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I'm planning a shelving system for my workshop and will have a span a little over 12' that I need to support. I'm not really sure what weight the shelves will need to support in the end but want them to be strong enough that I never have to think about it so probably at least 2000lbs.

In my current design I'm using two 2x8s to cover this span. Will that be enough? If not should I double them up to make a total of four 2x8s or move up to two 2x10s, 2x12s?

The beams are attached to 4x4 vertical posts on both ends and will be attached with joist hangers.

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  • $\begingroup$ What is the rating of 2 by 8? cheap grade or expensive? $\endgroup$
    – Solar Mike
    Commented Sep 25, 2022 at 14:38
  • $\begingroup$ @SolarMike: I've never heard of different ratings applied to dimensional lumber and it doesn't specify from the box stores. Is that an actual thing or just redneck engineering? It would likely be kiln dried southern yellow pine though. $\endgroup$
    – jesse_b
    Commented Sep 25, 2022 at 16:39
  • $\begingroup$ Don't have rednecks this side of the pond... But surely timber - even yellow pine gets ratings so you can work out max loading etc. $\endgroup$
    – Solar Mike
    Commented Sep 25, 2022 at 16:46
  • $\begingroup$ @SolarMike: I found some descriptions of lumber "grades" but they seem fairly subjective. These would be either grade 1 or 2 though. $\endgroup$
    – jesse_b
    Commented Sep 25, 2022 at 16:51
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    $\begingroup$ @jesse_b A will answer your question later. and will elaborate. $\endgroup$
    – kamran
    Commented Sep 26, 2022 at 1:26

1 Answer 1

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I will Begin with my assumptions.

  1. You wish to select the size, species, and grade of a 12-foot-long timber shelf beam with the strength to support a 2000-pound load uniformly distributed over the beam length.

a. Possible alternative loading assumptions.

 i. 2000 lbs concentrated at center of beam.
 ii.2000 lbs is distributed over a specified length of shelf.

  1. The lumber specifications are unknown. I have assumed visually graded Douglass Fir No.1

  2. Tabulated unfactored working stresses based on normal load duration: Fb = 1000 psi & Fv = 180 psi (Size Factor CF taken as 1.0)

Internal forces acting on member cross section.

  1. Bending: M = wL*2/8 = (2000/12/12)[12(12)]^2/8 = 36,000 in-lb
  2. Shear: V = wL/2 = 2000/2 = 1,000 lb

Internal stresses acting on a nominal 2x8 cross section. (Actual dimensions = 1.5x7.25)

  1. Bending: fb = M/S, S = 1.5(7.25^2)/6 = 13.14 in^3, fb = 36000/13.14 = 2739.6 psi
  2. Horizontal shear: fvh = 1.5(V/A) = 1.5(1000)/(1.5*7.25) = 137.93 psi

Stress ratios.

  1. Bending: fb/Fb = 2739.6/1000 = 2.74 > 1 NG
  2. Horizontal shear: fvh/Fvh = 137.93/180 = 0.77 < 1 OK

As we can see the 2x8 is overstressed in bending by a factor of 2.74. This means you would need three of them based on bending and my assumptions. The best choice is to go deeper if you have the headroom.

The actual depth required for a single 2x board is sqrt[(7.25^2)2.74] = 12 in.

The actual depth required for a double 2x board is sqrt[(7.25^2)2.74/2] = 8.48 in.

Based on this analysis, if bending controls the design, the required size is: Double 2x10.

Check bearing perpendicular to the grain: fc = (2000/12/12)/3 = 4.63 psi

Allowable bearing: Fc = 625 psi > 4.63 psi OK

In addition, the connection to the posts will need to be considered. There may be joist hangars for your situation that will work. Your hardware supplier should be able to tell you. If my assumption regarding the loading, lumber grade & species and anticipated cumulative load duration is wrong, that will change the outcome. These assumptions will need to be either confirmed or corrected before the solution can be known.

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  • $\begingroup$ Could you please break up the wall of text into paragraphs & make it more easily readable. $\endgroup$
    – Fred
    Commented Dec 21, 2022 at 2:13
  • $\begingroup$ I understand your difficulty. However, your request seems a bit terse considering the fact that I am doing this free of charge. I am pretty new on this site. The text put in the answer box is not always formatted the same as what comes out in the end. I will attempt to make the format you see more like what I originally had. $\endgroup$
    – Steven Thomas
    Commented Dec 21, 2022 at 6:48

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