Where the liver is not navigable, the trusses may be con structed with a beam at the bottom : in this case, there is no difficulty. The forms for the trusses of roofs with tie-beams, may form the grand or principal part of the truss for the centre. But when the river is navigable, the centre requires as large an opening as is consistent with its strength, in order that vessels may pass under it ; and as the horizontal tie is interrupted, this disposition of the timbers will require much greater skill in the carpenter.
If the river over which a bridge is to be built he not navigable, the manner of constructing the centre is so easy, that it would be unnecessary to give any examples here ; but where the river is navigable, instead of the horizontal tie, a number of ties are disposed around the polygon, forming the interior part of the centre ; lint as in many practical cases the most judicious and well-skilled theorist might be deceived as to the equilibrium of the arch to be supported, or the points in which it has the most tendency to 11111, it would be very difficult to say what arc tics and what are strutts ; and even if the true pressure of the arch could he ascertained, the knowledge of this alone would not be sufficient ; for the same parts of the vaults. in the process of execution, vary their pressure in every succeeding additional part. and what was a tie at one time. becomes sometimes a strutt ; while a strutt, on the contrary, will become either in building, or at the completion of the vault. This ought to be well considered ; and where the pressure is doubtful, or any of the lengths of timber forming the centre are ascertained to be in the two different states above mentioned, such timbers should be made to act in either case.
Though the timbers upon which the vault immediately rests, cannot be supported transversely throughout, the othm pieces, which support the arch from the several pressing points, may all be made to act, by a judicious arrangement, in the direction of their lengths. The abutting joints, which are pressed, will be sufficiently resisted, when their shoulders are made perpendicular to the direction of their force, and with the small tenon; but if the timbers are drawn in a direction of their length, the joints ought to be strapped.
The beauty of every truss is to have as few quadrilaterals as possible. All the openings should be triangles : the inter section of the timber should be as direct as possible. Oblique
directions exert prodigious strains, which require timbers of very large sections to withstand them. and press upon the abutments so much as to make the whole truss sag by the compression of the intermediate joggles.
If proper attention be paid to these circumstances, and the bearings of the timbers be well ascertained, a centre, constructed upon such principles, must answer its intended purpose, provided a proper estimate be taken of the corn nmnicating forces during the execution of the vault, and the centre be well secured at its abutment.
A centre for the arch of a bridge over a navigable river, may either be accomplished with one centre around the interior of the entire arch, supported between the piers ; or, if the span of the arch will admit, the aperture may be sub divided into two or more apertures, by one or more supporters, each consisting of one or more posts of wood, braced together when necessary ; these supporters, together with the sides of the stone piers, support the centre of the aperture, on which the stone arch is to be erected over the whole. By this mode, the centering is much more simple in its construction and requires fewer timbers, and these of smaller scantlings than when made in one centre.
If a centre be truly constructed, every point of the vault to be built ought to be supported, without giving any trans verse strain to the incumbent part of the centre: but this is impracticable ; for, as it would require a multiplicity of joints, it would, from the shrinking of the timber, be less sufficient than if composed of few pieces, supporting only a certain number of points disposed at judicious distances, leaving the intervals to be supported by timbers in which the super incumbent part of the arch might act transversely, but still presenting such a resistance, as not to be materially bent or put out of form by the load of the arch above.
By these precautions, the centre will be constructed so as not to yield, or give way, though the load should vary during the erection of the arch, and will stand as firm as if the whole had been constructed out of a single solid : the only thing to be attended to, as before observed, being to make the timbers sufficiently strong to withstand either tension or compression.