The above statement, as regards the relation of the breaking strain of the bottom flange to the constant, is shown by the following formula : - Thus, to find the sectional area of the bottom flange in square inches, let a represent the area, W the breaking weight, I the length, C the constant (.75), d the depth of beam, then a = W x l/c(.75) x d

As in a preceding paragraph in this chapter we have given dimensions of various parts of timber roofs of spans of a useful variety, we now do the same office for wrought-iron roofs; on the trusses illustrated in fig, 475 - "king post" and in fig. 476, " queen post." We shall take the king post roof in fig. 475 first; in this the trusses are from 6 to 10 feet apart, according to circumstances. The rafters ca, cd, are of the form, and placed in the position illustrated in fig. 476.

## King Bolt Roofs Or Trusses

Rafters.

 Span. "Width of Upper Flange c d. Thickness of do. e b. Total Depth of Rafter a b. Thickness of Rib orWeb A, as g h, fig. 475. 18 1¾" 3/10 " 2¼" 5/10 " 20 2" ¼" 2½" 3" 22 2¼" 5/16" 2¾" 7/10" 24 2 3/8" 5/16" 2⅞" ½" 26 2½" 3/8" 3" 9/16" 28 2⅝" 3/8" 31/8" 9/16" 30 2¾" 7/16" 3¼" 9/10"

Struts or Braces b f, or b c, fig. 476.

 Span. Width of Upper Flange c d. Thickness of do. eb. Total Depth of Rafter a b. i Thickness of Rib or web A, as g h, fig. 455. 18 13/16" 3/16 " 1 3/16" 3 1/16" 20 1¼" ¼" 1½" ¼" 22 1½" 5/16" 19/16" ¼" 24 1¾" 5/16" I¾" ¼" 26 1 7/16" 7/16" 17/8" 5/16 " 28 2" 7/16 " 2" 3/8" 30 2⅛" 7/16" 2"1/8 7/16 "

Tie Rod.

 Span. Diameter. 18 ⅞" 20 ¾" 22 ⅞" 24 1" 26 1⅛" 28 1⅛" 30 13/16"

King Bolt.

 Span. Diameter. 18 7/16" 20 ¾" 22 ⅞" 24 1" 26 1⅛" 28 1 1/8" 30 13/16"

## Queen Bolt Roofs Or Trusses

Rafters e d, fig. 477.

 Span. Width of UpperFlange c d. Thickness of do. e b. Total Depth ofRafter a b. Thickness of Rib orWeb A, as g h. 32 2⅝" 3/8" 3" 7/16 " 34 2¾" ⅜" 3¼" 7/16" 36 3" 7/16" 3½" ½" 38 3⅛" 3/8" 3¾" 9/16" 40 3¼" ½" 4" ⅝"

Struts or Braces, as a c, fig. 476.

 Span Width of UpperFlange c d. Thickness of do. e b. Total Depth ofRafter a b. Thickness of Rib orWeb A, as g h. 32 1¾" ¼" 2¼ " ⅜" 34 2⅛" ¼ " 2½" ⅜" 36 2¼ " ¼ " ¼" ⅜" 38 2⅜|" 5/16" 5/16" 7/16" 40 3½" ⅜ " ⅜" ½"

Tie Rod, as c e, fig. 476.

 Span. Diameter. 32 1⅛" 34 1⅛" 36 1 3/16 " 38 1 3/16 " 40 l¼ "

King Bolt, as c d, fig. 476.

 Span. Diameter. 32 7/8" 34 ⅞" 36 15/16 " 38 1" 40 1⅛"

Queen Bolt, as c b, fig. 476.

 Span. Diameter. 32 ⅝" 34 ⅝" 36 ¾" 38 ¾" 40 13/16 "

Iron roofs may be covered with any of the usual materials, they are frequently, however, in the case of sheds, etc., covered with galvanised iron or zinc; a square foot of galvanised sheet-iron, No. 16 Birmingham wire gauge, weighs 40 oz., the thickness being 1/16 th of an inch; No. 22, same gauge, which is the thirty-second part of an inch, weighs 16 oz. to the square foot; a square, that is 100 superficial feet of zinc, No. 16 Birmingham wire gauge, weighs 2 cwt.; 6 lbs., of No. 22, same gauge, 1 cwt. 4 lbs. Unless where the zinc is corrugated or curved it is usually placed on boarding, a square of which weighs 2½ cwt. Where pan tiles are used it takes 180 of 10-inch gauge to make a square, and the weight of each tile is 75 oz.; that of a plane tile is 37; a square of pan tiling weighs 7 cwt. 2 qrs.; of plain tiling, 14 cwt. 2 qrs.; of " Queen's" slates a square weighs 7½ cwt.

Fig. 475.

Fig. 476.

Fig. 477.

Fig. 478.

A square of sheet-lead, 7 lbs. to the square foot, weighs 6 cwt. 1 qrs.; a cwt. will cover 16 superficial feet. In estimating the pressure of weights to which roofs are subjected, in addition to the materials employed, it is usual to allow for the pressure of the wind 36 cwt.; or, say, in round numbers, 2 tons to the square. In a preceding paragraph we have given illustrations and descriptions of the methods used to connect and secure the various parts of iron framing, as roofs, etc., such as bolts and pins; we now give a remark or two on the subject of projecting or delineating bolts and nuts.

Fig. 479.

Nuts are generally of two classes, square as at A, fig. 478, or hexagonal as at B. In the latter the height or the thickness of the nut, as a b, is equal to the diameter c d of the bolt. The width across the flat sides of the nut, as e f, or g h, is to be equal in fifths of inches, as there are eighths of inches in the diameter of the bolt. The head of the bolt, as l, is square, even with hexagonal nuts; the height, as j k, equal to half the width e f, or g h of nut; the side of the square m n, equal to g h, or e f. In delineating or setting out the forms of screws, whether with threads square or angular, the process is somewhat complicated (see vol. in this series on Machine Construction and Drawing); but on the small scale the screw thread of the bolt may be shown, as at o p, or still more simply at q. The upper surfaces of square nuts are often left quite flat; but in some cases the corners are filed down at an angle towards the centre, as at s, or with a curve, as at r. In the hexagonal nut, as in fig. 479, the upper surface is finished off with a spherical rounded part. Let e d be the height of the nut; and project the sides, as c d, etc., by lines from the various points of the plan at A, then bisect the three divisions in the g h and i, and through them draw central lines, as b g. From point e or f, with the " set square" draw the line f g at an angle of 45° (along the hypothenuse of the set square), intersecting b g in g. From g describe an arc touching the line e f; the centres of the side arcs are at h and i, where the centre lines cut the diagonal f g, e g. The centre of the arc a b c is on b g produced to j; and the arc is of such a radius as to touch the outsides of the arcs described from centres h and i. In the other elevation of the nut A, as at B, the projection is taken as before, by producing (shown by the dotted lines) the points of A, and bisecting the two sides k l, and drawing the central lines - lines from the points m and n at the angle of 45°, cutting these central lines on points o and p will give the centres o and p of the arcs q and r, touching the line q r. Fig. 480 shows an arrangement known as the "lock nut," or "jamb nut," on which a second nut a a is placed above or below the first nut b b; both are hexagonal.