Compression

What this calculator checks

The calculator determines the design resistance of the cross-section to uniform compression, \(N_{c,Rd}\), according to EN 1993-1-1 §6.2.4, and compares it with the design axial force \(N_{Ed}\).

The verification required by the code is expression (6.9):

\(\frac{N_{Ed}}{N_{c,Rd}} \le 1.0\)

The resistance depends on the cross-section class. For Classes 1, 2 and 3 the gross area is used — expression (6.10):

\(N_{c,Rd} = \frac{A \cdot f_y}{\gamma_{M0}}\)

For Class 4 sections, where local buckling occurs before the yield strength is reached, the gross area is replaced by the effective area — expression (6.11):

\(N_{c,Rd} = \frac{A_{eff} \cdot f_y}{\gamma_{M0}}\)

Important: cross-section resistance is not the full check

This calculation covers the cross-section only. It assumes the member does not buckle — an assumption that holds in practice only for very short members or members restrained laterally along their full length.

In a real compression member, flexural buckling almost always governs before the section yields, and the governing resistance is \(N_{b,Rd}\), which is lower than the \(N_{c,Rd}\) computed here. For the stability check, with the reduction factor \(\chi\) and the buckling curves of §6.3.1, use the flexural buckling calculator.

The result on this page is therefore an upper bound: if the section fails here, there is no point continuing to the buckling check.

Input data

• \(N_{Ed}\) — the design compressive axial force, in kN, at Ultimate Limit State.
• Profile and section — the gross area \(A\) is taken automatically from the European profile catalogue (HEA, HEB, HEM, IPE, UPN, SHS, RHS, CHS).
• Steel grade — the yield strength \(f_y\) is determined according to EN 1993-1-1 Table 3.1, as a function of the governing thickness. For S275, for instance, \(f_y = 275\) N/mm² for \(t \le 40\) mm and drops to 255 N/mm² above that thickness. The calculator applies the reduction automatically.
• Cross-section class — for I and H profiles it is computed automatically from Table 5.2, for uniform compression. It can be overridden manually. See also the dedicated cross-section classification calculator.
• \(\gamma_{M0}\) — the partial safety factor for cross-section resistance. The recommended value is 1.0, but the National Annex takes precedence.

Worked example

Profile HEA 200, steel grade S275, axial force \(N_{Ed} = 500\) kN.

The gross area is \(A = 53.83\) cm². The governing thickness is the flange thickness, \(t_f = 10\) mm, therefore below the 40 mm threshold of Table 3.1 and \(f_y = 275\) N/mm². The section classifies as Class 1, so the gross area applies:

\(N_{c,Rd} = \frac{53.83 \cdot 100 \cdot 275}{1.0} \cdot 10^{-3} = 1480.3 \text{ kN}\)

\(\frac{N_{Ed}}{N_{c,Rd}} = \frac{500}{1480.3} = 0.34 \le 1.0\)

The section passes, with a utilisation of 34%. Buckling remains to be checked and will govern for a member of ordinary length.

Assumptions and limitations

• Concentric compression: the axial force acts at the centroid, with no eccentricity and no simultaneous bending moment. For compression with bending, see bending and axial force and bending and compression.
• Buckling is not included — neither flexural, nor torsional, nor flexural-torsional.
• For Class 4, the effective area \(A_{eff}\) must be entered manually; it is determined according to EN 1993-1-5.
• Reductions due to bolt holes are not treated. Unlike tension, holes filled by bolts may generally be neglected in compression, but the decision remains with the designer.
• The calculation covers hot-rolled structural steels. For cold-formed sections, see cold-formed section stability.

Related calculations

• Flexural buckling — the governing check for compression members
• Cross-section class — classification to EN 1993-1-1 Table 5.2
• Tension resistance — the opposite case, with net section
• Bending and axial force — \(M\)–\(N\) interaction