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I'd like to build a simple desk; just a single plank of wood (or a few side-by-side) with solid supports on each end of the desk. What I'm trying to figure out is how thick a plank I want to use for the surface. Ideally, the desk will be able to support my weight (since sometimes I stand on my desk to change lights, etc), plus the weight of my computer stuff, plus some amount of safety margin.

So, supposing I have a desk surface that's eight feet wide, what equation do I need to use to figure out how thick it needs to be to support, e.g., 300lbs, placed in the middle? What properties of the wood type that I'm using do I need to determine? Is this an issue of tensile strength, or something entirely different?

This is obviously more a structural engineering problem than a physics one, but I didn't see a structuralengineering.stackexchange.com. Sorry if I posted to the wrong place.

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closed as off-topic by Manishearth Jul 12 '13 at 14:09

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In general "there isn't an X.stackexchange.com" isn't a valid excuse to post a question here, but I think this is closely enough related to physics that it's okay here. –  David Z Jul 28 '11 at 2:05
    
Yeah, I didn't think it was an absurd stretch, just thinking that if anybody had a better place for my question, I'd be happy to hear it. –  tsuraan Jul 28 '11 at 2:28
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Maybe Home Improvement? –  Kevin Reid Jul 28 '11 at 3:56
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As the answers already show this is a tough problem and depends on a lot of material parameters. In any case, you don't want to sit at a desk that flexes even a little bit, this can get very annoying. So I would recommend a very thick (about 5 cm) plank that won't flex if the support is not too far apart. –  Alexander Jan 24 '12 at 15:26

2 Answers 2

Calculating the straight of a wooden plank is more an art then science. The type of wood you choose oak or pine for example. The quality and condition of the wood this things come whit experience and years of working whit wood. But a rule of thumb is a pine 2x4 in good condition whit no knots has similar tensile straight of a 1x1x1/8 cold roll square tube.

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This is a fairly complex problem to answer starting from scratch as it has multiple components so I will just summarise the calculations that will need to be done.

In terms of the stresses in the desk, typically as a minimum you will need to calculate the following forces:

  • Bending moments
  • Shear forces
  • Bearing stresses

These will need to be calculated for different load cases including different locations for the weights on the beam as different positions for the load will give different worst case results. The method of calculation for the stresses will vary depending on the structural details you adopt for the desk but in the case you describe will probably be based on what is known as a simply supported beam.

Having calculated the forces in the beam, you will need to calculate some geometric properties of the beam in order to calculate the stresses. Typical geometric properties will be Second Moment of Area (for bending moments), Shear Area (for shear force), and Bearing Area (for bearing stresses). Again the calculation of these properties will depend on the detailing you choose, as will the use of these properties to calculate the stresses.

The final calculations you will have to do will be the stresses that the wood can withstand. Again, this is somewhat complex because wood, being an organic material, has different strengths in different loading conditions with factors such as grain direction, load type, load duration, wood type, etc. all affecting the calculation. You will also need to include an appropriate factor of safety in the calculations.

My suggestion for your desk is to avoid doing calculations if you are not used to them, but to find a desk that is similar to the one you want and copy the sizes used and use the same type of wood.

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Reading Your answer, I ask how ever someone could successfully built a framework house or bridge or table from wood :=). Do You know this bridge : de.wikipedia.org/wiki/Holzbr%C3%BCcke_bei_Essing Its a kind of Mecca for civil engineers. –  Georg Jul 28 '11 at 10:08
    
@Georg, it's actually faily simple to building things out of wood - it's only if you want to do calculations that things get a little difficult. –  Ian Turner Jul 28 '11 at 10:11
    
the important wood types for civil engineering have been tested and there are regulations for the allowed forces. But tables and most other furniture are not constructed by such guidelines. –  Georg Jul 28 '11 at 10:16
    
@georg agreed, although the question specifically asked for the equations used to design rather than the best way to design. If it asked for the best way to deign it probably shouldn't be on the physics site. –  Ian Turner Jul 28 '11 at 14:49

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