Tension

What this calculator checks

The calculator determines the tension resistance of a plate weakened by bolt holes, according to EN 1993-1-1 §6.2.3. This is the typical case of a splice plate or a gusset, not of a rolled member without holes.

The resistance is the lesser of two failure modes — expression (6.5):

\(N_{t,Rd} = \min\left(N_{pl,Rd} \; ; \; N_{u,Rd}\right)\)

Yielding of the gross section (6.6) — ductile failure, with large and visible deformation:

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

Rupture of the net section at the holes (6.7) — brittle, sudden failure:

\(N_{u,Rd} = \frac{0.9 \cdot A_{net} \cdot f_u}{\gamma_{M2}}\)

The 0.9 factor and \(\gamma_{M2} = 1.25\) (larger than \(\gamma_{M0} = 1.0\)) are not accidental: the code deliberately penalises the brittle mode. Good design aims for \(N_{pl,Rd}\) to govern, so the member yields before it ruptures — giving warning before failure.

Hole arrangement

The net area depends on how the holes are placed. The calculator covers three cases, illustrated on the page:

Single line — one hole in the critical section: \(A_{net} = A - \phi \, t\)

Two aligned lines — two holes in the same straight section: \(A_{net} = A - 2\,\phi \, t\)

Staggered — the holes are offset, so the failure path may be straight (through one hole) or zig-zag (through two). The worse of the two governs, with the correction term of §6.2.2.2:

\(A_{net} = \min\left(A - \phi t \; ; \; A - t\left(2\phi - \frac{s^2}{4p}\right)\right)\)

The \(s^2/(4p)\) term recovers part of the area: a zig-zag failure line is longer, hence stronger, than a straight line of the same projection. The larger the stagger \(s\) relative to the spacing \(p\), the more the offset helps.

Input data

• \(N_{Ed}\) — the design tensile force, in kN.
• Hole arrangement and the associated dimensions (\(p_1\), \(p\), \(s\)), in mm.
• \(t\) — plate thickness, in mm.
• \(\phi\) — the diameter of the hole, not of the bolt. Normal clearance holes are 1–2 mm larger than the bolt, and the code counts the hole.
• \(f_y\) and \(f_u\) — yield strength and ultimate tensile strength, per EN 1993-1-1 Table 3.1.
• \(\gamma_{M0}\) (recommended 1.0) and \(\gamma_{M2}\) (recommended 1.25) — the National Annex takes precedence.

Assumptions and limitations

• It checks the plate, not the connection. Bolt resistance, bearing and block tearing (§3.10.2) are separate checks and may govern.
• Concentric tension is assumed, with no eccentricity and no simultaneous bending.
• Connections with a single bolt row where secondary bending arises from eccentricity are not treated (§3.10.3, angles connected through one leg).
• Fatigue and Serviceability Limit State verification are not covered.

Related calculations

• Compression resistance — the opposite case, where filled holes may generally be neglected
• T-stub — the EN 1993-1-8 T-stub model for bolted connections
• End plate — bolted end-plate connection