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
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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 a 5 × 12 inch. The safe distributed load for a 5 × 12 inch white pine beam, 12-foot span, is by Rule 1, page 5,
This, divided by the floor area it supports (84 square feet), gives about 86 pounds per square foot as the safe strength.
Fig. 16.—Floor with “Trimmers” and “Headers.”
Strength of Trimmers.—The trimmers have to support two loads. On one side they support a floor load equal to one-half that supported by the common joists, and on the other side they support a concentrated load equal to one-half the load on the header. To support the distributed load will require a thickness of beam equal to one-half that of the common joists, or in this case 1 inch, leaving a 4 × 12 inch beam to support the concentrated load. The safe load for a 4 × 12 inch white pine beam, 18-foot span, loaded at a point 4 feet 3 inches from one end, we find from Rule 6, page 7, to equal
The floor area supported by the header is 84 square feet, and as one-half will be supported at each end the floor area to be supported by the stirrup on the trimmer will be 42 square feet. Dividing the safe load, 2662 pounds, by 42, we have 63 pounds as the safe strength per square foot of floor.* Comparing now the different parts of the floor, we have:
Safe strength per square foot of common joists = 80.
Safe strength per square foot of header = 86.
Safe strength per square foot of trimmer joists = 63.
As the strength of the floor must be rated by the strength of the weakest part, we can only rate the strength of this floor at 63 pounds per square foot, and the safe load at 42 1/2 pounds. By adding 1 inch to the thickness of the trimmer we increase its safe strength (for the concentrated load) one-fourth, making it 78 3/4 pounds and the safe load for the floor 58 1/4 pounds. If the trimmer supports stair carriages its size should be increased to offset the stair load.
Example IV.—How shall we determine the safe load per square foot of the floor, shown in Fig. 17, all of the timber being spruce, the beams covered with two thicknesses of flooring and with corrugated iron ceiling?
Answer.—This example is very much like Example III, except that the trimmers have two concentrated loads instead of one. We also assume that the trimmer B supports the stairs, for which an allowance of 1800 pounds must be made.
By Rule 1 we find the safe strength of the common joist equals