and o D. Make Af equal to a C. Divide the given bracket into any number of equal parts, and from the points of division on the curve line drop the lines 1.1.1, 2.2.2, &c., parallel to fA E, cutting the line EO in the figures 1, 2, &c. Draw Eh perpendicular to Eo, and equal to Ag. Draw 1.1, 2.2, &c., parallel to Eh, and make the lengths of the perpendiculars respectively equal to those opposite. Between the base ac, and the curve g 1, 2, &c., and through the points thus found, draw the curve of the angle rib required. The dotted curve shows the bevel, or splay of the bracket, to form the plane that shall coincide with the plane of the given brackets. Figure 2 Exhibits the method of finding the bracket for an internal right angle, and is precisely the same as Fig. 1, with the exception of bevelling the angle bracket, which is not necessary for an internal angle. CARPENTRY. CARPENTRY is the art of cutting and jointing timbers in the construction of buildings. To cut timbers and adapt them to their various situations, so that one of the sides of every piece shall be arranged according to a given plane or surface, shown in the designs of the architect, is a department of carpentry which requires a thorough knowledge of the finding of sections of solids, their coverings, and the various methods of connecting timbers, &c. PRINCIPLES OF FRAMING. The art of combining pieces of timber to increase their strength and firmness, is called framing. The form of a frame should be adapted to the nature of the load which it is designed to carry. In carpentry, the load is usually distributed over the whole length of the framing; but it is generally supported from point to point by short beams or joists. First, let us consider a case where the load is collected at one point of the frame; and, in order that the advantage of framing may be more obvious, let us suppose all the parts of a certain piece of frame-work to be cut out of a single beam, which, in a solid mass, would be too weak for the purpose. PLATE XIV. Let Fig. 1 be a piece of timber cut in the various directions indicated by the lines passing through it; and let the triangular pieces shown at E and F be removed. Then raise the pieces, AE and AF, till they make close joints at E and F; and increase their lengths till they form a frame, or truss, as represented at Fig. 2. A small rod of iron, with suitable nuts, will be required to support the centre of the tie, as seen in the drawing. If the depth of the frame at the middle be double the depth of the beam, the strength of the frame will be a little more than three times the strength of the beam, and its firmness will be a little more than eight times as great as that of the beam. If the depth of the frame be three times the depth of the beam, as represented at Fig. 2, it will be about six times as strong as the beam, and about eighteen times as firm, that is, it will bend only an eighteenth part of the distance which the beam would bend under the same weight. To render the strength more equal, and to obtain two points of support, there may be a level piece of timber placed between the inclining ones, as shown at Fig. 3, but if a greater weight be placed at G, than at II, there will be a tendency to spring outwards at H, and inwards at G, which may be effectually prevented by the suspension rods, a a, as shown in the same figure. It now remains to show why the strength of a piece of timber is increased by forming it into a truss; and to have a clear conception of this subject, is of the utmost importance in the science of carpentry. Let ABC, Fig. 4, be a truss to support a weight applied at A. It is evident that the force of the weight will tend to spread the abutments, в and c; and the nearer we make the angle, ABC, to a straight line, the greater will be the pressure, or tendency to spread, or increase the distance between the abutments, в and c, by the same load at A. On the contrary, if the height be increased, as at Fig. 5, the tendency to spread the abutment will be less. The advantage of framing timbers together for the purpose of giving strength and firmness, having been shown, let us proceed to explain how the strain on any part may be measured, PLATE XV. Figure 1. To find the pressure on oblique supports, or parts of trusses, frames, &c. Let A B be a heavy beam, supported by two posts, AC and BD, placed at equal distances from E, the centre of the beam. The pressure on each post will, obviously, be equal to half the weight of the beam. But if the posts be placed obliquely, as in Fig. 2, the pressure on each post will be increased in the same proportion as its length is increased, the height AC, being the same as before; that is, when AF is double a c, the pressure on the post in the direction of its length is double the half weight of the beam. Hence it is very easy to find the pressure in the direction of an inclined strut, for it is as many times half the weight supported as ac is. contained in AF. Therefore, if the depth A c, of a truss to support a weight of two tons be only one foot, and AF be ten feet, the pressure in the direction of AF will be ten tons. It will be observed that when the beam is supported by oblique posts, as in Fig. 2, these posts will slide out at the bottom, and together at the top, if not prevented by proper abutments. The force with which the foot F, tends to slide out, is to Therefore, when FC is equal to half the weight of the beam AB, as FC is to AC. AC, the tendency to slide out is equal to half the weight supported; and if Fc be ten times a c, the tendency to spread out would be ten times the weight supported. Hence, it is evident that a flat truss requires a tie of immense strength to prevent it from spreading. If a flat truss produces any degree of stretching in the tie, the truss must obviously settle; and by settling it becomes more flat, and consequently exerts a greater strain. In a flat truss, therefore, too much caution cannot be used in fitting the joints and choosing good materials. When the spreading of a frame is to be counteracted, it is most effectually done by a straight tie-beam connecting the points together; but sometimes a carpenter is so limited as to the space in which the truss is to be formed, that he cannot obtain a straight tie, and then it is desirable to know the strain on such a tie as can be procured. Figure 3. Let ACD be a truss, to which a straight tie AED, cannot be applied without interfering with the architect's design. In this case, let AB and BD be the ties. Draw the lines in the centre of the pieces forming a triangle, AC B. Then as CB is to AB, so is half the load at c, to the strain it produces on the tie A B; and the strength of the frame ABCD, is to the strength of a frame of the same quantity of material having a straight tie, ACD, as CB is to cE. In the example we have drawn, the frame would have only one third the strength of one with a straight tie. It is a serious objection to this kind of framing, that any settling, however small it may be, tends to spread out its supports, as represented at A and D, while a straight tit has scarcely any other sensible effect than that it draws the supports together, which is less objectionable than spreading them apart. Figure 4 Exhibits a very cheap and expeditious" plan for framing a roof to span from 40 to 70 feet. It requires no explanation further than to say that the tie need not be more than 5 x 10 inches; the rafters and braces 5 x 8; the battens of 1 inch boards, spiked to the timbers with large nails. It is believed to be the best roof that can be constructed, as it has all the advantages of a solid mass, without the great weight and the disadvantages of the shrinkage of material, which is almost entirely obviated by the crossing of the fibres of the wood. OBSERVATIONS ON THE FORMS OF ROOFS. All gable-ended roofs have a tendency to spread out the walls, particularly when the walls are thin, or when they are a great distance apart. In the construction of roofs of every description, the ties extending from one plate to another, or to the wall plates, should be well connected at the angular points, for when the building is carried up on a polygonal plan, every two adjacent, or opposite hips, will act in the same manner as the two principals in a framed roof, |