Pieces subjected to a tensile strain are frequently suspended vertically. In this case, at the upper end, the strain is due not only to the weight attached at the lower end, but also to the weight of the rod itself. Usually, in timber, this is small in comparison with the load, and may be neglected; although in very long timbers, and where accuracy is decidedly essential, as, also, when the rod is of iron, it may form a part of the rule. Taking the effect of the weight of the beam into account, the relation existing between the weights and the beam requires that the rule for the weight should be as follows:
Rule XIV. - Divide the value of T for the material of the beam or rod, Table II., by the factor of safety; from the quotient subtract 0.434 times the specific gravity of the material in the beam or rod multiplied by the length of the beam or rod in feet; multiply the remainder by the area of cross-section in inches, and the product will be the required weight in pounds; or -
W=A (T/a - 0.434ls). (17.)
N. B. - This rule is based upon the condition that the suspending piece be not cut by mortices or in any other way.
Example. - What weight may be safely sustained by a white-pine rod 4x6 inches, 40 feet long, suspended vertically? For white pine the value of T is 12000; this divided by 8, as a factor of safety, gives 1500; from which subtracting 0.434 times 0.458 (the specific gravity of white pine, Table II.) multiplied by 40, the length in feet, the remainder is 1492.049; which multiplied by 24 (= 4x6, the area of cross-section) equals 35,761 pounds, the required weight to be carried. The weight which the rule would give, neglecting the weight of the rod, would have been 36000; ordinarily, so slight a difference would be quite unimportant.