1330
THEORY AND PRACTICE OF ENGINEERING.
Cook II.
The. simple King-post Truss is usually adopted in buildings where the span does notexceed 30 feet, and the rise given to it varies as the inclination of the rafters are formed toreceive different kinds of covering: for thatched buildings the height is made equal tohalf the span; for pantiles two-ninths ; plain tiles two-sevenths, and for slate one quarter, aquarter of the span forming an inclination of angle of 26£°.
The king-post suspends as well as supports, and must be proportioned according to thespan ; its scantling may be found by multiplying the length of the post in feet by the span
Fig. 2130.
in feet, and again their product by 012 for fir and by 0T3 for oak, which latter productwill be the sectional area of the king-post in inches; by dividing this area by the breadth, orby the thickness, cither may be obtained; the area divided by breadth gives thickness, anddivided by thickness gives breadth.
Tie-beams have two strains, one in the direction of their length, and the other from theweight of the ceiling, or whatever is suspended from it: the thrust of the rafters is neverso great as to pull the beam asunder, and the chief strain which the tie-beam is subjectedto, and which is to be guarded against, is the weight of the ceiling, or any thing whichinduces it to sag in the middle, or any other part of its length. The weight it carries willbe proportional to the length which is unsupported : where a ceiling has to be supported,the scantling of the tie-beams is found by dividing the length of the longest unsupportedpart, by the cube root of the breadth, and then multiplying the quotient by 1 *47 for the depthof fir in inches, and by 1 *52 for that of oak : where rooms or warehouse floors are held up orsupported, then their strength must be provided for in the same way as for girders. Tofind the scantling for the principal rafters, where the king-post is in the middle, multiplythe square of its length by the span in feet, and divide the product by the cube of the thick-ness in inches : for fir, multiply the quotient by 0-9G, which will give the depth in inches.
Struts and Braces must be proportioned to the effect they have depending upon them, orupon the load they are to carry ; when they are placed at the back of the principal, in aright angle, or perpendicular to its inclination, the strain upon them is the least, and whenthe same inclination is given them as to the roof, the same strain is thrown on the principalas is borne by the strut. By multiplying the square root of the length supported in feet, bythe length of the strut in feet, and then multiplying the square root of the product by 0-8 forfir, the depth may be obtained, which multiplied by 0*6 will give its breadth in inches.
Common Rajlers, being uniformly loaded, they are usually made 2 or 2.J inches in thickness,and their depth is found by dividing the length of bearing in feet by the cube root of thebreadth in inches, and multiplying the quotient by 072 for fir or 0-74 for oak, to obtainthe depth in inches.
Purlins must have their scantling proportioned to the distance the principals are apart,and as the weight diffused over them is uniform, the stiffness is reciprocally as the cube ofthe length. By multiplying the cube of their length in feet, by their length of bearing infeet, the fourth root of the product will be the depth in inches for fir; or, multi-plying by 1*04, will give the depth for oak : this multiplied by 0-6 will give the breadth.Purlins should never be framed into the principal rafters, which are weakened by havingmortises cut into them ; it is better to lay them on the principals, and simply notch downand secure them ; when the purlins arc weak, the roof is materially damaged, proper strengthbeing of the highest importance to them.
When king-post roofs are adopted, the following scantlings for the chief timbers may beadopted.