Arches
 

 

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Arches

 

The masonry arch is one of the oldest types of bridge.  The first known ones were probably built in the middle east around 5500 years ago.  Books often refer to something called a corbelled arch, which is not an arch under the usual definition.

 

Analysis of masonry arches and vaults

Click on the link above to find a computer program for analysing arches.

 

The following is an extract from The Elements of Structure by W. Morgan 

The great churches of the Middle Ages were stone and brick. These materials are only suitable for resisting compression, and structures had to be designed so that no tensile stresses (or only very small ones) were produced. This explains the widespread use of the arch, the vault and the dome.  Using the traditional materials of stone and brick, these methods of construction are not of great importance today, but similar shapes using the more recent materials - steel, aluminium, reinforced concrete and pre-stressed concrete ­ are being increasingly used.

 

 The loads from the beams give vertical pressures on the
columns - as shown by the dotted lines.

FIG. 4.1

 (The principles of design of these modern structures are in the main, different from those of traditional masonry structures.)

One of the fundamental problems in structural engineering is the bridging of openings. A simple solution is a horizontal beam sup­ported by walls or columns (Fig. 4. 1).

This method has been used since time immemorial by employing beams of stone and timber.  Stone, however, being granular and brittle, breaks very easily in tension, and as tension is caused by bending, only very small spans can be obtained by using stone lintels.  Longer spans can be bridged by timber, and, of course, timber is still used in this way today.  It is, however, unsuitable (in the solid form) for very long spans because of the difficulty of obtaining timber of the necessary size. (Modern construction using laminated timber has enabled larger openings to be bridged than was possible only a few years ago.)

The ancient builders no doubt gave a great deal of thought to how they could utilize the great strength of stone and brick in compression without having to be limited by its very small strength in tension.  The arch is a satisfactory solution to this prob­lem, but before the true arch came into existence it was probably preceded by preliminary intuitive attempts as depicted in Fig. 4.2.

 


 

(a)                                                                                                                                                                 (b)                                          

FIG. 4.2

By corbelling out the masonry blocks as shown in Fig. 4.2, a greater span could be bridged than by a single block used as a beam. This method of construction was used for roofing internal chambers of the Egyptian pyramids.

The next step in the evolution of the arch was probably the use of two inclined stone beams, as shown in Fig. 4.3, a method which also was used in the pyramids.  With adequate depth of the stone "beams" no tensile stresses are produced, and this structure can therefore support heavier loads than can be supported by a horizontal beam. A new problem arises, however. With a hori­zontal beam the pressures on the columns or other supports are purely vertical. With the inclined beams an inclined thrust is produced which must be resisted if failure is not to occur, as shown in Fig. 4.3 (b).

 

 

 

 

 

 

                                                            (a)                                                                                                                                                                       (b)

FIG. 4.3

 

The next step in the evolution of the arch was probably the introduction of a third stone, as shown in Fig. 4.4 (a). As long as there is sufficient resistance supplied to the thrust by the abutments, the stones can be said to support one another by their mutual com­pression and cannot fall into the space below them. This can be said to be an intuitive approach to the problem. By using still more stones or bricks, longer spans can be bridged, as in Fig. 4.4 (b).

 

 

 

 

 

 

                                                             (a)                                                                                                                      (b)

                                                                                                             FIG. 4.4

The discovery of the arch was truly a great achievement in that the arch utilized the ability of stones and bricks to resist com­pression and avoided the subjection of the materials to tensile stresses for which their nature made them unsuitable. 

Arches were used in Egypt and Iraq centuries before the birth of Christ and were used extensively by the Romans for the construc­tion of bridges, and for the aqueducts built from about 300 B.C

The thrusts at the supports (abutments) are greater with shallow arches than with arches of steeper curvature, and methods of resisting arch thrusts gave rise to great ingenuity in the design of arches, vaults and domes.  An Arab proverb states that "the arch never sleeps," and this could be taken as meaning that the arch is constantly exerting thrust and trying to "flatten out." 

The avoidance of tensile stresses in the stones or bricks of the arch is accomplished by making the arch ring of sufficient thickness.  If the arch is too thin it could fail by the joints opening as indicated in Fig. 4.5. 

The determination of the pressures in an arch and their directions is not an easy problem, and many engineers and mathematicians have investigated the behaviour of arches.  As far as is known, mathematicians in the 17th century made the first attempts at a theoretical solution.  De la Hire (1640-1718),  Robert Hooke and Rondelet, among many others, tackled the problem, but even in 1951 it was stated, "A general survey of the methods in use for the design or analysis of a voussoir arch indicated that these were largely of an empirical nature."  This statement is in the introduction to Research Paper No. 11, "A Study of the Voussoir Arch" (National Building Studies), published by H.M. Stationery Office.  An arch made up of separate small blocks is called a voussoir arch;  other terms used to describe the various parts of an arch are given in Fig. 4.6.

 

 

 

 

 

 

 

 

 

 

 

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Last Edited :  04 October 2011 23:14:38