Rule XV. - Multiply 0.434 times the specific gravity of the suspending piece by the length in feet; deduct the product from the quotient arising from a division of the value of T, Table II., by the factor of safety, and with the remainder divide the given weight in pounds; the quotient will be the required area in inches; or -
A= W (18.)
T/a - 0.434ls
N.B. - This rule is based upon the condition that the rod be not injured in anywise by cutting.
Example. - What should be the area of a bar of English cast iron 20 feet long to sustain safely, suspended from its lower end, a weight of 5000 pounds? Taking the factor of safety at 7.0, and the specific gravity also at 7, and the value of T, Table II., at 17000, we have the product of 0.434 x 7.0 x 20 - 60.76; then 17000 divided by 7 gives a quotient of 2428.57; from which deducting the above 60.76, there remains 2367.81; dividing 5000, the given weight, by this remainder, we have the quotient, 2.11, which is the required area in inches.
120. - Transverse Strains: Rupture. - A load placed upon a beam, laid horizontally or inclined, will bend it, and, if the weight be proportionally large, will break it. The power in the material that resists this bending or breaking is termed the resistance to cross-strains, or transverse strains.
While in posts or struts the material is compressed or shortened, and in ties and suspending pieces it is extended or lengthened, in beams subjected to cross-strains the material is both compressed and extended. (See Art. 91.) When the beam is bent the fibres on the concave side are compressed, while those on the convex side are extended. The line where these two portions of the beam meet - that is, the portion compressed and the portion extended - the horizontal line of juncture, is termed the neutral line or plane. It is so called because at this line the fibres are neither compressed nor extended, and hence are under no strain whatever. The location of this line or plane is not far from the middle of the depth of the beam, when the strain is not sufficient to injure the elasticity of the material; but it removes towards the concave or convex side of the beam as the strain is increased, until, at the period of rupture, its distance from the top of the beam is in proportion to its distance from the bottom of the beam as the tensile strength of the material is to its compressive strength.