What Is a Stub Column?

Per EN 1993-1-1, a stub column has an effective length L_cr small enough that the non-dimensional slenderness λ̄ does not cause buckling reduction. When λ̄ ≤ 0.2 (the plateau limit per Clause 6.3.1.2(4)), buckling effects may be ignored and the compression resistance equals the squash load N_c,Rd = A × f_y / γ_M0.

In UK practice, a stub column typically has a physical length between floors (3.0–4.5 m) but with sufficient rotational restraint at both ends to keep the effective length short. The SCI P362 "Green Book" provides extensive guidance on column restraint categorisation.

Compression Resistance — EN 1993-1-1 Clause 6.2.4

For Class 1, 2, or 3 cross-sections in pure compression:

N_c,Rd = A × f_y / γ_M0 (Clause 6.2.4(2))

For Class 4 cross-sections, the effective area A_eff replaces A:

N_c,Rd = A_eff × f_y / γ_M0

Where:

• A = gross cross-sectional area
• f_y = yield strength (275 MPa for S275, 355 MPa for S355)
• γ_M0 = 1.00 (UK NA to EN 1993-1-1, Clause NA.2.4)

For UK design, γ_M0 = 1.00 is confirmed in the UK National Annex. This differs from some European National Annexes which adopt γ_M0 = 1.05 or 1.10.

Section Classification for Compression

Per EN 1993-1-1 Table 5.2, classify the cross-section for pure compression:

For S275: ε = sqrt(235/275) = 0.924. For S355: ε = sqrt(235/355) = 0.814. For S460: ε = sqrt(235/460) = 0.715.

Class 1–3 sections use gross area A. Class 4 sections require effective area A_eff per EN 1993-1-5. UK rolled UC sections are almost always Class 1 or 2 in pure compression — Class 4 is rare for standard UC sections.

EN 1993-1-1 Buckling Curves — Clause 6.3.1.2

The buckling reduction factor χ is determined from the appropriate buckling curve:

χ = 1 / [Φ + sqrt(Φ² − λ̄²)] ≤ 1.0

Where Φ = 0.5 × [1 + α(λ̄ − 0.2) + λ̄²] and λ̄ = sqrt(A × f_y / N_cr) for Class 1–3 sections.

The imperfection factor α depends on the buckling curve:

For UK UC sections in S275 buckling about the weak axis (y-y), curve c (α = 0.49) applies per EN 1993-1-1 Table 6.2. For strong-axis buckling (z-z), curve b (α = 0.34) applies, giving a higher χ value for the same slenderness.

Effective Length — EN 1993-1-1 Clause 6.3.1

The effective length L_cr = K × L where K depends on end restraint:

For typical UK simple construction with nominally pinned column bases and flexible end plate beam-to-column connections: K = 1.0 (both axes), per SCI P362 Section 5.2. For continuous columns in braced frames with moment-resisting beam connections, K = 0.85 is commonly adopted by UK engineers.

UK NA Specific Provisions

The UK National Annex to EN 1993-1-1 modifies several key parameters relevant to stub column design:

• γ_M0 = 1.00 (NA.2.4) — confirmed, no increase over the recommended value
• γ_M1 = 1.00 (NA.2.5) — for buckling resistance calculations
• Buckling curve selection unchanged from the main standard — the UK NA does not reassign buckling curves
• Serviceability deflection limits — NA.2.23 references BS 5950-1 traditional limits where the Eurocode is silent

The UK NA also confirms that the non-dimensional slenderness plateau limit λ̄₀ = 0.2 is adopted without modification.

Worked Example 1 — Short UC Column (S275)

Problem: A 254x254x73 UC (S275) forms a stub column between two braced floors at 3.0 m centres in a Manchester office building. The column supports factored axial load N_Ed = 2100 kN. Verify the section capacity.

Section Properties (254x254x73 UC):

Step 1 — Section Classification:

Flange: c/T = (254/2)/14.2 = 8.94. For S275, ε = 0.924. Class 1 limit = 9ε = 8.32. 8.94 > 8.32 but Class 2 limit = 10ε = 9.24. 8.94 < 9.24 → Class 2 flange.

Web: d/t = (254 − 2×14.2)/8.6 = 26.2. Class 1 limit for web in uniform compression = 33ε = 30.5. 26.2 < 30.5 → Class 1 web.

Section is Class 2 overall (governed by flange).

Step 2 — Non-Dimensional Slenderness (weak axis):

L_cr = 1.0 × 3000 = 3000 mm. N_cr = π² × E × I_y / L_cr² = π² × 210000 × (93.1 × 0.644² × 10⁴) / 3000². I_y = A × r_y² = 9310 × 64.4² = 38,620,000 mm⁴. N_cr = π² × 210000 × 38.62 × 10⁶ / 9 × 10⁶ = 8,908 kN.

λ̄_y = sqrt(9310 × 275 / 8,908,000) = sqrt(2,560,250 / 8,908,000) = sqrt(0.287) = 0.536.

Step 3 — Buckling Reduction (Curve c, α = 0.49):

Φ = 0.5 × [1 + 0.49(0.536 − 0.2) + 0.536²] = 0.5 × [1 + 0.165 + 0.287] = 0.726. χ = 1 / [0.726 + sqrt(0.726² − 0.536²)] = 1 / [0.726 + sqrt(0.527 − 0.287)] = 1 / [0.726 + 0.490] = 0.823.

Step 4 — Buckling Resistance:

N_b,Rd = χ × A × f_y / γ_M1 = 0.823 × 9310 × 275 / 1.00 / 1000 = 2,108 kN.

N_Ed / N_b,Rd = 2100/2108 = 0.997. Marginal — consider 254x254x89 UC for additional reserve.

Step 5 — Cross-Section Squash Load (for reference):

N_c,Rd = A × f_y / γ_M0 = 9310 × 275 / 1.00 / 1000 = 2,560 kN.

The buckling reduction is 2,108/2,560 = 0.823, consistent with the calculated χ. If K = 0.85 were used instead of 1.0, L_cr would reduce to 2550 mm and λ̄ would reduce to 0.455, giving χ ≈ 0.87 and N_b,Rd ≈ 2,227 kN.

Worked Example 2 — S355 Column with Lower Utilisation

Problem: A 203x203x52 UC (S355 JR) supports a factored axial load N_Ed = 1500 kN between braced floors at 3.5 m centres in a London commercial building. UK simple construction (K = 1.0). Check adequacy.

Section Properties (203x203x52 UC):

Step 1 — Section Classification:

Flange: c/T = (204/2)/12.5 = 8.16. For S355, ε = 0.814. Class 1 limit = 9ε = 7.32. 8.16 > 7.32 but Class 2 limit = 10ε = 8.14. 8.16 ≈ 8.14 → borderline Class 2.

Web: d/t = (206 − 2×12.5)/7.9 = 22.9. Class 1 limit = 33ε = 26.9. 22.9 < 26.9 → Class 1.

Section is Class 2 overall.

Step 2 — Non-Dimensional Slenderness:

I_y = 6630 × 51.2² = 17,370,000 mm⁴. L_cr = 3500 mm. N_cr = π² × 210000 × 17.37 × 10⁶ / 3,500² = 2,935 kN. λ̄_y = sqrt(6630 × 355 / 2,935,000) = sqrt(2,353,650 / 2,935,000) = sqrt(0.802) = 0.896.

Step 3 — Buckling Reduction (Curve c, α = 0.49):

Φ = 0.5 × [1 + 0.49(0.896 − 0.2) + 0.896²] = 0.5 × [1 + 0.341 + 0.803] = 1.072. χ = 1 / [1.072 + sqrt(1.072² − 0.896²)] = 1 / [1.072 + sqrt(1.149 − 0.803)] = 1 / [1.072 + 0.588] = 0.602.

Step 4 — Buckling Resistance:

N_b,Rd = 0.602 × 6630 × 355 / 1.00 / 1000 = 1,418 kN.

N_Ed / N_b,Rd = 1500/1418 = 1.058 > 1.0. FAIL — upgrade to 203x203x60 UC (A = 76.4 cm², r_y = 51.6 mm, N_b,Rd ≈ 1,650 kN, utilisation = 0.91).

Takeaway: S355 offers higher squash load than S275, but the higher slenderness ratio (ε is lower at 0.814 vs 0.924) can result in deeper buckling reductions at intermediate lengths. Always check both yield and buckling when switching steel grades.

Practical Design Considerations for UK Engineers

Base plate bearing: A stub column delivering N_c,Rd = 2,560 kN requires a base plate sized for the bearing capacity of the concrete foundation. For C30/37 concrete with a 600×600 mm foundation (A2) and 300×300 mm base plate (A1), the design bearing strength is f_jd = 0.67 × f_cd = 0.67 × 30/1.5 = 13.4 MPa. Required area = 2,560 × 10³/13.4 = 191,000 mm² → 437 mm square plate. A 450×450×30 mm base plate in S275 with 4-M24 holding-down bolts is typical for this column size.

Fire resistance: UK Approved Document B requires 60–120 minute fire resistance for columns in multi-storey buildings. Stub columns at high utilisation (0.85+) may require additional intumescent coating thickness or board encasement. The SCI P375 fire design guide provides section-specific protection tables.

Column splice location: UK practice typically locates column splices 600 mm above floor level per SCI P358. The splice must develop the full column capacity in compression (bearing splice with machined ends) or a proportion of it (bolted cover plate splice). For S275 UC sections, a bearing splice is preferred for economy.

FAQ

What is the λ̄₀ = 0.2 plateau and when does it apply?

EN 1993-1-1 Clause 6.3.1.2(4) states that buckling effects may be ignored when λ̄ ≤ 0.2 OR N_Ed/N_cr ≤ 0.04. For a typical UK column, λ̄ = 0.2 corresponds to a physical slenderness λ = 0.2 × 93.9 × ε = 17.4 for S275. This is a very short column — less than 1.0 m for most UC sections. In practice, very few building columns qualify for the plateau exemption.

How does the UK National Annex differ from the EN 1993-1-1 recommended values?

The UK NA adopts γ_M0 = 1.00 and γ_M1 = 1.00 (the same as the recommended values for buildings). The key UK-specific provisions relate to serviceability limits and execution tolerances, not the resistance calculations. Some European countries (Netherlands, Germany) adopt different γ_M values, which is why it is critical to use the UK NA for UK projects.

When should I use S355 instead of S275 for stub columns?

Use S355 when the 29% increase in yield strength (355/275 = 1.29) justifies the ~10–15% higher material cost. For stub columns where buckling reduction is small (χ > 0.85), the full strength gain is realised. For longer columns where χ may drop further with S355 (because ε shrinks), the net gain is smaller — check both grades and compare the delivered N_b,Rd.

What is the difference between a UC and UB section used as a column?

UC (Universal Column) sections have approximately equal depth and width with thicker flanges and webs — optimised for compression. UB (Universal Beam) sections have greater depth relative to width and thinner elements — optimised for bending. A UB can be used as a column when the strong-axis governs, but the weak-axis buckling resistance will be inferior to a UC of similar mass.

Does the SCI P362 Green Book cover stub column design?

Yes. SCI P362 provides full design guidance for columns of all slenderness ranges, including classification tables, buckling curve selection, and worked examples. For UK steel design, P362 is the primary desk reference alongside the BCSA "Blue Book" for section properties. The Green Book is updated to align with EN 1993-1-1:2005 + UK NA — always verify against the current edition.

Related Pages

• UK Column Design — Full EN 1993-1-1 Guide
• UK Column Buckling — Euler & Perry-Robertson Curves
• UK Column K-Factor — Effective Length Reference
• UK Compact Section Limits — Classification Tables
• UK Steel Properties — py Values for S275/S355/S460
• UK Combined Loading — Axial + Moment Interaction
• UK Web Bearing & Buckling — EN 1993-1-5
• UK Anchor Bolts — Holding-Down Bolt Design
• UK Base Plate Design — EN 1993-1-8
• UK Purlin Design — Cold-Formed & Hot-Rolled Purlins
• Column Capacity Calculator — Free Tool

Educational reference only. Verify against current EN 1993-1-1:2005 + UK National Annex and SCI P362 Green Book. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent Chartered Engineer verification.