Timber Beam Allowable Bending Moment
Timber Beam Allowable Bending Moment
Sizing a timber beam for bending is a direct application of the flexure formula, but timber's allowable bending stress is typically much lower — and more variable — than steel's, since it depends on species, grade, moisture content, and load duration, all of which get folded into a single design value. This calculation finds the moment capacity a rectangular timber section can carry once that allowable stress is known.Because wood is a natural, variable material, allowable bending stresses already carry conservative adjustment factors (for duration of load, moisture, size) baked into the reference design value used here — using an unadjusted "clear wood" strength value instead of the properly adjusted allowable stress is a common and significant error that overstates real capacity.
The allowable bending moment is M_allow = F_b·S, the allowable bending stress times the rectangular section modulus S = b·h^2/6. where F_b is the allowable bending stress for the timber grade and species, b is the beam width, h is the beam depth, S is the resulting rectangular section modulus, and M_allow is the allowable bending moment.
Inputs
F_b := 9 MPa=9 MPa
b := 200 mm=200 mm
h := 300 mm=300 mm
For a rectangular timber section, the section modulus depends on the square of the depth, which is why increasing depth is much more effective than increasing width for bending capacity.
S := b·h^2/6=3e-03 m^3
Multiplying the section modulus by the allowable bending stress converts a material property into a usable moment capacity for the beam.
M_allow := F_b·S=27000 Nm
Results
An allowable moment of about 27 kN·m for this 200 mm by 300 mm section is a reasonable capacity for a moderate-span floor or roof beam in solid sawn or glulam timber. Because S scales with h^2, doubling the depth quadruples the section modulus and therefore the moment capacity, while doubling the width only doubles it — which is why deep, narrow timber sections are the efficient choice for bending-governed spans. This check covers bending strength alone; deflection often governs timber beam sizing before bending stress does, given wood's relatively low stiffness, so a separate deflection check is typically also required.
Assumptions & limitations
- Bending stress F_b already includes applicable adjustment factors (duration of load, moisture, size) for the design condition.
- Rectangular, solid cross-section assumed — no notches, holes, or lateral-torsional buckling reduction included.
- Simply supported beam with the moment applied about the strong axis.
- Deflection and shear are governed by separate checks, not covered here.