Strength Of Beams, Floor And Roofs - Including Directions For Designing And Detailing Roof Trusses, With Criticism Of Various Forms Of Timber Construction. Frank E. Kidder
safe strength. Thus if the safe strength of a given floor is equal to 80 pounds per square foot of floor, and the materials used in the construction of the floor (and ceiling) weigh 20 pounds per square foot of floor, then the safe load will be 60 pounds per square foot. The load on a floor usually consists either of people, furniture, machinery or merchandise. The strength, or the safe load, of a floor is usually spoken of as so many pounds per square foot, as that is the only practicable unit of measurement.
WEIGHT OF WOODEN FLOOR CONSTRUCTION.
Wooden floors usually consist of beams, commonly called “joists” or “floor joists,” one or two thicknesses of flooring boards, and in a finished building of a ceiling underneath the beams. In figuring the weight of 7/8-inch flooring boards it will be sufficiently accurate to estimate the weight of a single thickness at 3 pounds per square foot. The joists may also be figured at 3 pounds per foot, board measure, with the exception of hard pine and oak joists, which should be figured at 4 pounds per foot, board measure. The weight of the joists must also be reduced to their equivalent weight per square foot of floor. Thus the weight of a 2 × 12 inch joist is about 6 pounds per lineal foot. If the joists are spaced 12 inches on centers, this will be equal to 6 pounds per square foot, but if the joists are 16 inches on centers, there will be but 1 lineal foot of joist to every 1 1-3 square feet, which will be equivalent to 4 7/8 pounds per square foot, and if they are 20 inches on centers, the weight will be equal to 3 3-5 pounds per square foot; spaced 24 inches on centers, the weight will be 3 pounds per square foot.
The weight of a lath and plaster ceiling should be taken at 10 pounds per square foot, and of a 3/4-inch wood ceiling at 2 1/2 pounds per square foot. Corrugated iron ceiling weighs about 1 pound per square foot.
Table V will be found convenient in figuring the weight of floor joists.
Table V.—Weight of Floor Joists per Square Foot of Floor.
We will now show how the strength and safe load of a few simple forms of floor construction may be computed.
The simplest floor is that which consists of a series of parallel joists of equal size, spaced a uniform distance apart, and supported at each end either by walls or partitions. Such a floor is shown in Fig. 14.
Fig. 14.—Plan of Simple Form of Floor Construction
The strength of such a floor is measured by the strength of a single beam, but the strength per square foot may be obtained directly by:
Rule 1.—To find the safe strength per square foot in pounds, multiply twice the breadth of a single joist by the square of the depth, and the product by the value of A; divide by S times the square of L; S being the distance between the centers of the joists in feet, and L the span in feet. A represents the strength of the wood, as given in Table I, page 5.
Placed in the shape of a formula the above rule will read: Safe strength per square foot in pounds =
Having determined the safe strength, subtract from it the weight of the floor construction, and the result will be the safe load.
Example I.—What is the safe strength per square foot of a floor formed of 2 × 10 inch spruce joists, 16 inches on centers and 16-foot span?
Answer.—Following Rule 1, we multiply twice the breadth of a single joist by the square of the depth, which gives us 4 × 100 = 400, and this by the value of A for spruce, which gives us 28,000. S times the square of L equals 1 1/3 × 256 = 341.3. Dividing 28,000 by 341.3, we have 82 pounds per square foot as the safe strength of the floor. The weight of one square foot of the floor construction, supposing that there is a plastered ceiling and double flooring, will be for the joists, 3 3/4 pounds; flooring, 6 pounds; lath and plaster, 10 pounds; total, 19 3/4 pounds. This, subtracted from 82 pounds, gives 62 1/4 pounds for the safe load per square foot.
Very often the joists are considerably scant of the nominal dimensions, and when such is the case the actual dimensions of the joists should be taken for the breadth and depth. Thus if the joists in the above case actually measured 1 3/4 × 9 1/2 inches the safe strength would be but 64.7 pounds and the safe load about 45 pounds, or about three-fourths of what it would be were the joists of full dimensions.
STRENGTH OF FLOOR SUPPORTED BY GIRDER.
When the floor joists are supported by a girder, as in Fig. 15, the strength of the joists will be the same as if supported by a wall, but the strength of the girder must also be determined. The method of doing this is best shown by an example.
Fig. 15.—Plan and Side Elevation of Floor Supported by a Girder.
Example II.—In the floor, shown in Fig. 15, the distance L is 16 feet and the distance L′ 14 feet. The distance R between the column caps supporting the girders is 12 feet. The floor joists are of 2 × 10 inch spruce, placed 16 inches on centers, and the girder 8 × 10 inch yellow pine. There will be two thicknesses of flooring and a lath and plaster ceiling below. What is the safe load of the floor?
Answer.—As the joists are of the same size, spacing and wood, as in Example I, the safe load for the 16-foot span will be the same, or 62 1/4 pounds. The floor area supported by the girder is that inclosed between the dotted lines a, b, c, d, and is equal to
Example III.—How shall we determine the safe load for the floor, shown in Fig. 16, all the timbers being white pine?
Answer.—By Rule 1 we find the safe strength of the common joists to equal
Strength of Header.—The floor area supported by the header is equal to its length multiplied by one-half of the distance a b, or 12 × 7 = 84 square feet. If the tail beams are framed into the header they will weaken it so as to lose, we will say, the equivalent of 1 inch of its thickness, leaving the strength of the beam about equal to that of