Beam Deflection
Maximum deflection, moment and shear of a linear-elastic prismatic beam per Euler-Bernoulli theory. Pick an IPE, HEA, HEB or RHS section or enter your own properties.
Maximum deflection δ_max1.38mm
- Maximum moment M_max
- 7.5 kN·m
- Maximum shear V_max
- 5 kN
- Bending stress σ = M / Wx
- 38.7 MPa
- Deflection ratio
- L / 2176
- Flexural rigidity EI
- 4,080 kN·m²
- Serviceability: L/2176 — common limit L/250
- Utilisation against S235 yield: 16 %
METHOD
How it is calculated
Simply supported, point: δ = PL³ / 48EI M = PL / 4 Simply supported, UDL: δ = 5wL⁴ / 384EI M = wL² / 8 Cantilever, tip load: δ = PL³ / 3EI M = PL Cantilever, UDL: δ = wL⁴ / 8EI M = wL² / 2 σ = M / Wx
ASSUMPTIONS & NOTES
- Self-weight is not included; add the section mass (kg/m × 9.81 / 1000 kN/m) to the distributed load if needed.
- Shear deformation and lateral buckling are ignored. Check lateral-torsional buckling for long, slender beams.
- L/250 is a general serviceability limit; use code limits for floors, crane runways etc.
Results are for preliminary design and checking; base the final design on the governing standard and safety factors.
RELATED TOOLS