Beam Load Calculations — Step-by-Step Guide with Formulas

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

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

Check your beam load calculation online — free calculator

Every formula in this guide can be verified in seconds with the free Buildref Beam & Frame Calculator: draw the beam, add the supports and the factored load, and it plots the full bending moment and shear force diagrams, support reactions and deflection — for simply supported beams, cantilevers, continuous beams and even 2D frames. It handles uniform and trapezoidal distributed loads, point loads and internal hinges, runs in the browser and needs no sign-up. Model the worked example above (w = 45 kN/m, L = 6 m) and you will read off M = 202.5 kN·m and V = 135 kN straight from the diagrams.

If you want to understand how those diagrams are constructed by hand — shape rules, sign conventions and three fully worked examples — see the companion guide: Shear Force and Bending Moment Diagrams — Step-by-Step.

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.