196. The girders are the chief support of a framed floor, but their depth is often limited by the size of the timber; therefore, the method of finding the scantling should be divided into two cases.

Case 1. - To find the depth of a girder for the floor of a dwelling-house when the length of bearing and breadth are given.

Rule. - Divide the square of the length in feet by the breadth in inches; and the cube root of the quotient multiplied by 4.2 for fir, or by 4.34 for oak, will give the depth required in inches.

197. Case 2. - To find the breadth when the length of. bearing and depth are given.

Rule. - Divide the square of the length in feet by the cube of the depth in inches; and the quotient multiplied by 74 for fir, or by 82 for oak, will give the breadth in inches.

Example to Case 2. - Let the bearing be 20 feet, and the depth 13 inches; to find the breadth, so that the girder shall be sufficiently stiff.

The cube of the depth is 2197, and the square of the length is 400; therefore 400/2197x 74 = 13.47 inches, the breadth required.

In these rules the girders are supposed to be 10 feet apart, which ought never be exceeded; but should the distance apart be less or more than 10 feet, the breadth of the girder should be made in proportion.

Girders for long bearings should always be made as deep as the timber can be obtained; an inch or two taken from the height of a room is of little consequence compared with a ceiling disfigured with cracks, besides the inconvenience of not being able to move without shaking everything in the room.

For warehouse or other floors which have to sustain heavy loads, the strength of the girders should be calculated for each particular case by the Rules given in Arts. 102 to 107, and 182, Sect. II.

198. When the breadth of a girder is considerable, it is often sawn down the middle and bolted together with the sawn sides outwards; the girders in Fig. 59 are supposed to be done in this manner. This is an excellent method, as it not only gives an opportunity of examining the centre of the tree, which in large trees is often in a state of decay, but also reduces the timber to a smaller scantling, by which means it dries sooner, and is less liable to rot. Thin slips should be put between the halves or flitches to allow the air to circulate freely between them. It is generally imagined that a girder is strengthened when cut down, reversed, and bolted together again; it is in fact weakened by the operation, but the method is recommended for the reasons stated.

Others suppose that girders are cut down merely for the purpose of equalizing their stiffness; but admitting a girder to be bent considerably, the difference between the deflections at any two points equally distant from the middle would not be sensible in those of the usual form. The person who first practised the method of cutting girders down the middle undoubted!" did it with the view of preserving, and not of stiffening them. We find that Vitruvius, the oldest author extant on architecture, directs a space of two fingers' breadth to be left between the beams for forming the architrave over columns, in order that the air may circulate between and prevent decay.* Every one must have observed that decay begins at the joints and other places where the pieces are neither perfectly close nor yet sufficiently open to allow any dampness to evaporate.

199. When the bearing exceeds about 22 feet, it is very difficult to obtain timber large enough for girders; in such cases it is usual to truss them. The methods formerly adopted for that purpose are shown in Figs. 61 and 62, which have the appearance of much ingenuity; but, in reality, they are of very little use. If a girder of fir be trussed with oak, all the strength that can possibly be gained consists merely in the difference of compressibility between the two, which is very small indeed; and unless the truss be extremely well fitted at the abutments, it would be much stronger without trussing. All the apparent stiffness is obtained by cambering the beam, which cripples and injures the natural elasticity of the timber; and the continual spring, from the motion of the floor, upon parts already crippled, as may easily be conceived, will soon render the truss a useless burden upon the beam. This fact has long been known to many of our best carpenters, and has caused them to seek a remedy in iron trusses, which are quite as bad as the former, unless there be an iron tie to prevent the truss from spreading, for the failure is occasioned by the enormous compression applied to a small surface of timber at the abutments.

Fig. 61.

Fig. 62.

* ' Vitruvius,' lib. iv., cap. 7.

200. Barlow made some experiments on trusses similar to Figs. 61 and 62, the results of which are shown in the following Table, which confirm the above remarks.

 Description. Length of bearing. Weight. Deflection produced by the weight. feet. inches. lbs. Two oak trusses meeting against a king bolt in the centre, with plate bolts at the abutments 4 2 600 0.87 Piece of the same size, without trusses................................. 4 2 600 1.00 Three trusses, with two queen bolts with plate bolts at the abutments.......................... 5 8 500 2.25 Piece of the same size, without trusses................................... 5 8 500 1.55

The pieces were 2 inches deep and 1 7/8 inch in breadth. In the experiment with the girder having a king bolt and two truss-pieces, there appears to be a slight advantage in trussing; but in that with three lengths, it was much weaker than the untrussed piece.*

The attempt to make a solid beam stronger in the same bulk, without using a material stronger than the beam itself, is ridiculous; yet such has been the aim of most writers on Carpentry.†

* See Barlow's ' Essay on the Strength and Stress of Timber.' † See Smith's ' Carpenter's Companion,' Price's ' British Carponter,' and Langley's ' Builder's Complete Assistant.'

Though the mode of trussing girders above mentioned cannot be relied upon, nor, indeed, any other timber truss that is made within the depth of the beam; yet, by adding to the depth, there are several methods that may be applied with success in extending the bearing of timber girders. But where the depth is limited, and the bearing considerable, or where a great weight has to be supported, iron must be employed, and the best for the purpose is wrought iron, which is not so liable to flaws, or to fracture from the fall of heavy loads or other causes, as cast iron.