Timber Beam

How it calculates

Structural model and load combinations

The calculator models the timber beam as a one-dimensional element and computes bending moment, shear, and deflection diagrams under each EN 1990:2002 load combination. Loads are entered by type - permanent (G), variable (Q), wind (W), snow (S) - and the calculator generates governing ultimate limit state (ULS) and serviceability limit state (SLS) combinations. Two deformation combinations are generated: instantaneous (characteristic combination) and final (accounting for creep via k_def).

Material partial factor and k_mod

Characteristic strengths from the strength class (or custom input) are divided by the material partial factor gamma_M per EN 1995-1-1:2004 Cl 2.4.1 Table 2.3 (or the relevant National Annex). The resulting design strength is then multiplied by the modification factor k_mod, which accounts for service class (1, 2, or 3) and the governing load duration class (permanent through instantaneous) within each combination.

design strength = f_k × k_mod / gamma_M

Bending strength (EN 1995-1-1:2004 Cl 6.1.6)

The design bending stress sigma_m,d is computed from the applied bending moment and the elastic section modulus W_y = b × d² / 6. The allowable bending strength f_m,d is derived from the characteristic bending strength adjusted by k_mod and gamma_M. For members with multiple plies, the group modification factor is applied.

bending utilization = sigma_m,d / f_m,d ≤ 1.0

Lateral torsional buckling (EN 1995-1-1:2004 Cl 6.3.3)

When the compression edge of the beam is not fully laterally restrained, the calculator checks lateral torsional buckling. The relative slenderness for bending lambda_rel,m is computed from the critical bending stress sigma_m,crit. Where lambda_rel,m exceeds 0.75, a stability factor k_crit is applied:

reduced bending utilization = sigma_m,d / (k_crit × f_m,d) ≤ 1.0

Shear strength

Design shear stress tau_d is computed from the maximum shear force and the cross-section area (b × d). It is checked against the design shear strength f_v,d = f_v,k × k_mod / gamma_M.

shear utilization = tau_d / f_v,d ≤ 1.0

Bearing strength (EN 1995-1-1:2004 Cl 6.1.5)

At each support, compressive stress perpendicular to grain sigma_c,90,d is checked against the design compressive strength perpendicular to grain f_c,90,d, modified by a factor k_c,90 that accounts for the support length and configuration.

bearing utilization = sigma_c,90,d / (k_c,90 × f_c,90,d) ≤ 1.0

Deformation checks (EN 1995-1-1:2004 Cl 2.2.3 and Table 7.2)

Instantaneous deformation u_inst is computed under the characteristic serviceability combination using the mean modulus of elasticity E_mean. Final deformation u_fin includes creep, computed using the effective modulus E_mean / (1 + k_def), where k_def is a creep factor that depends on service class and load duration.

Both are checked against span-ratio limits from EN 1995-1-1:2004 Table 7.2 (or National Annex values), and against an optional user-defined absolute limit in mm.

Load linking

Support reactions are exported as linked outputs. Connected column and footing calculations placed downstream in the same project receive updated reactions automatically whenever the beam inputs change.