Why Doesn't My Calculated Section Modulus Match Standard Wood Beam Sizes?

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erinrcollins
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The Section modulus of a beam that I compute does not match wood design tables to determine the correct size of the wood framing member. Can anyone offer some insight?

I have to size a wooden beam. The span is 24 feet with a tributary area of 10.5 feet. The dead load value is 85psf, the live load value is 125 psf, for a total value of 210psf. I was given an Fb value of 1775. It is a simple beam equally supported on both ends.

First I calculated the weight for the total load: (10.5 ft)(210) = 2205 lbs/sf

I calculated the Moment for the total load -- wL^2 / 8 = ((2205lb/ft )(24^2))/8 = 158,760 psf
Then I calculated the section modulus S=M/Fb = (158,760 lbft (12 inches)) / 1775

I am looking at a chart of wood beam sizing entitled Section Properties of Standard Dressed Sawn Lumber but the S value on the chart highest value is 874 in^3.

Am I correct in assuming you have to take into account the tributary area to determine the Moment? If I leave the tributary area out and just use the deal/live load of 210, I calculate a 4x14 beam. But I can't imagine that that is correct.

Thanks!
 
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In the first place, how would you know if your answer was about right, or not? What would be the argument for leaving out the tributary area (or width, as I would prefer you called it?). In other words, are you thinking? I am confused by your sloppy presentation. Tributary "area" should be presumably tributary "width" with the units you have given it. You should always state your units, including for Fb. Your units for moment perhaps should be those of force x distance.