1312

THEORY AND PRACTICE OF ENGINEERING.

Rook If,

multiplied by 3*42 for fir, and 8*53 for oak, will give the depth in inches : when the lengthand depth are given, and the breadth is required, divide the square of the length in feet bythe cube of the depth in inches, and multiply the quotient by 40 for fir and 44 for oak,which will give the breadth. The above rules suppose the binders to be placed at adistance of 6 feet from each other.

Binding joists must be framed into the girders, and care must be taken that the bearingparts fit the mortise made for them very accurately: the tenon should be one-sixth of thedepth, and placed at one-third of the depth, measured fromthe lower side. When binding joists only arc employed tocarry the ceiling, their scantlings may be found in the samemanner as those of ceiling joists, which are small timbers,and only of a sufficient thickness to nail the laths to;when their length and bearing are given, their depth maybe found by dividing the length in feet by the cube rootof the breadth in inches, and multiplying the quotient by0*64 for fir, or 0*67 for oak, which will give their depth ininches. Ceiling joists are usually notched to the undersides of the binding joists, and nailed to them ; this is betterthan mortising, which weakens the binder, and gives more

BINDING JOIST.

labour.

Double-framed Floors depend entirely on the girders for their strength ; their verticalthickness should be not less than one-eighteenth* part of their length : the practice of halvingthem down, and reversing their sides, is only beneficial for the purpose of ascertaining thesoundness of the interior of the timber used; whenever the concentric l ings are cut through,and the series of inclosed cones destroyed, the timber loses a portion of its natural strength :a girder or piece of timber that has its breadth equal to double its thickness, when placededgeways, will carry considerably more ; for with pieces of equal length, the strength is ina compound ratio to the squares of their depth or vertical thickness and their width ; thus,a piece of timber 16 inches by 8, placed on edge, is to the strength of the same piece placedflat, as the square of 16 multiplied by 8, is to the square of 8 multiplied by 16, or, as 2048is to 1024, or as 2 is to 1 ; but this piece of 8 by 16 inches would not carry the half ofwhat a piece 16 inches square would do.

To find the Dejjth of a Girder , when its length of bearing and breadth are given. Squarethe length in feet, and divide this product by the breadth in inches ; the cube root of thequotient, multiplied by 4*2 for fir and 4*34 for oak, will give the depth in inches. To findthe breadth, when the length and depth are given, divide the square of the length in feet bythe cube of the depth in inches, and the quotient multiplied by 74 for fir, or by 82 for oak,will give the depth in inches: in giving the above rules it has been supposed that thegirders are not placed more than 10 feet apart; when that distance is exceeded, they mustbe increased in proportion.

The Strength of Girders, or any other piece of timber of the same length and thickness,are in proportion to the squares of their depth ; but when the thickness and depth areboth to be taken into consideration, then their relative strengths are in proportion to thesquare of the depth multiplied into the thickness: when the length, breadth, and thick-ness are taken together, the weights that will break each will be in proportion to thesquare of the depth multiplied into the thickness, and divided by the length : and if wemultiply the square of the depth of each piece into its thickness, and divide each productby its length, each quotient will give the proportionate strength of each piece of timber.When it is required to have girders of greater length than 20 feet, it being difficultto obtain timbers of that scantling, it is usual to form them of two pieces trussedand bolted together : the core of such trusses must not be let close into the groovesof the side beams, but must be well secured both at the ends and middle, or aweight laid upon the girders should net bend the braces, which would render themof no use; to prevent this effect, they should not be fitted in close ; then the girder cannever bend materially, as the side beams cannot do so without shortening their length, andin the act of bending, the braces force against the ends, and act on an opposite direction tothe side beams. When the truss is tightened, it is necessary to grease the head of theking-bolt, in order that it may slide freely by the ends of the trusses; and when theworkman by a smart blow drives the head of the king-bolt, another should be ready toturn the nut at the same time, so that the girders may be made to camber about aninch in a length of 20 feet: all the stiffness obtained on trussing a girder is byforcing the abutments, or cambering it; but this to a certain extent injures the naturalelasticity of the timber, and in the course of a short time the truss becomes a load anduseless: this has caused the introduction of an iron truss, with an iron tie as an abutment,and thus the compression which took place on the abutments is-in a great degreeremoved.

The common method of trussing girders is very defective, and where the depth is