When the distance between the walls of a building is greater than that which would be the limit for the length of ordinary single beams, it becomes requisite to introduce one or more additional supports. Where supports are needed for a floor and partitions are not desirable, it is usual to use a large piece of timber called a girder, sustained by posts set at intervals of from 8 to 15 feet; or, when posts are objectionable, a framed construction called a framed girder (Art. 196); or an iron box called a tubular iron girder (Art. 182). When a simple timber girder is used it is advisable, if it be large, to divide it vertically from end to end and reverse the two pieces, exposing the heart of the timber to the air in order that it may dry quickly, and also to detect decay at the heart. When the halves are bolted together, thin slips of wood should be inserted between them at the several points at which they are bolted, in order to leave sufficient space for the air to circulate freely in the space thus formed between them. This tends to prevent decay, which will be found first at such parts as are not exactly tight, nor yet far enough apart to permit the escape of moisture. When girders are required for a long bearing, it is usual to truss them; that is, to insert between the halves two pieces of oak which are inclined towards each other, and which meet at the centre of the length of the girder like the rafters of a roof-truss, though nearly if not quite concealed within the girder. This and many similar methods, though extensively practised, are generally worse than useless; since it has been ascertained that, in nearly all such cases, the operation has positively weakened the girder.

A girder may be strengthened by mechanical contrivance, when its depth is required to be greater than any one piece of timber will allow. Fig. 44 shows a very simple yet invaluable method of doing this. The two pieces of which the girder is composed are bolted or pinned together,, having keys inserted between to prevent the pieces from sliding. The keys should be of hard wood, well seasoned. The two pieces should be about equal in depth, in order that the joint between them may be in the neutral line. (See Arts. 120, 121.) The thickness of the keys should be about half their breadth, and the amount of their united thickness should be equal to a trifle over the depth and one third of the depth of the girder. Instead of bolts orpins, iron hoops, are sometimes used; and when they can be procured, they are far preferable. In this case, the girder is diminished at the ends, and the hoops driven from each end towards the middle. A girder may be spliced if timber of a sufficient length cannot be obtained; though not at or near the mid- die, if it can be avoided. (See Art. 87.) Girders should rest from 9 to 12 inches on each wall, and a space should be left for the air to circulate around the ends, that the dampness may evaporate.

163 Crirtlcrs 65

Fig. 44.

Construction Of Girders

164. - Girders: Dimensions. - The size of a girder, for any special case, may be determined by equations (21.), (22.), (25.), (27.), and (28.), to resist rupture; and to resist deflection, by equations (32.) and (35.). For girders in dwellings, equation (44.) may be used. In this case, the value of c is to be taken equal to the width of floor supported by the girder, which is equal to the sum of the distances half way to the wall or next bearing on each side. When there is but one girder between the two walls, the value of c is equal to half the distance between the walls. The rule for girders for dwellings, in words, is -

Rule XLVI. - Multiply the cube of the length of the girder by the sum of the distances from the girder half way to the next bearing on each side, and by the value of j for the material of the girder, in Art. 152; the product will equal the product of the breadth of the girder into the cube of the depth. To obtain the breadth, divide this product by the cube of the depth; the quotient will be the breadth. To obtain the depth, divide the said product by the breadth; the cube root of the quotient will be the depth. If the breadth and depth are to be in a given proportion, say as r: 1.0, then divide the aforesaid quotient by the value of r; take the square root of the quotient; then the square root of this square root will be the depth, and the depth multiplied by the value of r will be the breadth.

Example. - In the floor of a dwelling, what should be the size of a Georgia-pine girder 14 feet long between posts, placed at 10 feet from one wall and 20 feet from the other? The value of c here is 10/2 +20/2 = 30/2= 15. The value of j for Georgia pine (Art. 152) is 0.32. By the rule, 143 x 15 x 0.32 = 13171.2. Now, to find the breadth when the depth is 12 inches; 13171.2 divided by the cube of 12, or by 1728, gives a quotient of 7.622, or 7 5/8, the required breadth. Again, to find the depth, when the breadth is 8 inches: 13171.2 divided by 8 gives 1646.4, the cube root of which is 11.808, or, say, 11 7/8 inches, the required depth. But if neither breadth nor depth have been previously determined, except as to their proportion, say as 0.7 to 1.0, then 13171.2 divided by 0.7 gives 18816, of which the square root is 137.171, and of this the square root is 11 .712, or, say, 11 3/4 inches, the required depth. For the breadth, we have 11.712 by 0.7 equals 8.198, or, say, 8 1/4, the required breadth. Thus the girder is required to be 7 5/8 x 12, 8 x 11 7/8, or 8 1/4 x11 3/4 inches. This example is one in a dwelling or ordinary store; for first-class stores the rule for girders is the same as the last, except that the value of k is to be taken instead of j, in Art. 152.