Beam load calculations determine the forces acting on a beam, the resulting bending moments and shear forces, and whether the beam section is adequate to resist them. This guide covers the fundamental steps from load assessment through to section verification.
Step 1 — Identify the loads
Loads on beams are classified by their nature and duration:
Dead load (G or D) — permanent loads that do not change: self-weight of the beam, floor slab, finishes, partitions. Measured in kN/m or kN/m².
Live load (Q or L) — variable loads from occupancy, furniture, and people. Specified by building use category — typically 1.5–5.0 kN/m² for floors.
Wind load (W) — lateral load from wind pressure, relevant for roof beams and exposed structures.
Snow load (S) — roof load in cold climates, specified by location and roof geometry.
The total unfactored load on a beam per unit length is:
w = (Dead load + Live load) × tributary width
Step 2 — Apply load factors
Design loads are factored to account for uncertainty. Typical ultimate limit state (ULS) combinations:
Eurocode (EN 1990):
Design load = 1.35 × G + 1.5 × Q
ASCE 7 (US):
Design load = 1.2 × D + 1.6 × L
Example: Dead load = 5 kN/m², Live load = 3 kN/m², tributary width = 4 m
Unfactored: w = (5 + 3) × 4 = 32 kN/m
Factored (Eurocode): w = (1.35 × 5 + 1.5 × 3) × 4 = (6.75 + 4.5) × 4 = 45 kN/m
Step 3 — Calculate bending moment and shear
For a simply supported beam with a uniformly distributed load (UDL):
Maximum bending moment: M = wL² ÷ 8
Maximum shear force: V = wL ÷ 2
Where w is the factored load in kN/m and L is the span in metres.
Example: w = 45 kN/m, L = 6 m
M = 45 × 6² ÷ 8 = 45 × 36 ÷ 8 = 202.5 kN·m
V = 45 × 6 ÷ 2 = 135 kN
For a point load P at midspan:
M = PL ÷ 4
V = P ÷ 2
Common beam formulas
| Loading condition | Max moment | Max shear | Deflection |
| UDL, simply supported | wL²/8 | wL/2 | 5wL⁴/384EI |
| Point load at midspan, SS | PL/4 | P/2 | PL³/48EI |
| UDL, cantilever | wL²/2 | wL | wL⁴/8EI |
| Point load at tip, cantilever | PL | P | PL³/3EI |
| UDL, fixed both ends | wL²/12 (midspan) | wL/2 | wL⁴/384EI |
| Point load at midspan, fixed | PL/8 (midspan) | P/2 | PL³/192EI |
Where:
w = uniformly distributed load (kN/m)
P = point load (kN)
L = beam span (m)
E = Young’s modulus (kN/m²) — 210 × 10⁶ for steel, 30 × 10⁶ for concrete
I = second moment of area (m⁴) — from section tables
Step 4 — Check beam section capacity
The beam section must have sufficient moment capacity (Mp or Mc) and shear capacity (Vp or Vc) to resist the applied forces.
For a steel section, the plastic moment capacity is:
Mp = fy × Zpl
Where fy is the yield strength (e.g. 355 MPa for S355 steel) and Zpl is the plastic section modulus from section tables.
The section is adequate if:
M ≤ Mp (bending check)
V ≤ Vp (shear check)
δ ≤ L/360 (deflection check at serviceability)
Step 5 — Check deflection
Deflection is checked at serviceability limit state (SLS) using unfactored loads. The maximum allowable deflection is typically L/360 for floors or L/200 for roofs under imposed load.
For a simply supported beam with UDL:
δ = 5wL⁴ ÷ (384EI)
Where w is in kN/m, L in metres, E is Young’s modulus in kN/m² (210 × 10⁶ kN/m² for steel), and I is the second moment of area in m⁴.
Example: w = 32 kN/m (unfactored), L = 6 m, steel W310×39 (I = 84.4 × 10⁻⁶ m⁴)
δ = 5 × 32 × 6⁴ ÷ (384 × 210 × 10⁶ × 84.4 × 10⁻⁶)
δ = 5 × 32 × 1296 ÷ (384 × 17724)
δ = 207360 ÷ 6805836 = 0.030 m = 30 mm
Limit = 6000 ÷ 360 = 16.7 mm → section is inadequate, choose deeper section
Use our unit converter
Working across unit systems? Use the Buildref Unit Converter to switch between kN and lbf, MPa and psi, or metres and feet — all common in beam design calculations.
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