I need help knowing if I am selecting the correct wood beam.

The load will be all near the center and a 250 pound man will be doing pull ups on it. I would estimate a 1,000 pound dynamic load to be safe.

I am looking at a 3.5in x 12 in x 20ft Big Beam (LP makes it, it's an LVL). It will only be supported at the ends.

How can I calculate the correct beam size? Thanks.

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    $\begingroup$ What is the allowable or desired deflection? $\endgroup$ – Phil Sweet Feb 9 '19 at 3:54

If you can approximate it as isotropic material, then you can use Euler beam theory to find the stress and compare it to the yield stress:

$ \sigma = My/I$

  • $ \sigma $ = normal stress

  • $ y $ = distance from neutral plane (midplane of symmetric section beam). Maximum stress occurs at the outside edge so use $y=h/2$ where $h$ is the height of the beam (12 in).

  • $ I $ = 2nd moment of area of the section about the axis perpendicular to y and also in the plane of the section. For a rectangular section, $I=b h^3/12$. $b$ is the width of the beam. For other shapes like I-beam, see Google.

  • $ M $ is the bending moment. For a simply-supported beam (is it simply supported?) with point load at the center, the bending moment at the center (where it's maximum), is $ M = FL/4 $. $F$=load (1000 lb_f) and $L$ = length (20 ft).

Beware that there might be other failure modes too.

| improve this answer | |
  • $\begingroup$ Thank you for the response. I plugged in the numbers and get . $\endgroup$ – Don Feb 8 '19 at 10:30
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    $\begingroup$ Something's missing from your comment. $\endgroup$ – user1318499 Feb 9 '19 at 2:48
  • $\begingroup$ What are you suggesting to limit the bending stress too? NDS has free documents available with adjustment factors and formulas that are used for Structural design. $\endgroup$ – ShadowMan Jul 8 '19 at 21:36

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