To find the area of the cross-section of a post to sustain a given weight safely, the height of the post being less than ten times the diameter if round, or ten times the least side if rectangular, the pressure coinciding with the axis, we have -
Rule VI. - Divide the given weight in pounds by the value of C, in Table I. -, multiply the quotient by the factor of safety, and the product will be the required area in inches; or -
A = Wa/C. (6.)
Example. - A weight of 40,000 pounds is to be sustained by a white-pine post 4 feet high: what must be its area of section to sustain the weight safely? Here, 40000 divided by 6650, the value of C, in Table I., set opposite white pine, and the quotient multiplied by 6, as a factor of safety, the product is 36; this, therefore, is the required area, and such a post may be 6 x 6 inches. To find the least side, so that it shall not be less than one tenth of the height, divide the height, reduced to inches, by 10, and make the least side to exceed this quotient. The area divided by the least side so determined will give the wide side. If, however, by this process, the first side found should prove to be the greatest, then the size of the post is to be found by Rule IX., X., or XI.
In case the post is to be round, its diameter may be found by reference to the Table of Circles in the Appendix, in the column of diameters, opposite to the area of the post to be found in the column of areas, or opposite to the next nearest area. For example, suppose the required area, as just found by the example under Rule VI., is 36: by reference to the column of areas, 35.78 is the nearest to 36, and the diameter set opposite is
675, which is a trifle too small. The post may therefore be, say, 6 7/8 inches diameter.
When the height of a post is less than ten times its diameter, the resistance of the post to crushing is approximately in proportion to its area of cross-section. But when the height is equal to or more than ten diameters, the resistance per square inch is diminished. The resistance diminishes as the height is increased, the diameter remaining the same (Transverse Strains, Art. 643). The strength of a slender post consists in a combination of the resistances of the material to bending and to crushing, and is represented in the following rule: