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

By a simple transposition of the factors in equation (20.), we obtain -

b=Wal/Bd2 (21.)

a rule for the breadth of the beam.

Therefore, to ascertain what should be the breadth of a beam of given depth and length to safely sustain at the middle a given weight, we have -

Rule XVII. - Multiply the given weight in pounds by the factor of safety, and by the length in feet, and divide the product by the square of the depth multiplied by the value of B for the material in the beam, in Table III.; the quotient will be the required breadth.

Example. - What should be the breadth of a white-pine beam 8 inches deep and 10 feet long between bearings to sustain safely 2400 pounds at the middle? For white pine the value of B, in Table III., is 500. Taking the value of a at 4, and proceeding by the rule, we have 2400 x4x 10 = 96000; this divided by (82 x 500 =) 32000 gives a quotient of 3, the required breadth of the beam.

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