PROPOSMON X.—To discover the effect of bracing the angles of a roof flat on the top, supported by puncheons at the bottom of the rafters, to accommodate a semicircular ceiling within.
Figure 2. No. 1.—Let ABCDEF be the truss divested of its braces, the bottoms of the puncheons resting firmly on the walls at A and F, and the joints at B, C, D, E, to be quite move able, like rule-joints. Now, as this disposition of timbers would fall, and in falling, would assume the form of No. 2, the angles at C and D would become more and more obtuse, while those at A and E would, in the same proportion, become acute ; the latter would, therefore, require straining-pieces, and the former ties; the straining-pieces must have good abutments, and the ties must be well bolted at their extremities.
Let No. 3 be the truss, with braces disposed in the lower angles; this disposition will bend the rafters 13 C, D E, and the puncheons, B A, E F, convex towards the out side, which is entirely occasioned by the braces, G N 0 : the camber-beam, C n, is no otherwise affected than by its own weight. Let it now be supposed, that the angles c and D, No. 4, are braced at 1K, L m. In this disposition, the pun cheons, n A, E F, are not affected in respect of transverse strains ; the rafters C B, D E, and the beam c D, would all become concave on the outside ; and the points II and E, at the bottom of the rafters and top of the puncheons, would be pushed out beyond the perpendicular of A and F, at the bottom : here it is necessary to observe that the effect produced in this ease on the rafters c n and D E is contrary to the effect pro duced in No. 3, by the braces being disposed in the lower angles. Lastly, suppose that all the angles are braced, as in No. 5, it is evident, since the braces, nr a, N 0, produce a con trary effect to the braces K t. L M, these bending the rafters downwards, and those upwards, that the rafters c n and 13 E will become nearly straight, or assume an undulated line: the puncheons n A and E F, receiving the force of the braces n and N o at the points a and o, must still be bent. so as the under ends, a and o, of the braces do not coincide with the under ends, A and E, of the puncheons :.in this case, there is no other remedy than by giving the puncheons a scantling suf ficient to withstand this transverse strain, Or horizontal thrust, at the points o and o ; however, the shape of the contour may be pretty well secured by introducing two abutments, n t and m N, No. 6; these by being bolted through the two ends, will add greatly to the stillbess of the rafters n c and D E ; the bolts that go through the upper ends may also serve for the braces ix and L i,r : the shape of the horizontal beam, c 13, will likewise be very much preserved by the piece x L, bolted in three places, one at each end, into the braces I K and L and another in the middle : the contour of a roof, thus sup ported, would be quite unchangeable, if the rafters were inflexible; but, as this is not the case, and as they are acted upon transversely by the braces, the truss will therefore, in some degree, be expanded at B and a, and consequentlyoecasion lateral pressure on the walls • it will, therefore, be unfit for an oblong building, without other precautions for this purpose.
By inserting parabolic curves in the sides 13 c and D E, as in Plate IV. Figure 1, it will be effectually prevented.
In roofs of this description, joggle-pieces of wood should never be used, as their shrinking would tend greatly to alter the outline of the rafters.
Having laid down such principles as will enable the work man to judge of the strength and strain of timbers in the framings of carpentry, it will now be necessary to proceed to show the mode of constructing roofs to answer various purposes ; to give some practical observations relative to their strength, and to show the various modes of joining tim bers, the forms of traps, &e.
As we have above stated, the simplest form of a perfect trussed roof, consists of two principal rafters inclined to each other, and meeting at the apex, the lower ends being tied together by a horizontal tie-beam, to prevent their and thrusting out the walls upon which they are supported. As, however, the gravity of this tie-beam, especially if of any considerable length, is apt to cause it to sag in the centre, between the bearings, it is necessary to provide another bear ing for it between the walls, and this is effected by suspend ing it in the centre by means of what is termed a king-post, which, in its turn, is held up between the principal rafters at the apex of the roof. To assist in effecting the same object, the tie-beam is sometimes cambered or arched, but this plan can scarcely be recommended, for if the timbers settle, as in all probability they will do, the cambered beam being extended into a straight one is liable to push out the walls, and cause the mischief which it was intended to pre vent. The better plan is, to camber the beam only on the upper side, the lower side being horizontal, so as to have the greater scantling in the centre; this plan, however, is not without objection, for by it you have the greater weight at the centre, where it is most effective to cause the beam to sag. To afford the same assistance to the principals, and to prevent their sagging by their own weight and that of the covering which they have to support, short struts are carried from their centre to the foot of the king-post on either side of it, and on this they have their support. In a truss of this kind we have the tie-beam and king-post in a state of tension, while the principals and struts are subject to compression. Roofs of this class are very common, and are adapted for buildings where the span is not above 30 or 35 feet.