264. The stress upon purlins is proportional to their distance apart; and, the weight being uniformly diffused, the stiffness is reciprocally as the cube of the length.
Rule. - Multiply the cube of the length of the purlin in feet by the distance they are apart in feet, and the fourth root of the product for fir will give the depth in inches; or multiplied by 1.04 will give the depth for oak, and the depth multiplied by the decimal 0.6 will give the breadth. See Table 14 at the end of the volume.
Purlins should always be notched upon the principal rafters, and should be put on in as long lengths as they can be obtained, so that they may have a continuous bearing over the points of support, as the strength is increased by this means. The old method of framing the purlins into the principal rafters not only weakens the purlins, but also wounds the principal rafter, which in consequence should be increased in scantling.
There is no part of a roof so liable to fail as the purlins; in many cases they have been known to sink so much as to deform the external appearance of the roof. Weak purlins might be strengthened by bracing, a practice that was once very common among the builders in this country, and one that might always be adopted with advantage. When the roof trusses are large it is desirable to place them at a greater distance apart than when they are small, in order to save the expense and lessen the weight upon the walls. In such cases it is essential that the purlins should be trussed. A simple method of trussing beams of timber with wrought-iron rods is shown by Fig. 84. It has been frequently adopted in stagings, and for strengthening the beams of the travelling platforms used in the erection of large works. For purlins the depth of the truss might be taken at 1/12th of the span, and the distance apart of the stays C and D at 1/3rd of the span. With these proportions the following rules will give the diameter of the wrought-iron rods.
For the horizontal part C D
Rule. - Multiply the square-root of the weight in cwts. supported by the purlin, including one-half of its own weight, by the decimal 0.13, and the product will be the diameter of the rod in inches.
For the parts A C and D B.
Rule. - Multiply the square root of the gross weight, as in the last rule, by decimal 0.15.
When there is not sufficient thickness in the purlin to admit of the rods passing through its substance at the ends, the parts A C and D B might be formed of two rods or flat bars, which can bo fastened on each side of the timber and bolted to a cross-plate. In this case the sum of the areas of a cross section of the two rods or bars in inches should equal about 1/50th of the gross weight on the purlin in cwts. The cross section of a purlin trussed in this manner should be square, and the dimensions should be calculated as for a beam equal in length to the longest unsupported part of the purlin.
Sometimes it may be desirable to have only one stay in the centre, instead of two as in Fig. 81. To find the diameter of the rods in this case, multiply the square root of the gross weight in cwts. by the decimal 0.14, instead of 0.13 and 0.15 as in the foregoing rules.
The stays C and D should be either of wrought or cast iron. The strains on them would be wholly compressive if they were placed in the direction of the resultant of the stress on the rods A C and C D, or of C D and D B. But placed as in Fig. 84, there will be also a cross strain, to meet which the section of the stays should be proportioned accordingly, and a greater quantity of iron will be required in them than if they had to resist a compressive strain only.
The method of strengthening beams with wrought-iron flitches, as described in Art. 201, might also be used for purlins, besides a variety of other methods, for which the reader is referred to the Section on Bridges.
265. Common rafters are uniformly loaded, and the breadth need not be more than from 2 inches to 2 1/2 inches. The depth may be found by the following rule: -
Rule. - Divide the length of bearing in feet, by the cube root of the breadth in inches, and the quotient multiplied by 0.72 for fir, or 0.74 for cak, will give the depth in inches.
Example. - Let the length of bearing of a rafter of Riga fir be 7 feet, and the breadth 2 inches. The cube root of 2 is
1.26 nearly; therefore 7x0.72/1.26= 4 inches, the depth required. See Table 15.
Foreign fir makes the best common rafters and purlins, because it is not so liable as oak to warp and twist with the heat of the roof in summer; much, however, depends on the quality of the timber, as oak from old trees often stands very well.