardless of the equality of the angles they form between them.
141:
65:. The basket-handle arch is used in architecture, especially bridges. Its shape is similar to that of a semi-
163:
In the 18th century, the use of basket handle arches was common, often with three centers: the bridges of
17:
176:
93:
1321:
1296:
453:
With the same opening and rise, the curve drawn in this way differs very little from the previous one.
1305:
340:
Trace of a three-center cove using the method of Heron of
Alexandria (without construction circles)
238:
A few basket-handle arches remained in the second half of the 19th century and early 20th century:
1280:
918:, who also drew up tables for tracing curves with three, five, seven, and up to fifteen centers.
1438:
372:
Trace of a three-center cove using the method of Heron of
Alexandria (with construction circles)
462:
186:
172:
57:
to each other (smoothly transitioning), and the end ones tangent with supports. For example, a
1476:
1457:
1127:
The Great Road: The
Building of the Baltimore and Ohio, the Nation's First Railroad, 1828–1853
127:
is greater than half the opening), was not used in bridge construction until the Middle Ages.
1519:
1504:
1330:
293:
101:
934:
275:
and is still in use today, making it one of the oldest railroad bridges still in service.
8:
153:
904:
This method can construct curves with five, seven, and nine centers with the same ease.
1315:
1290:
450:
major axis and the extension of the minor axis, are the two centers we're looking for.
353:
272:
466:
1442:
1415:
1396:
1377:
1279:"Notice sur les courbes en anse de panier employées dans la construction des ponts".
1130:
912:
After Mr. Michal, the topic was taken up again by Mr. Lerouge, chief engineer of the
470:
398:
202:
198:
105:
1310:(in French). Pierre-Jacques Lerouge. Paris: Carilian-Goeury. 1839. pp. 335–362.
552:
His method of calculation can also be applied to curves with any number of centers.
123:, which, instead of reducing the excess height of vaults, accentuates it (since the
1514:
1434:
194:
53:(inner surface) formed by a sequence of circular arcs with neighboring ones being
1123:, The Maryland Surveyor, September 2000,pp 20-28, , accessed 6 April 2024 citing
349:
232:
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54:
443:
264:
209:
113:
34:
1357:
1498:
249:
With five centers: Annibal Bridge (1868–1870) and Devil's Bridge (1870–1872).
228:
213:
168:
61:
contains three arc segments with different centers; the other common type is
390:
289:
120:
1285:(in French). Zoroastre Alexis Michal. Paris: Carilian-Goeury. 1831. 49-61.
461:
For curves with more than three centers, the methods indicated by BĂ©rard,
300:
921:
However, his calculations are based on the condition that the successive
410:
131:
124:
109:
89:
37:
of the
Baltimore and Ohio railroad as an example of a basket handle arch.
30:
1353:(in French). Vol. 3. Bourges: Imprimerie Vve Tardy-Pigelet et fils.
1344:(in French). Vol. 1. Bourges: Imprimerie Vve Tardy-Pigelet et fils.
434:
224:
157:
145:
243:
217:
70:
278:
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50:
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is to be inscribed, we describe a half-circumference on AB as the
160:
in the following century are the earliest applications in France.
897:
884:
the second center. From this point m2, we draw a parallel to the
540:
361:
352:, it was sometimes used in the construction of other vaults. And
268:
212:
bridges were basket-handle arches: Cinq-Mars bridge (1846–1847),
164:
135:
66:
958:
263:
One basket-handle arch railway bridge in the United States, the
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560:
556:
345:
253:
180:
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through point E, the end of the minor axis, parallel to MF.
46:
1455:
940:
130:
The basket-handle arch appeared at the beginning of the
108:, forming a complete half-circumference. From the early
1358:
Ministère des
Transports, Direction des routes (1982).
456:
385:
was allowed to vary according to certain proportions.
235:
in London (1816–1818) was still basket-handle arches.
1429:
Woodman, Francis; Bloom, Jonathan M. (2003). "Arch".
1412:
544:
Trace of a seven-center cove using the Michal method.
438:
Trace of a three-center cove using the Bossut method.
414:
Trace of a three-center cove using the
Huygens method
1342:
Grandes Voûtes : Partie 1 – voûtes inarticulées
326:
27:
Plane curve drawn by an odd number of circular arcs.
946:
1351:Grandes Voûtes : voûtes inarticulées (suite)
344:Although the basket-handle arch was not used for
279:Comparison between basket handle arch and ellipse
259:With nineteen centers: Signac Bridge (1871–1872).
1496:
446:for tracing the same 3-center curve is faster.
307:
252:With seven centers: Emperor Francis Bridge in
242:With three centers: Edmonson Avenue Bridge in
1428:
1328:
1304:"Mémoire sur les voûtes en anse de panier".
1263:
1251:
1239:
1224:
1212:
1197:
1185:
1153:
1129:. Palo Alto, CA: Stanford University Press.
993:
976:
964:
913:
220:(1843–1845), Plessis-les-Tours (1855–1857).
208:In the 19th century, the first major French
96:in Orléans - Three-center basket-handle arch
893:concerning the first three m1, m2, and m3.
473:bridge, in proceeding by trial and error.
148:in Paris - Three-center basket-handle arch
1439:10.1093/gao/9781884446054.article.t003657
1348:
1339:
1108:
1096:
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528:Learn how and when to remove this message
1335:(in French). Vol. 2. Paris: Baudry.
539:
433:
409:
367:
335:
292:, but precisely because of this kind of
216:bridge (1846–1848), Morandière bridges:
156:in Toulouse in the 16th century and the
140:
88:
29:
1121:BENJAMIN LATROBE and the THOMAS VIADUCT
14:
1497:
872:If ABCD is the rectangle in which the
189:designed the arches of the bridges of
1474:
1409:
1390:
1371:
1329:Degrand, Eugène; Resal, Jean (1887).
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267:, was constructed in 1833-1835. The
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429:
1456:American Technical Society (1920).
469:, and others consisted, as for the
457:Curves with more than three centers
331:
24:
1481:A Treatise on Masonry Construction
1230:
1203:
1176:
1159:
1144:
943:, p. 395, Basket-Handle Arch.
500:tone or style may not reflect the
179:(1750–1760), Moulins (1756–1764),
25:
1531:
999:
982:
327:Tracing curves with three centers
231:(1824–1831) were elliptical, the
510:guide to writing better articles
489:
397:in the case of the curve of the
1462:Cyclopedia of Civil Engineering
1393:Ponts et Viaducs au xixe siècle
1272:
1257:
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941:American Technical Society 1920
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13:
1:
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283:
271:is now owned and operated by
308:Advantages and disadvantages
205:, which was reduced to 1/4.
7:
1433:. Oxford University Press.
1367:(PDF) (in French). Bagneux.
227:Bridge (1826–1827) and the
100:Since Roman times, bridges
10:
1536:
84:
1510:Piecewise-circular curves
1264:Degrand & Resal (1887
1252:Degrand & Resal (1887
1240:Degrand & Resal (1887
1225:Degrand & Resal (1887
1213:Degrand & Resal (1887
1198:Degrand & Resal (1887
1186:Degrand & Resal (1887
1154:Degrand & Resal (1887
994:Degrand & Resal (1887
583:
580:
577:
69:, which has a continuous
1125:Dilts, James D. (1996).
977:Woodman & Bloom 2003
965:Woodman & Bloom 2003
442:The following method by
49:with the profile of its
1414:(in French). Brissaud.
1395:(in French). Brissaud.
1376:(in French). Brissaud.
1361:Les ponts en maçonnerie
1349:Séjourné, Paul (1913).
1340:Séjourné, Paul (1913).
1027:, pp. 93, 97, 103)
1410:Prade, Marcel (1990).
1391:Prade, Marcel (1988).
1372:Prade, Marcel (1986).
1320:: CS1 maint: others (
1295:: CS1 maint: others (
914:
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223:In England, while the
187:Jean-Rodolphe Perronet
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38:
1483:. J. Wiley & sons
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371:
339:
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104:have been built with
92:
33:
1477:"Basket-Handle Arch"
1475:Baker, I.O. (1889).
1458:"Basket-Handle Arch"
1332:Ponts en maçonnerie
574:
570:the whole opening.
354:Heron of Alexandria
106:semicircular arches
59:three-centered arch
915:Ponts et Chaussées
908:The Lerouge method
573:
546:
440:
416:
406:The Huygens method
374:
342:
273:CSX Transportation
150:
98:
43:basket-handle arch
39:
1448:978-1-884446-05-4
1431:Oxford Art Online
1136:978-0-8047-2629-0
862:
861:
538:
537:
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504:used on Knowledge
502:encyclopedic tone
481:The Michal method
430:The Bossut method
138:to the supports.
16:(Redirected from
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512:for suggestions.
508:See Knowledge's
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332:The ancient oval
197:(1766–1769) and
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1085:Séjourné (1913a
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1073:Séjourné (1913a
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1061:Séjourné (1913a
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1049:Séjourné (1913a
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467:Émiland Gauthey
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233:Waterloo Bridge
94:George V bridge
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1266:, p. 371)
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1075:, p. 112)
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316:The number of
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114:segmental arch
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35:Thomas Viaduct
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350:ancient times
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229:London Bridge
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214:Port-de-Piles
211:
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193:(1757–1765),
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183:(1756-1770).
182:
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175:(1716–1724),
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63:five-centered
60:
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19:
1520:Arch bridges
1505:Architecture
1485:. Retrieved
1480:
1465:. Retrieved
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1273:Bibliography
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391:circular arc
387:
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290:ad infinitum
287:
262:
256:(1898–1901).
246:(1908–1909).
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185:
162:
151:
129:
121:pointed arch
118:
99:
78:
74:
62:
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42:
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1171:Prade (1986
613:3nd radius
610:2nd radius
607:1st radius
601:2nd radius
598:1st radius
592:1st radius
132:Renaissance
110:Middle Ages
79:basket arch
18:Basket arch
1499:Categories
1487:2024-04-05
1467:2024-04-05
1141:page 162.
953:Baker 1889
929:References
584:9 centers
581:7 centers
578:5 centers
518:March 2024
348:vaults in
294:elasticity
284:Aesthetics
225:Gloucester
167:, Lavaur,
158:Pont Royal
146:Pont Royal
136:tangential
1316:cite book
1291:cite book
979:, Basket.
244:Baltimore
218:Montlouis
154:Pont-Neuf
71:curvature
878:diameter
318:voussoir
301:intrados
210:railroad
51:intrados
1515:Bridges
898:ellipse
471:Neuilly
399:Neuilly
362:tangent
269:viaduct
203:Neuilly
199:Neuilly
177:Orléans
165:Vizille
85:History
67:ellipse
55:tangent
1445:
1418:
1399:
1380:
1133:
886:radius
850:0,419
847:0,265
827:0,445
824:0,289
804:0,472
801:0,312
795:0,396
787:0,443
784:0,228
781:0,166
775:0,498
772:0,346
766:0,423
758:0,474
755:0,251
752:0,185
746:0,525
743:0,359
729:0,504
726:0,276
723:0,203
717:0,551
714:0,383
708:0,477
700:0,535
697:0,296
694:0,222
688:0,578
685:0,406
679:0,504
671:0,556
668:0,318
659:0,604
656:0,431
642:0,597
639:0,341
636:0,259
627:0,455
621:0,556
557:circle
346:bridge
254:Prague
195:Nogent
191:Mantes
181:Saumur
169:Gignac
102:vaults
45:is an
1365:(PDF)
923:radii
874:curve
844:0,25
821:0,26
798:0,27
769:0,28
763:0,31
749:0,21
740:0,29
737:0,45
734:0,32
720:0,22
705:0,33
691:0,23
682:0,31
676:0,34
665:0,24
662:0,24
653:0,32
650:0,53
647:0,35
633:0,25
630:0,63
624:0,33
618:0,36
604:Drop
595:Drop
589:Drop
561:radii
173:Blois
1443:ISBN
1416:ISBN
1397:ISBN
1378:ISBN
1322:link
1297:link
1131:ISBN
792:0,3
778:0,2
711:0,3
152:The
125:rise
119:The
47:arch
1435:doi
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1460:.
1441:.
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1314:{{
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1289:{{
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41:A
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1299:)
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525:(
520:)
516:(
506:.
20:)
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