A practical treatise on the strength and stiffness of timber; intended as a guide for engineers, architects, carpenters ...: to which is added an ... for estimating by inspection the strength,

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1833 edition. Excerpt: ...pounds, at a point 16 feet from one support, and 4 feet from the other; and half the weight of a beam of these dimensions is 141 pounds; therefore 3464--141 = 3323 pounds, the same as the load proposed. Problem XX. In the equation mnw = 3lld3 there are given the diameter d, the length of bearing I, and the load w; to find m and n, the segments of the length separately. Divide both sides of the equation by the given load, and we get but m + n = / by the nature of the question. Hence, by the rule at Problem VII., we obtain for the segments of the length, the following expressions, viz. where m is the greater and n the lesser segment; from which the following practical rule is derived. Rule 36. Multiply 125 times the length of bearing in feet, by the cube of the diameter in inches; divide the product by the given load, and subtract the quotient from the square of the length; then, to or from the length, add or subtract the square root of the remainder, and half the sum, or half the difference, will give the greater or lesser segment accordingly. Example 26. A cylindrical beam of oak 7 inches in diameter, and 20 feet in length, is found to sustain a load of 3323 pounds, including the effect produced by its own weight; at what point of the length is the load applied? Here, by the rule, we get 125x20x7 ZKi 3323--144' then £ (20 + V 144) = 16, or 4, the distances from the points of support. The point just determined answers to the case, when the proposed load includes the effect produced by the weight of the beam; but to find the point where the beam will be able to sustain the proposed load externally, together with the effect produced by its own weight, we must recur to Equation (14), where mnw = d(m + ri) 31 d1--'lAmn). And the...