This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

A transposition of the factors in equation (21.), and marking it for extraction of the square root, gives a rule for the depth of a beam. Therefore, to ascertain what should be the depth of a beam of given breadth and length to safely sustain a given weight at the middle, we have -

(22.)

Rule XVIII. - Multiply the given weight by the factor of safety, and by the length in feet; divide the product by the product of the breadth into the value of B for the kind of wood, Table III.; then the square root of the quotient will be the required depth.

Example. - What should be the depth of a spruce beam 5 inches broad and 10 feet long between bearings to sustain safely, at middle, 4500 pounds? The value of B from the table is 550; taking a at 4, and proceeding by the rule, we have 4500 x 4 x 15 = 270000; this divided by (550 x 5 - ) 2750 gives a quotient of 98.18, the square root of which is 9.909, the required depth of the beam. The beam should be 5 x 10 inches.

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