What Is a Stub Column?

A stub column is a short compression member sufficiently stocky that overall buckling (flexural, torsional, or torsional-flexural) does not occur before the cross-section reaches its full compressive resistance. The "stub" length is typically 3-5 times the maximum cross-section dimension — long enough to develop a uniform stress distribution but short enough that the slenderness λ_bar ≤ 0.2, the threshold below which buckling effects are negligible per EN 1993-1-1 Clause 6.3.1.2(4).

In structural testing, stub column tests are used to determine the true stress-strain behaviour and residual stress patterns of steel sections, which form the basis of the column buckling curves (a, b, c, d).

Section Classification for Compression — Table 5.2

Section classification determines whether the full cross-section can develop its plastic resistance before local buckling occurs. For pure compression, the classification is based on the width-to-thickness (c/t) ratio of the most slender compression element:

Internal Compression Parts (Webs)

Outstand Flanges (Compression)

Where ε = sqrt(235/f_y). For S355 steel: ε = sqrt(235/355) = 0.814. For S235 steel: ε = 1.000. For S460 steel: ε = sqrt(235/460) = 0.715.

Compression Resistance — Clause 6.2.4

Class 1, 2, and 3 Cross-Sections

For sections not susceptible to local buckling (or where local buckling occurs after yield), the design plastic compression resistance (squash load) is:

N_pl,Rd = A × f_y / γ_M0

Where A is the gross cross-sectional area, f_y is the yield strength, and γ_M0 = 1.00 per EN 1993-1-1 Clause 6.1.

Class 4 Cross-Sections

For slender sections where local buckling reduces the effective area, the design buckling resistance is:

N_c,Rd = A_eff × f_y / γ_M0

Where A_eff is the effective cross-sectional area calculated per EN 1993-1-5, using effective widths for each slender compression element. The effective width for each internal compression element:

b_eff = ρ × b

Where the reduction factor ρ = (1 / λp) × (1 − 0.22 / λ_p) ≤ 1.0, and λ_p = (b/t) / (28.4 × ε × sqrt(kσ)) is the plate slenderness. The buckling coefficient k_σ = 4.0 for internal compression elements simply supported on both edges.

Squash Load Table — Standard European Sections (S355)

Effective Area for Class 4 Sections — Worked SHS 200×8 Example

Step 1 — Classification

ε = sqrt(235/355) = 0.814

Class 3 limit for internal compression: c/t ≤ 42 ε = 42 × 0.814 = 34.2

c/t = 176/8 = 22.0. Since 38 ε = 30.9 < 22.0 ≤ 38 ε = 30.9 — wait, let me recalculate.

Class 2 limit = 38 × ε = 38 × 0.814 = 30.9

c/t = 22.0 < 30.9 — actually the SHS 200×8 is Class 2 or better for compression. Let me use a more slender example.

Effective Width Calculation for a Class 4 Web (e.g., fabricated box with t = 4 mm)

For a plate with c/t = 50 (Class 4), k_σ = 4.0:

λp = (c/t) / (28.4 × ε × sqrt(kσ)) = 50 / (28.4 × 0.814 × 2.0) = 50 / 46.24 = 1.081

ρ = (1 / 1.081) × (1 − 0.22/1.081) = 0.925 × (1 − 0.204) = 0.925 × 0.796 = 0.736

b_eff = 0.736 × 176 = 129.5 mm

Effective area for four walls: A_eff = 4 × 129.5 × 4 = 2,072 mm² compared to gross area 2,816 mm² — 26% reduction in capacity due to local buckling.

Interaction with Member Buckling — Clause 6.3.1

For stub columns with λ_bar ≤ 0.2, the buckling reduction factor χ = 1.0 and N_b,Rd = N_pl,Rd (or N_c,Rd for Class 4). The stub column condition is:

λ_bar ≤ 0.2 or N_Ed / N_cr ≤ 0.04

For a HEB 200 stub column of length L = 0.5 m pinned-pinned:

N_cr = π² × E × I / L² = π² × 210,000 × 20.03 × 10⁶ / 500² = 16,602 kN

λ_bar = sqrt(A × f_y / N_cr) = sqrt(7,808 × 355 / 16,602,000) = sqrt(0.167) = 0.409

λ_bar = 0.409 > 0.2 — even at 0.5 m length, a HEB 200 stub column starts to see minor buckling effects. For truly negligible buckling (λ_bar ≤ 0.2), the maximum stub length for HEB 200 is:

L_max = π × sqrt(E × I × 0.04 / (A × f_y)) = π × sqrt(210,000 × 20.03 × 10⁶ × 0.04 / (7,808 × 355))

L_max = π × sqrt(16.82 × 10⁹ / 2,771,840) = π × sqrt(6,070) = π × 77.9 = 245 mm

This confirms that a 250 mm HEB 200 is a true stub column. At typical 500 mm length, a minor buckling reduction (χ ≈ 0.98) applies.

HEB 200 Stub Column — Worked Example

Step 1 — Cross-Section Resistance (Clause 6.2.4)

N_pl,Rd = A × f_y / γ_M0 = 7,808 × 355 / 1.00 = 2,772 kN

Step 2 — Buckling Check (Clause 6.3.1)

N_cr = π² × 210,000 × 20.03 × 10⁶ / 250² = 66,408 kN

λ_bar = sqrt(2,772 / 66,408) = sqrt(0.0417) = 0.204 ≈ 0.20

Therefore, χ ≈ 1.00 (buckling curve b, Table 6.1). N_b,Rd = 2,772 kN.

Step 3 — Design Check

For N_Ed = 2,000 kN: utilisation = 2,000 / 2,772 = 0.72 — OK.

Frequently Asked Questions

What is the difference between squash load N_pl,Rd and buckling resistance N_b,Rd?

The squash load N_pl,Rd (Clause 6.2.4) is the cross-section compression resistance assuming no buckling — the full plastic capacity of the steel area. The buckling resistance N_b,Rd (Clause 6.3.1) is the member resistance including the reduction factor χ that accounts for flexural buckling. For stub columns (λ_bar ≤ 0.2), χ = 1.0 and the two are equal. For slender columns, χ < 1.0 and N_b,Rd = χ × N_pl,Rd.

How does section classification affect the compression resistance?

Section classification determines whether local buckling reduces the cross-section capacity before or after the steel yields. Class 1 and 2 sections can achieve the full plastic resistance N_pl,Rd = A × f_y / γ_M0. Class 3 sections use the elastic limit: N_el,Rd = A × f_y / γ_M0 (same formula but limited to the elastic stress distribution). Class 4 sections use the effective area: N_c,Rd = A_eff × f_y / γ_M0 where A_eff < A due to local buckling of slender plate elements.

When is a stub column test used in structural engineering?

Stub column tests are used to: (1) validate the yield strength of full-scale sections (which may differ from coupon tests due to residual stresses from the rolling process); (2) determine the effective stress-strain curve of the cross-section for use in advanced analysis; (3) calibrate buckling curves for new section types or steel grades; (4) verify the section classification limits in the code for novel section geometries. In laboratory practice, the stub column length is selected to give λ_bar ≈ 0.15-0.25, ensuring the failure is governed by cross-section yielding and local buckling rather than overall member buckling.

Design Resources

• EN 1993 Column Design — Flexural Buckling per Clause 6.3
• EN 1993 Compact Section Limits — Table 5.2 c/t Ratios
• EN 1993 Column K-Factor — Effective Length for Sway/Non-Sway
• EN 1993 Steel Grades — f_y and f_u Values for All Grades
• EN 1993 Combined Loading — Axial + Bending Interaction
• All European Reference Guides →

Reference only. Verify all values against the current edition of EN 1993-1-1:2005 Clause 6.2.4, Table 5.2, and EN 1993-1-5 for effective widths. Section properties should be confirmed from the manufacturer's current catalogue. All design calculations must be independently verified by a licensed Structural Engineer. This guide is for educational purposes only and does not constitute professional engineering advice.