What is Beam Deflection

Open Source

FreeCAD WizardShaft - https://www.freecadweb.org/wiki/PartDesign_WizardShaft. This provides moment of inertia, but not deflection.

Yes! Quick analysis for different beam shapes in different materials - https://www.engineering.com/calculators/beams.htm

1 lb force, on a 12" shaft. Force point in middle of shaft, so this would be worst case scenario

Interpretation: for reference, this is about 100 micron deflection, but if shaft were supported on one end, so actual result is better.

What would a 3" rod withstand if it were to bend 100 microns (5 thou)?

About 9000 lb!