1396

THEORY AND PRACTICE OF ENGINEERING.

Book II.

are not sufficiently smooth to slide, unless the plane on which they are placed ceases to behorizontal, experiments have been made to ascertain at what inclination they can supportthemselves; and it has been found that hard stone, which slides most easily, does not beginto do so until inclined about 30°. The same experiments made with stone bedded infresh mortar give for hard stone from 34° to 36°, and for soft, which by absorbing themoisture of the mortar forms itself into a body almost immediately, up to 45°, whenthe centre of gravity of the stone does not fall out of its base. Thus by taking 30° forthe point where the voussoirs begin to slide, we are sure of results above those whichexperience would give; whence it would appear that the centre ought only to beginat that height. In several constructions of ancient bridges, such as the Pont du Gardeand Ponte Sisto at Rome , we still see

the projecting stones on which the bases % _ ^

of the centres were placed; they arefrom 25° to 28° above the springing ;nevertheless for centres of vaults of greatdiameter, the tie-beam of which is re-quired to be supported at a certaindistance, it is better to begin the centreat the springing, so as to strengthen thetie-beam underneath. The weight onthe centres is not material until above30° ; it then goes on augmenting withthe voussoirs, until the key is placedwhich supports the vault and relievesthe centre of its weight.

In order to find a combination ofpieces of timber which shall resist theefforts of the voussoirs, we must firstdetermine the position of the tie-beam.

For this purpose, whatever may be thecentre of the arch, whether lofty,a semicircle, or an ellipsis, draw fromthe points A and D, figs. 2320, 2321,

2322, 2323., two indefinite tangentswhich meet at the point F, throughwhich draw a perpendicular to the curve;the point K, where it intersects, willdetermine the position of the tie-beam :having then divided the part K D intotwo or three parts, in proportion toits developed length, draw through thepoints of division E and G other per-pendiculars to the curve, which willindicate the position of two intermediateking-posts. From the point I, wherethe direction of the first will meet thetie-beam, draw the line III L, which Fig. 2321.

will indicate below the position of an inclined piece to support the bearing of the tie-beam,and above, that of a brace to sustain the top of the king-post LT, supported on the otherside by the brace LII, which abuts against the king-post of the centre. The partbelow the tie-beam will be divided into two, three, or four parts in proportion toits length, through which mustbe passed the binding pieces It, S, Fto support the inclined pieces,posts and braces which unitethese, as well as to prevent theiryielding in the direction of theirlength.

The scantlings of the varioustimbers must be found in themanner before indicated, takingcare to observe which are pressedin the direction of their ends,and which in their width, andit is important to consider thatit is not only requisite that eachof these pieces should have

ig. 2320.

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