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 5

Many persons doubtless think that the strength of wooden beams is a matter of conjecture and not of mathematics, but except for a slight variation in the strength of the wood, due to different conditions inherent in the tree and also in the degree of seasoning, the strength of a given beam can be very accurately determined by simple calculations. Even with the variation due to the wood, it is possible to determine the maximum load that it is safe to put upon a beam, which is usually the information desired.

Fig. 1.—Showing Meaning of Terms Used.

Fig. 2.—Some Forms of Cantilever Beam.

Before giving any rules, however, it will be well to consider some of the facts relating to the strength of beams. The strength of a beam depends upon its size and shape, its span, (or if a cantilever, the projection beyond the point of support), the kind of wood and its condition, and also the manner of loading. The following facts are also true of all rectangular wooden beams:

1. The strength of a beam decreases in the proportion that its span is increased. Thus the strength of a given beam, with a span of 10 feet, is one-half that of the same beam with a 5-foot span. With a span of 12 feet the strength will be five-sixths what it would be with a span of 10 feet. Or if we have a beam with a span of 20 feet and place a support under the center we just double the strength.

2. The strength of a beam increases exactly as its breadth or thickness is increased. Thus a beam 2 inches thick is twice as strong as a beam 1 inch thick, provided the other conditions remain the same.

3. The strength of a beam increases in proportion to the square of its depth. A 2 × 8 inch beam will be four times as strong as a 2 × 4 inch beam, and a 2 × 12 inch beam will be nine times as strong as a 2 × 4 inch beam, the square of four being 16, and of twelve 144, or nine times as great.

It follows from the second and third paragraphs that the strength of a rectangular beam is in proportion to the product of the breadth by the square of the depth if the span remains the same. A knowledge of these facts is very important for the wise use of timber.

A beam 8 × 8 contains 64 square inches in cross section, and a beam 6 × 10 contains 60 square inches, yet their strength will be in the proportion of 512 (8 × 8 × 8) to 600 (6 × 10 × 10), the 6 × 10 beam being the stronger. The strength of a 6 × 8 inch beam on edge in proportion to the strength of the same beam laid flat wise is as 6 × 8 × 8 to 8 × 6 × 6, or 384 to 288.

Deep beams are also very much stiffer than shallow beams, the resistance of a beam to bending increasing in proportion to the cube of the depth. The stiffness therefore of a 2 × 12 inch beam and a 2 × 10 inch beam is in the proportion of the cube of 12 to the cube of 10, or 1728 to 1000. This property of stiffness is very important in floor joists, where the span in feet is usually greater than the depth in inches, but for shorter beams it need not be considered.

In speaking of the strength or stiffness of beams the breadth of the beam always refers to the thickness measured horizontally, and the depth to the height of the beam as it sets in place, without regard to which is the larger dimension. When a beam is supported at each end the distance between supports is called the span. The distance which the ends rest on their support is called the bearing.