Timber member design

What this calculator checks

This tool verifies a rectangular member in solid timber or glulam at the ultimate limit state, to EN 1995-1-1 (Eurocode 5). It covers tension and compression parallel to the grain, uniaxial and biaxial bending, shear, combined actions, column buckling and lateral torsional buckling.

The essential difference from steel lies in how the design strength is obtained. In timber you do not simply divide by a partial factor: a further factor accounts for moisture and for how long the load acts (expression 2.14):

\(X_d = k_{mod} \cdot \frac{X_k}{\gamma_M}\)

The same member, with the same cross-section, has different capacities under a permanent load and under a wind gust. \(k_{mod}\) ranges from 0.50 to 1.10 — a factor of more than two, larger than any other single influence in the calculation.

Design strengths

\(k_{mod}\) is read from Table 3.1, at the intersection of the service class (the equilibrium moisture content of the timber) and the load duration class:

The partial factor \(\gamma_M\) comes from Table 2.3 and depends on the product: 1.30 for solid timber, 1.25 for glulam, 1.20 for LVL. Glulam is rewarded because the manufacturing process spreads the natural defects of timber out instead of leaving them concentrated in a single section.

The size effect

Timber is stronger in small members. The reason is statistical: the larger the section, the higher the chance that a knot or a deviated grain falls exactly in the most highly stressed zone. The code corrects for this through \(k_h\), which increases the characteristic strength in bending and tension — but not in compression:

• solid timber below 150 mm: \(k_h = \min\left[(150/h)^{0.2};\, 1.3\right]\) — §3.2(3)
• glulam below 600 mm: \(k_h = \min\left[(600/h)^{0.1};\, 1.1\right]\) — §3.3(3)

The reference depth is the side perpendicular to the bending axis; in tension, the largest cross-section dimension. For a 100 × 200 mm beam, \(k_h = 1\) for major-axis bending but 1.084 for minor-axis bending — so the two bending strengths differ, and the calculator treats them separately.

Bending and the factor \(k_m\)

Bending is checked through two expressions, not one (§6.1.6):

\(\frac{\sigma_{m,y,d}}{f_{m,y,d}} + k_m \frac{\sigma_{m,z,d}}{f_{m,z,d}} \le 1 \qquad (6.11)\)

\(k_m \frac{\sigma_{m,y,d}}{f_{m,y,d}} + \frac{\sigma_{m,z,d}}{f_{m,z,d}} \le 1 \qquad (6.12)\)

\(k_m = 0.7\) for rectangular sections in solid timber, glulam or LVL, and it recognises that the material redistributes part of the stress before failure. It is applied to each axis in turn, and the larger utilisation governs. Under uniaxial bending the two reduce to the same condition and \(k_m\) has no effect.

Combined actions

Here the code makes a distinction that surprises on first reading — the axial term is linear in tension but squared in compression:

\(\frac{\sigma_{t,0,d}}{f_{t,0,d}} + \frac{\sigma_{m,y,d}}{f_{m,y,d}} + k_m \frac{\sigma_{m,z,d}}{f_{m,z,d}} \le 1 \qquad (6.17)\)

\(\left(\frac{\sigma_{c,0,d}}{f_{c,0,d}}\right)^2 + \frac{\sigma_{m,y,d}}{f_{m,y,d}} + k_m \frac{\sigma_{m,z,d}}{f_{m,z,d}} \le 1 \qquad (6.19)\)

The square is not a transcription error. The real interaction between compression and bending is more favourable than a linear one when the axial force is small, and the quadratic form captures that. In tension the behaviour stays linear.

Buckling and lateral torsional buckling

For compression members, §6.3.2 replaces the cross-section check once the relative slenderness exceeds 0.3 about at least one axis:

\(\lambda_{rel} = \frac{\lambda}{\pi} \sqrt{\frac{f_{c,0,k}}{E_{0,05}}}\)

Below that threshold the member is short enough for buckling not to matter, and expressions 6.19 / 6.20 remain valid. Above it, the compressive capacity is reduced by \(k_c\), computed separately for each axis with the straightness factor \(\beta_c\) (0.2 for solid timber, 0.1 for glulam). The calculator applies the substitution automatically — you will never see §6.2.4 and §6.3.2 reported together, because that would count the same effect twice.

Lateral torsional buckling (§6.3.3) appears in deep, narrow beams without lateral restraint to the compression edge. The critical stress follows from expression 6.32:

\(\sigma_{m,crit} = \frac{0.78 \, b^2}{h \, l_{ef}} E_{0,05}\)

Note the dependence on \(b^2\): for a 100 × 400 mm beam, doubling the width to 200 mm quadruples the critical stress. Lateral torsional buckling is solved more efficiently through width or through lateral restraints than through a higher strength class.

\(l_{ef}\) is not the beam span. Table 6.1 adjusts it for the support conditions and the type of loading, and the difference matters: the same 6 m beam has \(l_{ef} = 6.0\) m under constant moment but 4.8 m under a point load at midspan — 20% less, which raises \(\sigma_{m,crit}\) by 25%. The calculator can derive it from the table or take it directly. The load-position correction applies too: a load on the compression edge is destabilising and adds \(2h\) to \(l_{ef}\), while one hung from the tension edge subtracts \(0.5h\).

Bearing at supports

The check that catches people out most often in timber. Strength perpendicular to the grain is roughly ten times lower than parallel — 2.5 against 21 N/mm² for C24. A beam that passes bending comfortably can fail by crushing on too short a bearing (§6.1.5):

\(\sigma_{c,90,d} = \frac{F_{c,90,d}}{A_{ef}} \le k_{c,90} \cdot f_{c,90,d}\)

The effective area is not strictly the contact surface: the real length is extended by 30 mm on each side, capped by the distance to the member end, by the contact length itself, and by half the distance to the next support. The extension represents the neighbouring fibres, which carry part of the force too.

\(k_{c,90}\) starts at 1.0 and rises only in specific configurations, conditional on \(l_1 \ge 2h\) and valid for softwood only: 1.25 on a continuous support in solid timber, 1.50 on a continuous glulam or discrete solid support, and 1.75 on a discrete glulam support with \(l \le 400\) mm. The absolute cap is 1.75.

Input data

• Strength class — softwood C14…C50 and hardwood D30…D70 to EN 338, glulam GL20…GL32 (homogeneous "h" or combined "c") to EN 14080.
• Service class — 1 (heated interior), 2 (covered, unheated), 3 (exposed).
• Load duration — the class of the leading action in the combination.
• Cross-section — width \(b\) and depth \(h\), in mm.
• Actions — axial force (with its type), moments about both axes, shear force.
• Buckling lengths — \(l_{ef,y}\) and \(l_{ef,z}\), for compression only.
• Lateral torsional buckling — from Table 6.1 (support + load type + application point) or with \(l_{ef}\) entered directly; can be skipped if the compression edge is continuously restrained.
• Bearing at supports — the force \(F_{c,90,Ed}\), the contact length, and optionally the distances \(a\) and \(l_1\).

The rule people forget

\(k_{mod}\) is not chosen from the leading action but from the one with the shortest duration in the combination (clause 3.1.3(2)). A combination mixing permanent self-weight (\(k_{mod} = 0.60\)) with short-term wind (\(k_{mod} = 0.90\)) is checked entirely with 0.90. Each combination is checked separately with its own \(k_{mod}\) — which is why the page asks for a single duration class per run.

Assumptions and limitations

• Solid rectangular sections only. Built-up, hollow or tapered sections are not covered.
• The ultimate limit state is checked. Deflections (§7.2) and vibrations (§7.3) are not — those involve \(k_{def}\) from Table 3.2, not \(k_{mod}\).
• \(k_{cr} = 0.67\) is the code's recommended value for shear; the national annex may change it, which is why it is editable.
• Expression 6.32 for lateral torsional buckling is given in the code for rectangular softwood sections. For glulam or hardwood the result is indicative, and the page flags this.
• Not covered: torsion (§6.1.8), connections (section 8), tapered or curved beams (§6.4).
• The size effect \(k_h\) is applied to each bending axis separately, using the side perpendicular to that axis, as the distinct symbols \(f_{m,y,d}\) and \(f_{m,z,d}\) in expressions 6.11 and 6.12 suggest. Some implementations use a single strength derived from \(h\); results differ by a few percent under biaxial bending.
• For solid timber, \(k_h\) applies only when \(\rho_k \le 700\) kg/m³ (§3.2(3)) — of the classes in the catalogue, D70 is excluded.
• Accidental combinations (\(\gamma_M = 1.0\), §2.4.1(2)) are not handled — \(\gamma_M\) can however be overridden manually.

Related calculators

• Reinforced concrete section — the EN 1992 equivalent for concrete members.
• Compression — buckling — the same relative-slenderness logic, in EN 1993.
• Bending — lateral torsional buckling — lateral torsional buckling for steel members.
• Single-span beams — the input actions for a simply supported beam.