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THEORY AND PRACTICE OF ENGINEERING.

Book IT*

Perronet has given in his works a description of the movements which have takenplace in great arches which he constructed, both whilst their voussoirs were carried bytheir centres, and after the keys were placed and the centres removed; he has indicatedthe means of striking these centres, so as not to expose the curve of the arches to anychange, and the precautions which are necessary to be taken in placing the voussoirs : theobservations he has published form a complete system, and are of considerable value.It is generally remarked, he says, that the first course of the voussoirs may be placedwithout the assistance of the wooden centre, which only becomes necessary as they beginto slide-one over the other, which happens when the bed of the joints makes an angle of40° with the horizon: the centre then begins to carry a portion of the weight of thevoussoirs ; it sinks in its lower part, and when the centres are forced up, it would rise atthe summit, if an opposition were not used to resist this movement, by making it support aweight more or less considerable. In the arch of Saint Edme, at Nogent-sur-Seine (seepage 265.) these effects were observed and described with the greatest care; it wasstruck from three centres, its span being 96 feet, and 29 feet 9 inches from the springingto the key; its thickness at the summit is 4 feet 3 inches ; each half of the arch is com-posed of forty-seven courses of voussoirs, not comprising the key. The first twentycourses of voussoirs having been placed, the five last separated, on account of the sinkingof the centre on which they rested, the joint opened | inch at the extrados above the fifteenthcourse, and a vertical disjunction took place between the arch and the horizontal beds ofthe abutments, the effect of which was evident to the seventh course: in continuing themasonry, the joints closed, and the point of separation of the acting and resisting partsbeing carried higher by the effect of the addition of a greater number of voussoirs, thejoints opened at the extrados about ^ inch from the twenty-sixth to the thirty-first course.

At the bridge of Neuilly (see page 268.), in the arches adjacent to the abutments, thehalf of which is composed of fifty-six courses of voussoirs, not including the key, the jointsopened successively at the extrados, on account of the advancement of the laying of thevoussoirs, from g to ^ inch from the eleventh to the thirty-sixth course ; analogous effectshave been observed in other bridges. After the placing of the key these effects producedby the weight of the voussoirs manifest themselves in a different manner, the centres,which at first had been loaded in the lower part, inducing the summit to rise, were nowcharged in the middle, tending on the contrary to rise at the haunches; at the arches ofthe bridge at Neuilly the last joints opened at the extrados, and on each side other jointsopened at the intrados, starting from the key. At the bridge of Nogent the verticaldisjunction which took place between the voussoirs and the laying of the abutments almostentirely disappeared, and the last joints opened at the extrados, in the upper part of thearches, again closed. Before the striking of the centres, there had been traced on the headsof this latter bridge three right lines, one horizontal, at the summit of the arch, from abovethe twenty-eighth course on one side to the corresponding one on the other, and the othersinclined, traced on the haunches from the extremity of the first line to the point where thejoint of the seventh course meets the tangent vertical at the springing: the position of theextremities of these lines had been made with relation to fixed points, and the object wasto know by the changes which should show themselves in their position and form, whatwould be the play of the voussoirs during the sinking. The curve of the upper lineindicated a vertical sinking, which diminished uniformly from its centre to its extremities :as for the other two lines there was formed in their curve a point of inflexion at the meetingof the joint of the sixteenth and seventeenth course, which indicated, besides the verticalsinking and the closing of the joints in the upper courses down to and including the seven-teenth, a closing also of the joints of the lower part, which was even carried down to thejoints of the abutments.

It may be concluded from these observations, which may be repeated in all constructionsof a similar kind, that the upper part does not tend to push out the lower by sliding onthe joints of rupture, as was supposed by Lahire, and consequently that the result of thecalculations made upon this hypothesis is erroneous : to form a just idea of the nature ofthe thrust, we must consider successively the two principal epochs of the construction ofan arch. When the greatest number of voussoirs is placed, and we are near arriving at thekey, the centre becomes considerably loaded in its upper part, because it entirely supportsthe weight of the arch, and it consequently undergoes a sinking, the effect of which is mostsensible towards the summit: each voussoir descends in proportion to its proximity to thekey, and it is evident that that cannot take place but as it turns round its inferior edge,which obliges the joint to open at its extrados; this opening is above all evident at thepoint where, on account of the inclination of the planes of the joints, compared to thedirection of the weight, the vertical sinking is distributed more unequally in the consecutivevoussoirs, and therefore in the bridge of Nogent the most open joint was found towardsthetwemy-shuh course.

When the key is placed and the centre is struck, the upper parts of the arch DE,dE,are no longer supported by their reciprocal pressure, on account of the sinking hence