209. The depth of a binding joist is generally determined by the depth of the floor, but not always. Rules must therefore be given for at least two cases.

Case 1. - To find the depth of a binding joist, the length and breadth being given.

Rule. - Divide the square of the length in feet, by the breadth in inches; and the cube root of the quotient multiplied by 3.42 for fir, or by 3.53 for oak, will give the depth in inches.

210. Case 2. - To find the breadth, when the depth and length are given.

Rule. - Divide the square of the length in feet, by the cube of the depth in inches; and multiply the quotient by 40 for fir, or by 44 for oak, which will give the breadth in inches.

These rules suppose the distance apart to be 6 feet; if it be greater or less than 6 feet, the breadth given by the rule must be increased or diminished in proportion. The breadth of the binding joists next the wall may be two-thirds of the breadth of the others; but in general they are made the same, or those most defective are selected for that purpose.

211. The binding joists may be from 4 to 6 feet apart, but should not exceed 6 feet; a bearing of about 6 inches on the wall is sufficient.

The manner of framing binding joists into girders is shown by Fig. 72; and in fixing them great care should be taken that both of the bearing parts a and b should fit the corresponding parts of the mortise. This is the most important part of fitting in a binding joist, yet it is often the least attended to. The tenon should be about one-sixth of the depth, and at one-third of the depth from the lower side.

212. Binding joists that have only to carry a ceiling may have their scantlings found by the same rule as for ceiling joists (see Art. 214), except that the quotient must be multiplied by 1.2 instead of 0.64 for fir, and by 1.25 instead of 0.67 for oak joists.