Eurocode 5 Timber Column Design Calculator (EN 1995-1-1)

Check timber columns in compression and combined bending + compression according to Eurocode 5 (EN 1995-1-1). Includes slenderness, buckling reduction factor and interaction checks.

This tool is for preliminary design and educational use. Always verify results against the full Eurocode 5 text and project-specific requirements.

Input Data

1. Material & Design Parameters

Typical: 0.6–1.1 depending on service class and load duration (EN 1995-1-1, 3.1.3).

For columns mainly in compression, kcrit ≈ 0.2 is commonly used.

Material values are pre-filled for C24. Choose “Custom values” to override with your own data.

2. Geometry & Buckling Length

Pinned–pinned ≈ 1.0, fixed–fixed ≈ 0.7, fixed–pinned ≈ 0.8.

3. Design Actions (ULS)

Results (Eurocode 5 Checks)

Section properties

A = – mm²

Iy = – mm⁴

Iz = – mm⁴

iy = – mm

iz = – mm

Slenderness & buckling

ℓcr,y = – mm

ℓcr,z = – mm

λy = –

λz = –

χc,y = –

χc,z = –

Design strengths

fc,0,d = – N/mm²

fm,d = – N/mm²

Nc,Rd (governing axis) = – kN

Utilization ratios

Pure compression: ηN = –

Combined bending + compression (major axis): ηy = –

Combined bending + compression (minor axis): ηz = –

How the Eurocode 5 timber column calculator works

This calculator follows the main design rules of Eurocode 5 (EN 1995-1-1) for axially loaded and beam-column timber members. It checks:

  • Section properties of a rectangular timber column
  • Slenderness and buckling reduction factors χc for both axes
  • Design compression resistance Nc,Rd
  • Combined bending and compression interaction according to EN 1995-1-1, 6.3

1. Section properties

For a rectangular section with width \( b \) and depth \( h \):

\( A = b \cdot h \)

\( I_y = \dfrac{b h^3}{12} \)

\( I_z = \dfrac{h b^3}{12} \)

\( i_y = \sqrt{\dfrac{I_y}{A}}, \quad i_z = \sqrt{\dfrac{I_z}{A}} \)

2. Slenderness and buckling (EN 1995-1-1, 6.3.2)

Effective buckling lengths are obtained from the member length \( L \) and effective length factors \( k_y, k_z \):

\( \ell_{cr,y} = k_y \, L \)

\( \ell_{cr,z} = k_z \, L \)

\( \lambda_y = \dfrac{\ell_{cr,y}}{i_y} \sqrt{\dfrac{f_{c,0,k}}{\pi^2 E_{0,mean}}} \)

\( \lambda_z = \dfrac{\ell_{cr,z}}{i_z} \sqrt{\dfrac{f_{c,0,k}}{\pi^2 E_{0,mean}}} \)

The non-dimensional slenderness \( \lambda \) is then used to compute the buckling reduction factor \( \chi_c \) using the Eurocode 5 buckling curve:

\( \phi = 0.5 \left[ 1 + k_{crit} (\lambda - 0.3) + \lambda^2 \right] \)

\( \chi_c = \dfrac{1}{\phi + \sqrt{\phi^2 - \lambda^2}} \le 1.0 \)

3. Design strengths

Characteristic strengths are converted to design strengths using the modification factor \( k_{mod} \) and material partial factor \( \gamma_M \):

\( f_{c,0,d} = \dfrac{k_{mod} \, f_{c,0,k}}{\gamma_M} \)

\( f_{m,d} = \dfrac{k_{mod} \, f_{m,k}}{\gamma_M} \)

4. Compression resistance

The design compression resistance is governed by the weaker buckling axis:

\( N_{c,Rd,y} = \chi_{c,y} \, A \, f_{c,0,d} \)

\( N_{c,Rd,z} = \chi_{c,z} \, A \, f_{c,0,d} \)

\( N_{c,Rd} = \min(N_{c,Rd,y}, N_{c,Rd,z}) \)

The pure compression utilization is:

\( \eta_N = \dfrac{N_d}{N_{c,Rd}} \)

5. Combined bending and compression (interaction check)

For members subjected to axial compression and bending, Eurocode 5 uses an interaction formula (EN 1995-1-1, 6.3.3). A simplified form used here is:

\( \eta_y = \dfrac{N_d}{N_{c,Rd,y}} + \dfrac{M_{y,d}}{M_{y,Rd}} \le 1.0 \)

\( \eta_z = \dfrac{N_d}{N_{c,Rd,z}} + \dfrac{M_{z,d}}{M_{z,Rd}} \le 1.0 \)

where the bending resistances are:

\( W_y = \dfrac{I_y}{h/2}, \quad W_z = \dfrac{I_z}{b/2} \)

\( M_{y,Rd} = W_y \, f_{m,d} \)

\( M_{z,Rd} = W_z \, f_{m,d} \)

The governing utilization is the maximum of \( \eta_N, \eta_y, \eta_z \). Values < 1.0 indicate that the column satisfies the Eurocode 5 design checks for the given inputs.

Design tips

  • Reduce slenderness by shortening the effective buckling length (better end restraints, bracing).
  • Increase section size (b or h) to improve both compression and bending resistance.
  • Use higher strength class timber (e.g. C30 or glulam) when appropriate.
  • Check both major and minor axes – the minor axis often governs for rectangular columns.

Disclaimer

This calculator simplifies several aspects of Eurocode 5 timber design and does not cover all clauses (e.g. stability of frames, second-order effects, fire design, connections, or serviceability). It is intended as a quick check and educational tool. For final design of structural elements, always consult the full Eurocode 5 standard, national annexes, and a qualified structural engineer.