Having given these descriptions of various kinds of roofs, it will not be out of place to give some rules for the proper scantlings of the different members, as determined by Tredgold, and the manner in which each member is affected.
king-post is intended to support the ceiling, and by means of the braces, to support part of the weight of the roof. The weight suspended by the king-post, will be proportional to the span of the roof; therefore, to find the scantling the length of the post in feet. by the span in feet. Then multiply this product by the decimal 0.12 for fir, or by 0.13 for oak, which will give the area of section of the king-post in inches; and this area divided by the breadth, will give the thickness ; or by the thickness, will give the breadth.
and suspending-pieces are strained in a similar manner to king-posts. but the load upon them is only proportional to that part of the length of the tie-beam suspended by each suspending, pie'e or queen-post. In queen-posts, the part suspended by each is generally half the span.
the length in feet, of the queen-post or suspending piece, by that part of the length of tic-beam it supports. also in feet. This product multiplied by the decimal 0.27 for fir, or by 0.32 for oak, will give the area of the section of the first in inches ; and this area divided by the thiCkness will give the breadth.
tie-beam is affected by two strains, the one in the direction of the length from the thrust of the principal rafters, the other is a cross strain from the weight of the ceiling. In estimating the strength, the thrust of the rafters need not be considered, because the beam is always abundantly strong to resist this strain ; and when a beam is strained in the direction of the length, it rather increases the strength to resist a cross strain. Therefore the pressure of the weight supported by the tie-beams will be proportional to the length of the longest part of it that is unsupported.
To find the scantling of a tie-beam, which has only to support a ceiling, the length of the longest unsupported part beino. given : the length of the longest unsupported part by the cube-root of the breadth ; and the quotient multiplied by 1.47, will he the depth required for fir, in inches; or multiply by 1.52, which will give the depth for oak in inches.
Principal estimating the strength of princi pal rafters, we may suppose them supported by struts, either at or very near all the points where the purlins rest upon. The pressure on a principal rafter, is in the direction of its length, and is in proportion to the magnitude of the roof; but the effect of this pressure does not hear the same propor tion to the weight, when there is a king-post, as when there are queen-posts ; therefore the same constant number will not answer for both eases.
Case 1.—To find the scantling of the principal rafter, when there is a king-post in the middle.
the square of the length of the rafter in feet, by the span in feet, and divide the product by the cube of the thickness in inches. For fir, multiply the quotient by 0.96, which will give the depth in inches.
Case 2.—To find the scantling of a principal rafter, when there are two queen-posts: Rule.—Multiply the square of the length of the rafter in feet, by the span in feet, and divide the product by the cube of the thickness in inches. For fir, multiply the quotient by 0.155, which will give the depth in inches.
Straining straining-beam is a horizontal piece between the heads of the queen-posts. In order that this beam may be the strongest possible, its depth should be to its thickness as 10 is to 7.
the square root of the span in feet, by the length of the straining-beam in feet, and extract the square root of the product. Multiply the root by 0.9, for fir, which will give the depth in inches.
To find the thickness, multiply the depth by the decimal 0.7.
Struts and part of a roof that is supported by a strut or brace, is easily ascertained from the design; but the effect of a load must depend on the position of a brace ; when it is square from the back of the rafter, the strain upon it will be the least ; and when it has the same inclination on the roof, the same strain will be thrown on the lower part of the principal rafter, as is borne by the strut. But as the degree of obliqueness does not vary much, we shall not attempt to include its effect in the rule for the scantling.