Design Input Data

Step 1 — Concrete Bearing Check per EN 1992-1-1

The concrete bearing strength per EN 1993-1-8 Clause 6.2.2(2) uses the joint coefficient β_j applied to the concentrated bearing resistance from EN 1992-1-1 Clause 6.7.

Concrete material properties: f_ck = 30 MPa, γ_c = 1.50 f_cd = f_ck / γ_c = 30 / 1.50 = 20.0 MPa

Confinement benefit — EN 1992-1-1 Clause 6.7 allows an enhancement factor for the concrete bearing when the loaded area is completely enclosed within the foundation area:

α_f = √(A_c1 / A_c0) where A_c0 = B × L = 420 × 420 = 176,400 mm²

The design distribution area A_c1 is truncated by the foundation edges: A_c1 = min(B_f × L_f, 3 × B × 3 × L) = min(900 × 900, 1260 × 1260) = 810,000 mm²

α_f = √(810,000 / 176,400) = √4.592 = 2.14 → limited to 2.00 (geometrically similar and concentric)

Joint coefficient per EN 1993-1-8 Clause 6.2.2(2): Grout quality kr = grout compressive strength / f_ck = 25 / 30 = 0.833 ≥ 0.2 → β_j = 2/3

Design bearing strength: f_jd = β_j × α_f × f_cd = 2/3 × 2.00 × 20.0 = 26.7 MPa

However, EN 1993-1-8 limits this to f_cd for uniform bearing: f_jd = min(26.7, 20.0) = 20.0 MPa

Bearing pressure under ULS load: σ_Ed = N_Ed / (B × L) = 1,250,000 / 176,400 = 7.09 MPa

Utilisation = 7.09 / 20.0 = 0.354 — OK, 35.4% utilisation

Check with reduced bearing zone: Assuming the effective bearing width extends from the column flange to the plate edge with a 1:1 slope through the grout:

Effective bearing area A_eff = (b_f + 2 × 30) × (h_c + 2 × 30) = (240 + 60) × (240 + 60) = 300 × 300 = 90,000 mm²

σ_Ed,eff = 1,250,000 / 90,000 = 13.89 MPa < 20.0 MPa — OK, 69.5% utilisation

Step 2 — Base Plate Bending (Compression Zone)

Per EN 1993-1-8 Clause 6.2.3, the base plate in the compression zone is checked as a cantilever projecting beyond the column flange.

Cantilever projection beyond column face: c = (B − h_c) / 2 = (420 − 240) / 2 = 90 mm

Design bending moment per unit width of plate: M_Ed = f_jd × c² / 2 = 20.0 × 90² / 2 = 81,000 N·mm/mm

Bending resistance per unit width: M_Rd = (t_p² × f_y) / (6 × γ_M0) = (30² × 355) / (6 × 1.00) = 53,250 N·mm/mm

Utilisation = 81,000 / 53,250 = 1.52 — NOT OK

Revise base plate thickness. Required minimum thickness from cantilever formula:

t_req = c × √(3 × f_jd / (f_y / γ_M0)) = 90 × √(3 × 20.0 / 355) = 90 × √(0.169) = 90 × 0.411 = 37.0 mm

Adopted: t_p = 40 mm (S355JR). Re-check:

M_Rd,new = (40² × 355) / (6 × 1.00) = 94,667 N·mm/mm Utilisation = 81,000 / 94,667 = 0.856 — OK

Step 3 — T-Stub Tension Zone Verification

Although the column is nominally pinned, the base plate must resist nominal tension from robustness requirements and any uplift from eccentricity. Design for a nominal tension of N_t,Ed = 80 kN (6.4% of compression).

Anchor bolt tension resistance per EN 1993-1-8 Table 3.4: M24 Class 5.6, f_ub = 500 MPa, A_s = 353 mm²

F_t,Rd = k_2 × f_ub × A_s / γ_M2 = 0.90 × 500 × 353 / 1.25 = 127,080 N = 127.1 kN per bolt

T-stub effective length (non-circular pattern, two bolts in a row): m = (g − t_w − 2 × 0.8 × a_w) / 2 = (300 − 10 − 2 × 0.8 × 8) / 2 = (300 − 10 − 12.8) / 2 = 138.6 mm (simplified to 139 mm)

Where a_w = 8 mm is the assumed fillet weld throat thickness.

e = e_1 = 60 mm n = min(1.25 × m, e) = min(1.25 × 139, 60) = min(173.8, 60) = 60 mm

Plastic moment resistance of T-stub flange per unit length: M_pl,Rd = 0.25 × t_p² × f_y / γ_M0 = 0.25 × 40² × 355 / 1.00 = 142,000 N·mm/mm

Effective length for end bolt row (non-circular pattern): l_eff,nc = min(4m + 1.25e, 2m + 0.625e + e_1) = min(4 × 139 + 1.25 × 60, 2 × 139 + 0.625 × 60 + 60) = min(556 + 75, 278 + 37.5 + 60) = min(631, 375.5) = 376 mm

Mode 1 (complete yielding): F_T1,Rd = 4 × M_pl,Rd × l_eff / m = 4 × 142,000 × 376 / 139 = 1,536,000 N = 1,536 kN

Mode 2 (bolt failure with yielding): F_T2,Rd = (2 × M_pl,Rd × l_eff + n × ΣF_t,Rd) / (m + n) = (2 × 142,000 × 376 + 60 × 2 × 127,100) / (139 + 60) = (106,784,000 + 15,252,000) / 199 = 122,036,000 / 199 = 613,246 N = 613.2 kN

Mode 3 (bolt failure only): F_T3,Rd = ΣF_t,Rd = 2 × 127.1 = 254.2 kN

Governing: Mode 3 — F_T,Rd = 254.2 kN (controlled by bolt strength, plate is thick enough)

Tension utilisation = 80 / 254.2 = 0.315 — OK

Step 4 — Anchor Bolt Combined Tension and Shear

Horizontal shear V_Ed = 85 kN distributed to 4 bolts: V_Ed,bolt = 85 / 4 = 21.25 kN per bolt

Shear resistance per bolt — EN 1993-1-8 Table 3.4, shear plane passes through unthreaded portion: F_v,Rd = 0.6 × f_ub × A / γ_M2 = 0.6 × 500 × 452 / 1.25 = 108,480 N = 108.5 kN per bolt

Or for the threaded portion: F_v,Rd = 0.6 × 500 × 353 / 1.25 = 84,720 N = 84.7 kN per bolt

Use the lower value: F_v,Rd = 84.7 kN

Combined tension and shear — linear interaction per EN 1993-1-8 Clause 6.2.6(2): F_t,Ed / F_t,Rd + F_v,Ed / F_v,Rd = 20 / 127.1 + 21.25 / 84.7 = 0.157 + 0.251 = 0.408 ≤ 1.0 — OK

Step 5 — Weld Design (Column to Base Plate)

Full-strength fillet welds are specified to connect the HEB 240 column to the base plate.

Column flange weld: Flange force F_f = N_Ed × (b_f × t_f) / (A_column) ≈ 1,250 × (240 × 17) / 10,600 = 481 kN (full distribution; simplified as proportional to flange area)

Required weld force per mm of flange perimeter: Two flanges, total weld length = 2 × (240 + 2 × 17) = 2 × (240 + 34) = 548 mm Force per mm = 481,000 / 548 = 878 N/mm

Weld capacity per mm per EN 1993-1-8 Clause 4.5.3.1: For 8 mm fillet weld (throat a = 8 / √2 = 5.66 mm): F_w,Rd = f_u / (√3 × β_w × γ_M2) × a = 490 / (√3 × 0.9 × 1.25) × 5.66 = 490 / 1.949 × 5.66 = 1,422 N/mm

Weld utilisation = 878 / 1,422 = 0.617 — OK for 8 mm fillet weld

Web welds are 6 mm fillet (nominal), providing attachment but not required for load transfer in a bearing (compression) connection.

Step 6 — Gusset Plate Summary

For the HEB 240 base plate at 420 × 420 × 40 mm with this compression-dominated loading:

Key Design Parameter Comparisons — HEB Series

Values are indicative for pinned base plates with C30/37 concrete. Moment-resisting base plates require significantly thicker plates and larger bolts.

Frequently Asked Questions

How is concrete confinement accounted for in EN 1993 base plate design? EN 1993-1-8 Clause 6.2.2(2) refers to EN 1992-1-1 Clause 6.7 for the concentrated bearing resistance. The confinement enhancement factor α_f = √(A_c1 / A_c0) accounts for the load spreading from the base plate area A_c0 through the foundation to the distribution area A_c1. This factor is limited to a maximum of 2.0 for geometrically similar and concentric loading, and can be as high as 3.0 for strip loading where the foundation is much wider than the base plate. For base plates near a foundation edge or corner, A_c1 is truncated by the concrete geometry, reducing the confinement benefit. The joint coefficient β_j = 2/3 applies when the grout compressive strength is at least 20% of the concrete cylinder strength. For poor grout quality (< 0.2 f_ck), β_j drops to 1/2 or lower as specified by the relevant National Annex.

What determines the minimum base plate thickness per EN 1993-1-8? The base plate thickness is governed by two mechanisms: compression-zone bending (Clause 6.2.3) where the plate cantilevers beyond the column face and resists the concrete bearing pressure, and tension-zone bending (Clause 6.2.4) using the equivalent T-stub model. The compression zone requires t_p ≥ c × √(3 × f_jd / f_y), where c is the maximum cantilever projection. The tension zone requires the T-stub flange to develop sufficient plastic moment to force a ductile failure mode (Mode 1 or Mode 2). For typical S355 base plates, thicknesses range from 15 mm for small pinned plates to 80 mm for large moment-resisting connections. Always round up by 5-10 mm for corrosion allowance and fabrication tolerance. A minimum nominal thickness of 20 mm is typical European practice for anything larger than a 200 × 200 plate.

When are gusset stiffeners required for column base plates? Gusset stiffeners (vertical plates welded to the column flange and base plate) are required when the base plate bending check fails without them. They reduce the effective cantilever projection by providing intermediate support to the base plate. Stiffeners are particularly necessary for moment-resisting base plates where the tension-zone bolt row is far from the column flange, creating a long cantilever that would otherwise require an impractically thick plate. Typical triggers: base plate thickness exceeding 50 mm, cantilever projection exceeding 100 mm with high bearing pressures (>15 MPa), or when the T-stub Mode 1 resistance is less than half the bolt tension resistance (indicating the plate is too flexible relative to the bolts). Gusset stiffeners are also used to transfer concentrated loads from bracing connections or shear lugs into the base plate.

What National Annex variations affect European base plate plate design? The UK National Annex to EN 1993-1-8 specifies γ_M2 = 1.25 for bolts (same as the recommended value) but modifies the joint coefficient for certain grout types. The German DIN EN 1993-1-8/NA includes additional verification requirements for the grout layer thickness (minimum 20 mm, maximum 50 mm unless specially justified) and requires minimum embedment depths for anchor bolts in cracked concrete. The French NF EN 1993-1-8/NA (Annexe Nationale) specifies modified T-stub effective lengths for base plate configurations and requires a minimum base plate projection of 30 mm beyond the column flange. The Italian NTC 2018, while aligned with EN 1993, requires an additional verification of anchor bolt pull-out cone failure in the foundation. Always consult the specific National Annex for the jurisdiction of the project.

Design Resources

• EN 1993 Base Plate Reference Guide
• EN 1993 Column Design — Buckling per EN 1993-1-1
• EN 1993 Steel Grade Properties — f_y and f_u Values
• European Steel Beam Sizes — IPE, HEA, HEB
• EN 1993 Bolt Capacity — Tension and Shear
• EN 1993 End Plate Connection Design
• All European Reference Guides

Reference only. Verify all values against the current edition of EN 1993-1-8:2005, EN 1992-1-1:2004, and the applicable National Annex. Design calculations must be independently verified by a licensed Structural Engineer. This worked example is for educational purposes only and does not constitute professional engineering advice. Not for direct use in construction documents.