Double a beam’s depth and its deflection drops 8-fold. Double its width and it only halves.
Bending stiffness follows I = b·h³/12 — depth enters cubed, width linearly. Joists stand on edge for a reason.
Only while the beam stays stable sideways. Make a joist very deep and thin and it buckles laterally well below its calculated bending capacity — which is why deep joists need noggins or a restrained compression flange. Past that point extra depth buys nothing.
At 20 mm the rule says 0.0008 m and the exact answer is 0.0008 m — within half a percent. It holds to within 2% up to 53.2 mm, then drifts.
The cube is bending only, and bending is not the whole deflection — there is a shear term that does not care about depth cubed. On a slender beam it is invisible. Make the beam deep and stubby and it stops being: the rule promises a stiffness the shear will not let you have.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Beam Deflection & Stress Calculator →Double a beam’s depth and its deflection drops 8-fold. Double its width and it only halves. Bending stiffness follows I = b·h³/12 — depth enters cubed, width linearly.