Structural beam analysis formulas
For a simply supported beam with uniformly distributed load (w) over span (L), maximum bending moment M = wL² / 8 and maximum deflection δ = (5wL⁴) / (384EI).
For a concentrated center point load (P), maximum moment M = PL / 4 and maximum deflection δ = (PL³) / (48EI).
Deflection is compared against standard serviceability limits, such as L/360 for brittle plaster ceilings and L/250 for general structural floors.
Worked example: 4m span residential steel beam
A 4.0-metre beam supports a 10 kN/m uniform design load. Maximum bending moment M = 10 × 4² / 8 = 20.0 kN·m.
Selecting a UB 203x133x25 section (Ix = 2899 cm⁴) produces 5.6 mm deflection, well below the 11.1 mm (L/360) allowable limit.
Steel beam calculator inputs
Span
Clear distance between support bearings in metres.
Load
Design load in kN/m (UDL) or total kN (point load).
CALCULATOR QUESTIONS
Steel beam deflection & stress calculator questions
What is the L/360 deflection limit?
L/360 means maximum allowable deflection is the span length divided by 360 (e.g. 10 mm on a 3.6m span) to prevent cracking of plaster and brittle finishes.
Can this calculator replace structural engineer sign-off?
No. This tool provides preliminary sizing estimates; permanent structural modifications must be verified and certified by a chartered structural engineer.