Читать книгу 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 - Страница 21

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 or in this case 180 square feet. The safe strength for an 8 × 10 inch yellow pine beam, 12-foot span, we find from Table III (page 19) to be 8 × 1666, or 13,328 pounds. The safe strength of the girder per square foot of floor will be obtained by dividing the safe strength of the girder by the floor area supported. Dividing 13,328 by 180, we have 74 pounds per square foot as the safe strength of the girder, and subtracting 20 pounds for the weight of the floor, we have 54 pounds per square foot for the safe load for the floor, as measured by the strength of the girder. As the safe load for the floor joists is 62 pounds, the girder must be increased or the span shortened to utilize the full strength of the joists.*

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 = 80 pounds.

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,

= 7200 pounds.

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

= 2662 pounds.

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 = 106 pounds. To find the strength of the headers we allow 1 inch of the thickness for loss of strength by framing, and determine the safe distributed load of a 3 × 14 inch spruce beam, 12 feet long, by Rule 1, page 5, or Table III, to be 6860 pounds. The floor area supported by one header is equal to 4 1/2 × 12 feet, or 54 square feet. Dividing the safe strength of the beam (6860 pounds) by the floor area supported (54 square feet), we have 127 pounds as the strength of the headers per square foot of floor.

To find the strength of trimmer A we must allow 1 1/4 inches of the breadth to support the distributed load, leaving 6 1/4 inches to support the headers. The safe loads for a 6 1/4 × 14 inch spruce beam, 22-foot span, loaded at points 8 feet 10 inches from each support, we find by Rule 8, page 8, equals

= 2427 pounds.

Fig. 17.—Another Example of Floor Construction.

One-half of the area supported by one of the headers is 27 square feet. Dividing 2427 by 27, we have 90 pounds as the strength per square foot of floor.

To determine the strength of the trimmer B we must first determine how thick a beam it will require to support the 1800 pounds stair load, which is practically concentrated at the center. Rule 4, page 6, should be used. By this rule we find that it will require a 14-inch beam, 2 7/8 inches thick. Hence we must deduct 2 7/8 + 1 1/4, or 4 1/8 inches, from the breadth of our trimmer, to see how much we have left to support the headers. Deducting 4 1/8 from 10 we have 5 7/8 inches for thickness left to support the headers. This is a little less than we had in trimmer A, hence the strength will not be quite as great, but as it is not likely that the full amount of all these three loads will come on the beam at the same time, we may safely rate its strength the same as that of trimmer A, or 90 pounds per square foot of floor. Comparing the strength of the different portions of the floor, we find the common joists have a strength of 106 pounds, the trimmers a strength of 90 pounds, and the headers a strength of 127 pounds per square foot, showing that the trimmers are the weakest part of the construction.

The weight of the floor itself will be 6 1/2 pounds for the joist, 6 pounds for flooring, and 1 pound for corrugated iron ceiling, or a total of 13 1/2 pounds, making the safe load for the floor 76 1/2 pounds each side of the stair well, and 92 1/2 pounds elsewhere.

These four examples will serve to show the method of determining the strength and bearing capacity of a floor already constructed or planned. When the floor supports partitions, these must also be taken into account. If the partition is parallel with the beams then only the beams under the partition are affected. When the partition runs across the beams all the beams are affected and the weight of the partition, reduced to pounds per square foot of the floor area, must be added to the weight of the floor before subtracting from the safe strength to obtain the safe load.

Thus if in Example I there were a lath and plaster partition 10 feet high running across the joists at the center of the span, we first find the weight of the partition per lineal foot of the floor. A lath and plaster partition with 2 × 4 studding may be figured at 20 pounds per square foot, and as it is ten feet high the weight per lineal foot will be 200 pounds. As the load is concentrated at the center of the span it will be equivalent to a distributed load of twice that amount, or 400 pounds. As this is distributed over a span of 16 feet, dividing 400 by 16, we have 25 pounds per square foot of floor to be subtracted from the safe load already found, making the final safe load 37 1/4 pounds.

If the partition were 4 feet from one wall, or one-fourth of the span, the effect on the beams would be one and one-half times what it would be if the load were distributed, or 18 3/4 pounds per square foot. If the partition comes at a distance of one-third of the span from one support the load should be multiplied by 1.78 to obtain the equivalent distributed load. (See page 11.)

If the partition supports a floor or ceiling above, the weight on the partition should be added to the weight of the partition itself.

It will be seen from all that has gone before that the strength of a floor often depends more upon the way it is framed, the size of the headers and trimmers and the position of the partitions, than upon the strength of the common joists.

It may be well to add that while every floor should be “bridged,” the bridging does not increase the bearing capacity of the floor, as a whole, but merely helps to distribute a concentrated load to three or four joists.

*As a general rule, if the girders have a safe strength equal to 90 per cent. of that of the floor joists it will be sufficient, as not more than 6/10 of the floor area is likely to be loaded at one time.

*Theoretically, this method of considering a beam loaded in different ways as made up of a number of single beams or slices is not strictly correct, but the error lies on the safe side, and as the method is very much simpler than that of determining the size of beam by the bending moments, the writer feels justified in recommending it.