Deflection vs bending strength — which limit sets a joist span, and why deeper beats stronger

What this diagram shows

A diagram of the two checks that set every joist span in the IRC tables, using a Douglas fir-larch number-2 2-by-10 at 16 inches on center with 40 psf live and 10 psf dead load. Check one is stiffness: live-load deflection must stay under span over 360 — the bounce test a floor fails long before it breaks — and allows 16 feet 5 inches. Check two is bending strength under total load, which allows 15 feet 7 inches. The allowable span is the smaller of the two, 15 feet 7 inches, so this number-2 joist is strength-limited; flip the grade to Select Structural and deflection governs instead, leaving the extra strength unused. A bar comparison shows why depth beats grade when you need more span: stiffness grows with the cube of joist depth and strength with the square, so upgrading a 2-by-8 from number-2 to the top Select Structural grade only adds 10 inches of span, while going one size deeper to a 2-by-10 number-2 adds 2 feet 10 inches.