What does this Eurocode 9 calculator do?

This calculator performs a simplified Eurocode 9 member check for prismatic aluminium members. It evaluates design bending resistance, axial resistance and shear resistance based on user-defined geometry, alloy properties and load effects, and reports utilisation ratios and pass/fail status.

Which aluminium alloys can I use?

The tool includes a few common aluminium alloys such as EN AW-6060 T6 and EN AW-6082 T6 with typical characteristic strengths. You can also select a custom alloy and manually enter the 0.2% proof strength and ultimate strength to approximate other alloys. Always verify values against EN 1999-1-1 and product certificates.

Does this replace a full Eurocode 9 design?

No. The calculator is an educational and preliminary design aid. It uses simplified formulas and assumptions and does not cover all clauses of EN 1999-1-1, such as detailed buckling curves, local buckling of thin-walled sections, joints, fatigue or fire design. Final designs must be checked by a qualified engineer using the full code and manufacturer data.

What partial factors does Eurocode 9 use?

For aluminium members, Eurocode 9 typically uses a material partial factor γM1 = 1.10 for member resistance in bending and axial force, and γM2 = 1.25 for net section checks and shear. National Annexes may specify different values, so always confirm the factors applicable in your country.

Eurocode 9 Aluminium Design Calculator (EN 1999-1-1)

Q: What is Eurocode 9 (EN 1999-1-1)?

Eurocode 9 (EN 1999-1-1) is the European standard for the design of aluminium structures. It covers material properties, cross-section classification, member resistance in bending, axial force and shear, stability checks and detailing rules for aluminium alloys and tempers.

Preliminary member check for aluminium beams and columns according to Eurocode 9 (EC9). Enter geometry, alloy properties and design actions to get utilisation ratios and pass/fail status.

EC9 Member Check

1. Design situation

Material partial factor γ_M1 Shear / net section factor γ_M2

Default values per EN 1999-1-1; check your National Annex.

2. Aluminium alloy

Alloy / temper

0.2% proof strength f_0.2,k [MPa]

Ultimate strength f_u,k [MPa]

Values are indicative; always verify with EN 1999-1-1 and product certificates.

3. Section properties

Use gross section properties. For thin-walled sections, local buckling may govern and is not fully covered here.

Area A [cm²]

Elastic section modulus W_y [cm³]

Web shear area A_w [cm²]

Member length L [m]

4. Design actions (ULS)

Design bending moment M_Ed [kNm]

Design axial force N_Ed [kN]

Design shear force V_Ed [kN]

Buckling reduction factor χ (if axial)

χ = 1.0 for members without buckling; otherwise obtain from EC9 buckling curves.

Results

Bending resistance

M_Rd: – kNm

Utilisation η_M = M_Ed / M_Rd = –

Axial resistance

N_Rd: – kN

Utilisation η_N = N_Ed / N_Rd = –

Shear resistance

V_Rd: – kN

Utilisation η_V = V_Ed / V_Rd = –

Note: This tool uses simplified expressions based on EN 1999-1-1 for compact sections and does not replace a full code check. See the explanation below for formulas and assumptions.

How the Eurocode 9 aluminium design check works

Eurocode 9 (EN 1999-1-1) provides rules for the design of aluminium structures, including material properties, cross-section classification, member resistance and stability. This calculator focuses on a simplified member check for prismatic members in bending, axial force and shear.

1. Material strengths and partial factors

For a given aluminium alloy and temper, Eurocode 9 defines characteristic strengths:

0.2% proof strength \( f_{0.2,k} \) (analogous to yield strength)
Ultimate tensile strength \( f_{u,k} \)

Design strengths are obtained by dividing by material partial factors:

\[ f_{0.2,d} = \frac{f_{0.2,k}}{\gamma_{M1}}, \qquad f_{u,d} = \frac{f_{u,k}}{\gamma_{M2}} \]

Typical default values (subject to National Annex) are:

\( \gamma_{M1} = 1.10 \) for member resistance in bending and axial force
\( \gamma_{M2} = 1.25 \) for shear and net section checks

2. Bending resistance \( M_{Rd} \)

For a compact cross-section where the full plastic or elastic moment can be developed without local buckling, a simplified design bending resistance about the major axis is:

\[ M_{Rd} = \frac{f_{0.2,k}}{\gamma_{M1}} \, W_y \]

where:

\( W_y \) is the section modulus about the relevant axis.

In the calculator, you enter \( W_y \) in cm³; it is internally converted to m³ and combined with \( f_{0.2,k} \) in MPa to give \( M_{Rd} \) in kNm.

The utilisation ratio in bending is:

\[ \eta_M = \frac{M_{Ed}}{M_{Rd}} \]

3. Axial resistance \( N_{Rd} \)

For a member in compression, Eurocode 9 requires a buckling check. This is usually expressed with a reduction factor \( \chi \) obtained from buckling curves:

\[ N_{b,Rd} = \chi \, \frac{f_{0.2,k}}{\gamma_{M1}} \, A \]

The calculator lets you input \( \chi \) directly (default 1.0 for no buckling reduction). The utilisation is:

\[ \eta_N = \frac{N_{Ed}}{N_{Rd}} \]

4. Shear resistance \( V_{Rd} \)

For webs not susceptible to shear buckling, a simplified shear resistance is:

\[ V_{Rd} = \frac{f_{0.2,k}}{\sqrt{3}\,\gamma_{M2}} \, A_w \]

where \( A_w \) is the effective shear area of the web. The utilisation ratio is:

\[ \eta_V = \frac{V_{Ed}}{V_{Rd}} \]

5. Combined bending and axial force

Eurocode 9 includes interaction formulas for combined bending and axial force. For simplicity, this tool reports separate utilisation ratios for bending and axial force. As a conservative quick check, you can ensure:

\[ \eta_M + \eta_N \leq 1.0 \]

For final design, use the exact interaction expressions in EN 1999-1-1, considering cross-section class and buckling mode.

6. Limitations and good practice

Only prismatic members with uniform properties are considered.
Local buckling, lateral–torsional buckling and joint design are not explicitly checked.
Fatigue, serviceability (deflections, vibrations) and fire design are outside the scope of this tool.
Always confirm alloy properties and partial factors with the relevant National Annex and product data.

Worked example

Consider a simply supported aluminium beam with:

Alloy: EN AW-6060 T6, \( f_{0.2,k} = 190 \) MPa
Section modulus: \( W_y = 200 \,\text{cm}^3 \)
Shear area: \( A_w = 10 \,\text{cm}^2 \)
Area: \( A = 20 \,\text{cm}^2 \)
Design actions: \( M_{Ed} = 20 \,\text{kNm} \), \( V_{Ed} = 30 \,\text{kN} \), \( N_{Ed} = 0 \)
\( \gamma_{M1} = 1.10 \), \( \gamma_{M2} = 1.25 \), \( \chi = 1.0 \)

Design bending resistance:

\[ W_y = 200 \,\text{cm}^3 = 200 \times 10^{-6} \,\text{m}^3 = 2.0 \times 10^{-4} \,\text{m}^3 \]

\[ M_{Rd} = \frac{190}{1.10} \times 2.0 \times 10^{-4} \approx 34.5 \,\text{kNm} \]

\[ \eta_M = \frac{20}{34.5} \approx 0.58 \]

Design shear resistance:

\[ A_w = 10 \,\text{cm}^2 = 10 \times 10^{-4} \,\text{m}^2 = 1.0 \times 10^{-3} \,\text{m}^2 \]

\[ V_{Rd} = \frac{190}{\sqrt{3}\times 1.25} \times 1.0 \times 10^{-3} \approx 87.8 \,\text{kN} \]

\[ \eta_V = \frac{30}{87.8} \approx 0.34 \]

Both utilisation ratios are below 1.0, so the member passes this simplified EC9 check in bending and shear.

FAQ

Is this calculator suitable for thin-walled extrusions?

Many aluminium structures use thin-walled extruded profiles where local buckling and class 4 behaviour are critical. This tool does not perform effective width calculations or local buckling checks, so it should only be used for preliminary sizing. For thin-walled sections, use manufacturer software or detailed EC9 procedures.

Can I change units?

The calculator works internally in SI units (MPa, m, kN, kNm). Inputs for section properties are in cm² and cm³ for convenience, and are automatically converted. Design actions are entered directly in kN and kNm.

How should I choose the buckling factor χ?

The buckling reduction factor χ depends on the member slenderness, end conditions and buckling curve for the relevant axis and alloy. Eurocode 9 provides buckling curves and formulas to compute χ. For short members or members braced against buckling, χ may be close to 1.0; for slender columns, χ can be much lower.