CENTER, or CENTRE, a word borrowed from the French name centre or entree, given to the frame of timber by which the brick or stone of arched vaulting is supported during its erection, and from which it receives its form and curvature.
It is not our intention to describe the variety of constructions which may be adopted in easy situations, where the arches are of small extent, and where sufficient foundation can be had in every part of it for supporting the frame. In such cases, the frequency of the props which we can set up dispenses with much care; and a frame of very slight timbers, connected together in an ordinary way, will suffice for carrying the weight, and for keeping it in exact shape. But, when the arches have a wide span, and consequently a very great weight, and when we cannot set up intermediate pillars, either for want of a foundation in the soft bottom of a river, or because the arch is turned between two lofty piers, as in the dome of a stately cathedral—we are then obliged to rest every thing on the piers themselves; and the framing which is to support our arch before the keystone is set, must itself be an arch, depending on the mutual abutment of its beams. One should think that this view of the construction of a centre would offer itself at the first, naturally derived from the erection it was to assist: but it has not been so. When intermediate pillars were not employed, it was usual to frame the mould for the arch with little attention to any thing but its shape, and then to cross it and recross it in all directions with other pieces of timber, till it was thought so bound together that it could be lifted in any position, and, when loaded with any weight, could not change its shape. The frame was then raised in a lump, like any solid body of the same shape, and set in its place. This is the way still practised by many country artists, who, having no clear principles to guide them, do not stop till they have made a load of timber almost equal to the weight which it is to carry.
But this artless method, besides leading the employer into great expence, is frequently fatal to the undertaker, from the unskillfulness of the construction. The beams which connect its extremities are made also to support the middle by means of posts which rest on them. They are therefore exposed to a transverse or cross strain, which they are not able to bear. Their number must therefore be increased, and this increases the load. Some of these cross strains are derived from beams which are pressed very obliquely, and therefore exert a prodigious thrust on their supports. The beams are also greatly weakened by the mortises which are cut in them to receive the tenons of the crossing beams: and thus the whole is exceedingly weak, in proportion to what the same quantity of timber may be made by a proper disposition of its parts.
The principles from which we are to derive this disposition are the general mechanical principles of carpentry, of which we have given some account in that article. These furnish one general rule: When we would give the utmost strength possible to a frame of carpentry, every piece should be so disposed that it is subject to no strain but what either pushes or draws it in the direction of its length: and, if we would be in-
debted to timber alone for the force or strength of the centre, we must rest all on the first of these strains; for when the straining force tends to draw a beam out of its place, it must be held there by a mortise and tenon, which possesses but a very trifling force, or by iron straps and bolts. Cases occur where it may be very difficult to make every strain a thrust, and the best artists admit of ties; and indeed where we can admit a tie-beam connecting the two feet of our frame, we need seek no better security. But this may sometimes be very inconvenient. When it is the arch of a bridge that we are to support, such a tie-beam would totally stop the passage of small craft up and down the river. It would often be in the water, and thus exposed to the most fatal accidents by freshes, &c. Interrupted ties, therefore, must be employed, whose joint or meetings must be supported by something analogous to the king-posts of roofs. When this is judiciously done, the security is abundantly good. But great judgment is necessary, and a very scrupulous attention to the disposition of the pieces. It is by no means an easy matter to discern whether a beam, which makes a part of our centre, is in a state of compression or in a state of extension. In some works of the most eminent carpenters even of this day, we see pieces considered as struts (and considerable dependence had on them in this capacity), while they are certainly performing the office of tie-beams, and should be secured accordingly. This was the case in the boldest centre (we think) that has been executed in Europe, that of the bridge of Orleans, by Mr Hupeau. Yet it is evidently of great consequence not to be mistaken in this point; for when we are mistaken, and the piece is stretched which we imagine to be compressed, we not only are deprived of some support that we expected, but the expected support has become an additional load.
To ascertain this point, we may suppose the piers to yield a little to the pressure of the archstones on the centre frames. The feet, therefore, fly outwards, and the shape is altered by the sinking of the crown. We must draw our frame anew for this new state of things, and must notice what pieces must be made longer than before. All such pieces have been acting the part of tie-beams.
But a centre has still another office to sustain; it must keep the arch in its form; that is, while the load on the centre is continually increasing, as the masons lay on more courses of arch-stones, the frame must not yield and go out of shape, sinking under the weight on the haunches, and rising in the crown, which is not yet carrying any load. The frame must not be supple; and must derive its stiffness, not from the closeness and strength of its joints, which are quite insignificant when set in competition with such immense strains, but from struts or ties, properly disposed, which hinder any of the angles from changing its amplitude.
It is obvious, from all that has been said, that the strength and stiffness of the whole must be found in the triangles into which this frame of carpentry may be resolved. We have seen that the strains which one piece produces on two others, with which it meets in one point, depends on the angles of their intersection; and that it is greater as an obtuse angle is more obtuse, or an acute angle more acute. And this suggests to us the general maxim, "to avoid as much as possible all
Center. very obtuse angles." Acute angles, which are not necessarily accompanied by obtuse ones, are not so hurtful; because the strain here can never exceed the straining force; whereas, in the case of an obtuse angle, it may surpass it in any degree.
Such are the general rules on this subject. Although something of the mutual abutment of timbers, and the support derived from it, has been long perceived, and employed by the carpenters in roofing, and also (doubtless) in the forming of centres, yet it is a matter of historical fact, that no general and distinct views had been taken of it till about the beginning of this century, or a little earlier. Fontana has preserved the figure of the frames on which the arches of St Peter's at Rome were turned. The one employed for the dome is constructed with very little skill; and those for the arches of the nave and transepts, though incomparably superior, and of considerable simplicity and strength, are yet far inferior to others which have been employed in later times. It is much to be regretted that no trace remains of the forms employed by the great architect and consummate mechanician Sir Christopher Wren. We should doubtless have seen in them every thing that science and great sagacity could suggest. We are told, indeed, that his centering for the dome of St Paul's was a wonder of its kind; begun in the air at the height of 160 feet from the ground, and without making use of even a projecting cornice whereon to rest it.
6 The earliest theory of the kind that we have met with, that is proposed on scientific principles, and with the express purpose of serving as a lesson, are two centres by Mr Pitot of the Academy of Sciences, about the beginning of this century. As they have considerable merit (greatly resembling those employed by Michael Angelo in the nave of St Peter's), and afford some good maxims, we shall give a short account of them. We crave the excuse of the artists if we should employ their terms of art somewhat aukwardly, not being very familiarly acquainted with them. Indeed, we observe very great differences, and even ambiguity, in the terms employed.
What we shall describe under the name of a centre is (properly speaking) only one frame, truss, or rib, of a centre. They are set up in vertical planes, parallel to each other, at the distance of 5, 6, 7, or 8 feet, like the trusses or main couples of a roof. Bridging joists are laid across them.—In smaller works these are laid sparingly, but of considerable scantling, and are boarded over; but for great arches, a bridging joist is laid for every course of archstones, with blockings between to keep them at their proper distances. The stones are not laid immediately on these joists, but beams of soft wood are laid along each joist, on which the stone is laid. These beams are afterwards cut out with the chisel, in order to separate the centre from the ring of stones, which must now support each other by their mutual abutment.
7 Illustrated Plate XIV. The centre is distinguishable into two parts, ALB (fig. 1.) and LDL, which are pretty independent of each other, or at least act separately. The horizontal STRETCHER LL cuts the semicircle ADB half way between the spring and the crown of the arch; the arches AL, LD, being 45° each. This stretcher is divided in the same proportion in the points G and H; that is, GH is one-half of LL, and LG, HL are each one-
fourth of LL nearly. Each end is supported by two STRUTS EI, GI, which rest below on a SOLE or BED properly supported. The interval between the heads of the struts GI, HK is filled up by the STRAINING BEAM GH, abutting in a proper manner on the struts (see CARPENTRY, Supplement). The extremities I, L, are united in like manner by butting joints, with the heads of the outer struts. The ARCH MOULDS AP, BP, are connected with the struts by cross pieces PQ, which we shall call BRIDLES, which come inwards on each side of the struts (being double), and are bolted to them. This may be called the lower part of the frame. The upper part consists of the king post DR, supported on each side by the two struts or braces ML, ON, mortised into the post, and also mortised into the stretcher, at the points L, N, where it is supported by the struts below. The arches LD, LD are connected with the struts by the bridles PQ, in the same manner as below.
There is a great propriety in many parts of this arrangement. The lower parts or haunches of the arch of this press very lightly on the centres. Each archstone is lying on an inclined plane, and tends to slide down only with its relative weight; that is, its weight is to its tendency to slide down the joint as radius to the sine of elevation of the joint. Now it is only by this tendency to slide down the joint that they press on the centering, which in every part of the arch is perpendicular to the joint: But the pressure on the joint, arising from this cause, is much less than this, by reason of the friction of the joints. A block of dry freestone will not slide down at all; and therefore will not press on the centering, if the joint be not elevated 35 degrees at least. But the archstones are not laid in this manner, by sliding them down along the joint, but are laid on the centres, and slide down their slope, till they touch the blocks on which they are to rest; so that, in laying the archstones, we are by no means allowed to make the great deduction from their weight just now mentioned, and which Mr Couplet prescribes (Mem. Acad. Sciences, 1729). But there is another cause which diminishes the pressure on the centres; each block slides down the planks on which it is laid, and presses on the block below it, in the direction of the tangent to the arch. This pressure is transmitted through this block, in the same direction, to the next, and through it to the third, &c. In this manner it is plain that, as the arch advances, there is a tangential pressure on the lower archstones, which diminishes their pressure on the frame, and, if sufficiently great, might even push them away from it. Mr Couplet has given an analysis of this pressure, and shews, that in a semicircular arch of uniform thickness none of the arch stones below 30° press on the frame. But he (without saying so) calculates on the supposition that the blocks descend along the circumference of this frame in the same manner as if it were perfectly smooth. As this is far from being the case, and as the obstructions are to the last degree various and irregular, it is quite useless to institute any calculation on the subject. A little reflection will convince the reader, that in this case the obstruction arising from friction must be taken into account, and that it must not be taken into account in estimating the pressure of each successive course of stones as they are laid. It is enough that we see that the pressure of the lower courses of archstones on the frame is diminished. Mr Couplet says, that the whole
whole pressure of a semicircular arch is but ths of its weight; but it is much greater, for the reason just now given. We have tried, with a well made wooden model (of which the circumference was rubbed with black candle lead to render it more slippery), whether any part of the wooden blocks representing the archstones were detached from the frame by the tangential pressure of the superior blocks; but we could not say confidently that any were so detached. We perceived that all kept hold of a thin slip of Chinese paper (also rubbed with black lead) between them and the frame, so that a sensible force was required to pull it out. From a combination of circumstances, which would be tedious to relate, we believe that the centres carry more than two-thirds of the weight of the arch before the keystone is set. In elliptical and lower pitched circular arches, the proportion is still greater.
It seems reasonable enough, therefore, to dispose the framing in the manner proposed by Pitot, directing the main support to the upper mass of the arch, which presses most on the frame. We shall derive another advantage from this construction, which has not occurred to Mr Pitot.
There is an evident propriety in the manner in which he has distributed the supports of the upper part. The struts which carry the king post spring from those points of the stretcher where it rests on the struts below: thus the stretcher, on which all depends, bears no transverse strains. It is stretched by the strut above it, and it is compressed in a small degree between the struts below it, at least by the outer ones. Mr Pitot proposes the straining beam GH as a lateral support to the stretcher, which may therefore be of two pieces: but although it does augment its strength, it does not seem necessary for it. The stretcher is abundantly carried by the strap, which may and should suspend it from the king post. The great use of the straining piece is to give a firm abutment to the inner struts, without allowing any lateral strain on the stretcher. N.B. Great care must be taken to make the hold sufficiently firm and extensive between the stretcher and the upper struts, so that its cohesion to resist the thrusts from these struts may be much employed.
The only imperfection that we find in this frame is the lateral strains which are brought upon the upper struts by the bridles, which certainly transmit to them part of the weight of the archstones on the curves. The space between the curves and ML should also have been trussed. Mr Pitot's form is, however, extremely stiff; and the causing the middle bridle to reach down to the stretcher, seems to secure the upper struts from all risk of bending.
This centre gives a very distinct view of the offices of all the parts, and makes therefore a proper introduction to the general subject. It is the simplest that can be in its principle, because all the essential parts are subjected to one kind of strain. The stretcher LL is the only exception, and its extension is rather a collateral circumstance than a step in the general support.
The examination of the strength of the frame is extremely easy. Mr Pitot gives it for an arch of 60 feet span, and supposes the archstones 7 feet long, which is a monstrous thickness for so small an arch; 4 feet is an abundant allowance, but we shall abide by his construction. He gives the following scantlings of the parts: