the number of sides to the plan, as square, pentagonal, hexagonal, octagonal, etc., domes. There are also sub-varieties due to differences in the elevation or vertical sections, such as ogee domes, gothic. or pointed domes, segmental, etc.
The construction of the dome, depending so greatly upon its size and circumstances of location, can only be referred to incidentally, the subject of this section being the method of obtaining the true shapeof the coverings, which is common to all.
A dome may be covered either by boards or metal sheets in vertical strips called " gores," or horizontal bands called " zones." Both methods are shown in the case of the spherical dome, Figs, i and 2, . page 161. We will consider the vertical method lirst.
Fig. 1, B and C, show respectively quarter plans of the outside and inside of the dome, Fig. 2 being the interior and exterior elevations. The radial lines in quadrant B are the plans of the joints of the boards, and the elliptic lines in Fig. 2 their elevation. Neither set of lines gives either the true length or the shape of the edge, but both are necessary to obtain the true shape.
To obtain the Projection of the Boarding - Divide the circumference of the plan into as many segments as the width of the boards to be used permits. Draw lines from these divisions to the centre. Next divide the circumference in the elevation, Fig. 2, into a number of equal parts as 1, 2, 3, 4. Draw indefinite horizontal projectors from these points, also vertical projectors into the plan, cutting the diameter in points 1, 2, 3, 4. With these points as radii, describe arcs from the centre of the plan, and projectors taken up from their intersections, with the various joint lines, to the corresponding horizontals, will give points in the elliptic curves forming the edges of the boards. Only one set of these projectors has been taken up, sufficient, however, to indicate the method ; these are distinguished by chain lines, the points found are marked I., II, III., IV.
ibe Coverings of Domes
Figs. I < nd 2. I'l?,n and F^lcvation of a Spherical Dome, with Developments of Coverings. Figs. 3 and 4. i'lar md Elevation of a Gothic Dome. Figs. 5 and 6. 1'lari and Elev ation of an Elliptic Dome
Taking the joint at N, the projectors are shown starting from points 1', 2', 3', 4', ami locate points n, I, II, III, IV on the horizontals in Fig. 2. Draw the curve through these points. We have next to discover the true shape of the board. Bisect the width of any board in plan and draw a line from the centre through the. point, extending it indefinitely as shown. Mark off upon this line points 1*, z", 3", 4", 5*, equal in length to the like numbered points upon the circumference in elevation—that is, make a stretch-out of the curved line. Draw perpendiculars to the mid line through these points and make them equal in width to the corresponding portions of the respective arcs, passing across the plan of the same board—i.e. is made equal to the stretch out of arc 1 in the plan, and so on. In the scale drawing it is near enough to make each ordinate equal to a straight line across the plan, but when setting out full size it is necessary either to develop the segment ot the arc: or to make due allowance in the. width for the curving of the board when nailed down to the: purlins. Having thus obtained a series of points on the ordinates, draw the curved edges through them. One mould will answer for all the boards.
To obtain Shape of Boards laid horizontally as shown at A, Fig. 1, which may be taken to represent a half elevation of a dome covered 111 six zones.— As the boards have to be marked and cut whilst flat, it is necessary to convert the spherical surface into a series of planes, by drawing chords of straight lines between the ends of the segments of the circumference intersected by the joints.
If we extend these chords until they intersect a perpendicular or " pole " from the centre of the dome, we c an deal with the projection ot each board as if it were the section of a cone, and as the development of the surface of a cone has been fully explained on page 159, it will only be necessary to recapitulate here.
Take No. 2 board as example. Produce its chord line to meet the centre line in point II. This becomes the apex of its cone. From lliis point as centre, and the upper and lower edges of the board as radii, describe arcs indefinitely. Next project the ends of the chord to the base as at a-b; these projectors are shown in chain line. From the centre, with the points a-b as radii, describe arcs, which will represent the lower edges of the boards, Nos. 2 and 3, in plan. Note, to avoid confusion with the previous boarding, these plan lines are drawn in the quarter plan D, and numbered 2 and 3 respectively. These lines represent also the base and frustum of the cone we are to develop, and we divide the quadrant into a number of equal parts, stepping off the same number on the lower edge of the development of board No. 2. Join the last point, No. 7, to the apex and the length and shape of the board is determined. Of course the actual length of the board will depend upon the situation of the ribs, also the width of stuff available from which the curved segment is to be cut. The other boards are found in a similar manner, each board having its special " cone." The respective apices are numbered III, IV, V The lowest board, No. 1, has its apex beyond the edge of the page, and would be set out in lull size by the three-point method of drawing an arc. It will be noticed that with the vertical method of boarding it is necessary to use purlins, and these are made» to lie perpendicular to the curve. Two of these purlins are shown in the quarter plan C. When horizontal method of boarding is adopted, the ribs must be placed much closer together, consequently thinner stuff may be used than with the vertical method. The dome shown is supposed to be about 8 feet in diameter. As the interiors of these small domes are not seen, it is usual to leave the inner edges of the ribs straight, the purlins are shaped to reduce the weight.
A Gothic or Pointed Dome is shown in Figs. 3 and 4. These are usually boarded vertically, and the ribs are all of the same shape, the radius of the arc being equal to the span. The purlins are 111 such case placed horizontally, and are of just sufficient thickness to take the nails without
splitting, their width affording all the strength required. They need not equal the ribs in depth, and the housing to receive their ends should be stopped, as shown in the elevation of second rib, to afford an abutment.
The plan, Fig. 3, shows at A, plan of the boarding, at B plan of purlins anil curb, at C the geometrical construction for projection ot ribs and shape of the boarding.
To project the Ribs in Elevation.—Having first described the outline of roof, by arcs struck from points C and C, divide the curve of one side into a number of parts, and drop projectors into the plan, cutting the diameter in points 1, 2, 3, 4, 5, 6. Carry round these points to the face of the rib to be projected, by circles struck from the centre. These new points are marked i°, 2°, 30, 40, 50. Project them upwards to cut horizontals drawn from the original points in the elevation, and draw the curve through the intersections. The development of the boards is obtained as explained for a spherical dome.
An Elliptic Dome is shown in Figs. 5 and C. The solid on which this is based is termed an ellipsoid, the geometrical definition of which is a solid produced by the revolution of on ellipse upon its axis. Obviously, any section of the solid passing through the generating axis will be an ellipse, and, as when anything revolves, its path must be a circle, any section perpendicular to the axis—i.e. parallel with the transverse axis—will be a circle. We know from this that in an elliptic dome with its ribs arranged as show n in the plan, Fig. 5, all the ribs will be of the same contour, and that the covering boards must also be all alike. The procedure to obtain the projections and development of the covering is precisely as in the last case.
THE DRAWING OF ARCHES—BRICK AND STONE (page 165)
The Gauged or Flat Arch. Fig. i, is employed only in comparatively narrow openings, and, though generally drawn straight, upon the soffit or underside, is really slightly
cambered or curved upwards in practice, when made in brickwork. The term " gauged " is applied to these because the bricks are cut to a gauge or templet, to ensure them being the right size and shape in each course. The method of setting-out to be described is that pursued to obtain the templets. Draw a centre line and set off the width of opening on each side. Draw the soffit line perpendicular to the centre line, and measure upwards as many courses as the arch is to be deep, which in the example is four. The exact height will vary with the character of the work and must be measured directly therefrom. Having found this, draw the back or extrados line horizontal—-that is, parallel with the soffit line already drawn. Set up on the centre line, the camber, which should be J in. for each foot of span, and either bend a lath around to the three points and mark the curve by its aid, or use the turning-piece for the purpose. Next determine the angle of skewback which locates the common centre of the arch. There are various methods and ratios adopted for this. A common one is to make -J in. the depth of arch, the amount that the back is longer than the soffit on each side; another, to add 1£ in. for each foot in span. This lattermethod is shown in the example. Produce the line of skewback to meet the centre line, and all the joints are drawn to the intersection. From this centre, with radius equal the height to the crown, describe an arc, and upon this set out the voussoirs equally, starting with the key, which should be spaced equally on each side the centre line; draw the bed joints horizontal, and all the lines are then obtained for marking the templets. The hidden discharging arch at the back, which carries the load, is, of course, not set out on the rod, the necessary " pitch " being given to bricks in the jointing, when laying them over the core or bed, but in making the drawing on paper, start the skewback just clear of the end of the wood lintel, which is usually tailed into the wall the depth of half a brick, and pitch it 6o° to tind the centre for striking the curves.
The Mason's Flat or Camber Arch, Fig. 3, shows
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