EXPLANATION OF THE TABLES. Definitions of Terms and Phrases used in this Explanation. and in other Places in this Work. The LENGTH of a rafter is understood to be measured from the extreme point of the foot to the extreme point of its upper end.* But in these Tables no allowances are made for the projection of rafters be yond the plate, or for ridge poles; so that the length of common rafters is understood to be the distance from the upper and outer corner of the plate to the very peak of the roof. The RUN of a rafter is the horizontal distance from the extreme point of the foot to a perpendicular let fall from the upper end. In common roofs, the run of the rafters is half the width of the building. The RISE of a rafter is the perpendicular distance from the upper end of the rafter to the level of the foot. The GAIN of a rafter is the difference between its run and its length. For example, a rafter whose run is 12 feet, and whose length is 13 feet, has 1 foot gain. The learner will easily perceive that the length of any rafter is the hypotenuse of a right-angled triangle, of which its run and its rise are the other two sides. The length is therefore ascertained with perfect accuracy by adding the square of the run to the square of the rise, and extracting the square root of their sum. (See Part I., Prop. XXIV.) Example 1. The length of a common rafter is required in a building 24 feet wide, the roof of which is desired to have a pitch of 5 inches to the foot. The run is therefore 12 feet, the square of which Except in hip rafters, the length of which is always to be measured on the backing, or along the middle line of the upper surface; for when the side bevel is all cut on one side of the upper end, as it sometimes is, then the point of the rafter will extend half its thickness beyond its estimated length, as given in the table, &c. 8 (113) is the product of 12 multiplied by 12, or 144 feet. The rise is 12 times 5 inches, or 60 inches, or 5 feet, the square of which is 25 feet; which, added to 144, makes 169 feet, of which we extract the square root thus: (the rule for which may be found in any common. school arithmetic) and find it to be 13 feet, the exact length of the rafter required. 1)169(13 1 23)69 69 00 But in most cases the result is obtained in the form of a fraction; and it will be found convenient to reduce the run and the rise to inches, in the first place, and then the root is obtained in inches and decimals of an inch, which can be carried out to any degree of accuracy required. In these Tables they are carried to hundredths of an inch. Example 2. Required the length of a rafter for the building described in Plate 4 of this work. Width of building, 12 feet; rise of rafter, 6 inches to the foot. The run of the rafter is 6 feet, or 72 in., of which the square is 5184 แ "3 66 of which we proceed to extract the square root thus: and find it to be 80 inches and 49 hundredths of an inch; or, 6 feet 8 inches and, as given in the Table, which is the exact length of the required rafter. 8)6480(80.49 64 1604)8000 6416 16089)158400 144801 13599 The use of this Table is to furnish the practical carpenter with the precise lengths of common rafters for buildings of all sizes, and for roofs of every pitch. The Table is carried out to buildings of 60 feet in width; but should the length of rafters for a wider building be required, it will be necessary to add such numbers together in the lefthand column as will make their sum equal to the width of the building, and then the sum of the lengths of the rafters given in the Table opposite these numbers, thus added together, will be the true length of the rafters required. For example, suppose it were required to find the length of rafters for a building 84 feet wide, 6 inches rise. We find the length of a rafter of half that width, of the same pitch, to be 23 ft. 5.74 in., and double this number would be the length of the rafter required, or 46 ft. 11.48 in. Example 2. Required the length of the rafters for a building 102 feet wide, 5 inches rise. We perceive that 50 and 52 added together will make 102. The lengths of these two dimensions for this pitch, as given in the Table, are 27 ft. 1 in., and 28 ft. 2 in., the sum of which is 55 ft. 3 in., the length of the rafters required. (115) |