Choices of wooden beams used to support a floor that will sustain a uniformly distributed load of 2,200 pounds over a span length of 12 feet is being considered by a Project Engineer. Using structural-grade Douglas fir and limiting the deflection 1/300 of the span, the analyst found that there ae three common sizes that will meet the required conditions – 4 by 8 inches, 3- by 10 inches, and 2- by 12 inches. The 4- by 8- inch and 3-by 10- inch list as $175 per thousand board feet., and the 2-by 12- inch size can be obtained for only $150 per thousand board feet. Which size is the most economical?

Question

Choices of wooden beams used to support a floor that will sustain a uniformly distributed load of 2,200 pounds over a span length of 12 feet is being considered by a Project Engineer. Using structural-grade Douglas fir and limiting the deflection 1/300 of the span, the analyst found that there ae three common sizes that will meet the required conditions – 4 by 8 inches, 3- by 10 inches, and 2- by 12 inches. The 4- by 8- inch and 3-by 10- inch list as $175 per thousand board feet., and the 2-by 12- inch size can be obtained for only $150 per thousand board feet. Which size is the most economical?

Answer 1

a board foot is a unit of volume, namely 144 in^3. So, figure the board feet for each size, and check the unit rate. Note that since we are interested in 12-ft lengths (144in long), all we have to do is figure the cross-section area in in^2 to get the number of board feet. So, for example,

the 3x10 beam will need 30 bd-ft per beam. So, since it costs $175 per thousand bd-ft, its unit cost per beam is 30 * 0175 = $5.25

Do the same for the other choices, and compare the unit costs.