I want to calculate the deflection for an L bracket like https://imgur.com/a/0PabX0T to determine how thick I will need to make the steel for a workshop shelf.

I have done the calculation using the formulas from https://www.shortrunpro.com/content/158-beam-deflection and https://mechanicalc.com/reference/cross-section-tables but the result doesn't match my intuition:

The shelf will be 30 inches deep, trying it with a 0.25 inch thick steel bracket that is 1 inch wide, supported at one end (the wall) and with a load of 1 pound at the far end of the shelf:

Moment of inertia of a rectangle: wh^3/12 = 1 * 0.25^3 / 12 = 0.001302083

Deflection: Wl^3 / 3EI = 1*30^3 / 3*29,000,000*0.001302083 = 0.238344797

With that calculation a quarter inch steel plate would deflect 0.24 inches for each pound of load placed at the end?

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    $\begingroup$ I think this is a mechanical engineering problem best posted on an engineering site. $\endgroup$ – Bob D Mar 22 at 21:40

Yes, your calculations seems be right, it means your cantilever beam with length 30 inch, height 0.25 inch and width of 1 inch (section area 1x0.25=0.25 inch^2), will have around 0.24 inch displacement for tip per pound force applied to it's tip but as long as:

  • The steel material is in elastic range. (for your example after ~ 10 lb force, material moves to plastic range at top and button closest point to wall)
  • The bracket do not collapse or pull out from the wall because of buckling, weak nails etc.
  • Pretty much every other thing is under control!

I think this will fall into engineering criteria and should be asked in engineering site.

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