Beam Deflection — Simply Supported, Centre Load
Also known as simply supported deflection · PL³/48EI
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Strength decides whether a beam breaks; stiffness decides whether anyone will walk on it happily. A 20 kN load at the centre of a 4 m steel span with I = 4.167 × 10⁻⁶ m⁴ deflects δ = 20 000 × 4³ ÷ (48 × 200 × 10⁹ × 4.167 × 10⁻⁶) = 0.032 m — 32 mm, or L/125, far past any serviceability limit even if the stresses are fine. Codes usually cap live-load deflection at L/360 for plastered ceilings (the number dates from the era when plaster cracked visibly at about that curvature) and L/240 overall.
The L³ is the headline: doubling the span multiplies the sag by eight, and the only real cures are more depth (I goes as h³) or a shorter span. Note that E and I always appear together as the product EI, the flexural rigidity — which is why "use stronger steel" never fixes a bouncy floor, since all structural steels share E = 200 GPa. Remember to enter I as a plain number in m⁴, and to superimpose cases: a beam carrying both its own uniform weight and a point load deflects by the sum of 5wL⁴/384EI and PL³/48EI.
- = Maximum deflection
- = Point load
- = Span
- = Young's modulus
- = Area moment of inertia
- Maximum deflection — Beam Deflection — Simply Supported, Uniform Load, Projectile Maximum Height
- Point load — Max Bending Moment — Centre Point Load, Pulley System Effort Force
- Span — Max Bending Moment — Centre Point Load, Max Bending Moment — Uniform Load
- Young's modulus — Young's Modulus (E = σ/ε), Axial Deformation (δ = PL/AE)
- Area moment of inertia — Bending Stress (σ = Mc/I), Beam Deflection — Simply Supported, Uniform Load