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?