Free Tool · EN 1993-1-8 §6.2.7 + Annex J T-stub method

Endplate Moment Connection Calculator

Design bolted beam-to-column endplate moment connections using the T-stub method per EN 1993-1-8 §6.2.7. Per-bolt-row Mode 1/2/3 failure, Mj,Rd, compression check, weld sizing. Live results, no sign-up.

Inputs
Beam
Column
Endplate
Bolts
National Annex
Applied Moment
Results
207.17 kNm
M_j,Rd (moment resistance)
η = 43.4% PASS ✓
F_c,Rd (compression) 714.4 kN
m (T-stub lever arm) 23.7 mm
Min. weld throat a_w ≥ 15.5 mm
γ_M0 / γ_M2 1 / 1.25
S_j,ini (rot. stiffness) 41515 kNm/rad
Joint classification semi-rigid
Components
Column web panel shear §6.2.6.1 30.8%
Column web compression §6.2.6.2 36.9%
Column web tension §6.2.6.3 41%
Column flange bending §6.2.6.4 36%
Endplate bending §6.2.6.5 39.6%
Beam flange/web compression §6.2.6.7 39.6%
Beam web tension §6.2.6.8 49.4%
Bolts in tension §6.2.6.12 39.6%
Flange weld §4.5.3 88.6%
M-φ Curve
φ M M_j,Rd M_Ed
Bolt row resistances
Row h_r (mm) l_eff (mm) F_t,Rd (kN) Mode
1 364.3 94.2 282.15 M2
2 272.8 117.5 282.24 M3
3 182.8 117.5 150.01 M3
Step 1 — Geometry
m = 23.7 mm  |  m₂ = 15 mm (extended bolt above flange)
Step 2 — Compression zone
F_c,fc,Rd = 714.4 kN (beam flange §6.2.6.7)
F_c,wc,Rd = 765.5 kN (column web §6.2.6.2)
→ F_c,Rd = min = 714.4 kN
Step 3 — T-stub per bolt row (§6.2.4)
Row 1: l_eff,cp=94.2 mm l_eff,nc=100 mm → l_eff=94.2 mm
  M_pl,Rd=3345.8 kNmm F_t1=564.1 kN F_t2=282.2 kN F_t3=282.2 kN
  F_t,Rd (uncapped)=282.15 kN → limited by F_c,Rd balance → F_t,Rd=282.15 kN Mode 2
Row 2: l_eff,cp=149.1 mm l_eff,nc=117.5 mm → l_eff=117.5 mm
  M_pl,Rd=4169.5 kNmm F_t1=703 kN F_t2=313 kN F_t3=282.2 kN
  F_t,Rd (uncapped)=282.24 kN → limited by F_c,Rd balance → F_t,Rd=282.24 kN Mode 3
Row 3: l_eff,cp=149.1 mm l_eff,nc=117.5 mm → l_eff=117.5 mm
  M_pl,Rd=4169.5 kNmm F_t1=703 kN F_t2=313 kN F_t3=282.2 kN
  F_t,Rd (uncapped)=282.24 kN → limited by F_c,Rd balance → F_t,Rd=150.01 kN Mode 3
Step 4 — Moment resistance
M_j,Rd = Σ F_t,r × h_r = 207.17 kNm
Step 5 — Weld sizing (§4.5.3)
Lever arm = 318.5 mm → a_w ≥ 15.5 mm
Step 6 — Utilisation
η = M_Ed / M_j,Rd = 90 / 207.17 = 43.4%
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FAQ

What is the T-stub method and why does EN 1993-1-8 use it?
The T-stub (T-section stub) model (§6.2.4) idealises the column flange or endplate as a short cantilever T-section. Under bolt tension, three failure modes are possible: Mode 1 — complete yielding of the T-stub flange (ductile, 4 plastic hinges); Mode 2 — simultaneous bolt failure and partial flange yielding (2 plastic hinges + bolt failure); Mode 3 — pure bolt failure (brittle). Design resistance F_t,Rd = min(Mode1, Mode2, Mode3). The T-stub model is used because it captures the prying-action amplification of bolt forces that occurs when the plate is flexible. Mode 3 governs for thick plates; Mode 1 for thin, flexible plates.
What is the effective length l_eff in T-stub calculations?
The effective length l_eff (mm) is the length of the T-stub flange that participates in yielding for a given bolt row. Two patterns are checked per EN 1993-1-8 Table 6.4/6.5: circular (continuous yield line around the bolt, l_eff,cp) and non-circular (straight/irregular yield lines, l_eff,nc). The smaller governs. For interior rows: circular = 2πm; non-circular = min(4m + 1.25e, 2m + 0.625e + 0.5p). For extended endplate top rows: circular = 2πm₂; non-circular = 4m₂ + 1.25e. Larger m (flexible plate) → more circular yielding → larger l_eff,cp → potentially Mode 1 governing.
Why is the moment resistance limited by the compression zone?
Equilibrium of the joint requires that the sum of tension forces in bolt rows equals the compression force in the compression zone (beam flange + web bearing against column web). Each bolt row resistance is limited so that the cumulative tension does not exceed F_c,Rd. This means that if the compression zone is weak (thin column web, low grade), upper tension rows may be reduced. In EN 1993-1-8 §6.2.7(2), the rows are activated top-to-bottom until the compression capacity is exhausted.
What is the difference between extended and flush endplates?
A flush endplate ends at or within the beam depth — no bolt row can be placed above the top flange or below the bottom flange. An extended endplate projects beyond the beam flanges, adding one or two bolt rows outside the flange depth. These outer rows are farther from the compression centre, giving a larger lever arm h_r and thus more contribution to M_j,Rd per unit bolt force. Extended endplates can increase moment capacity by 30–60% for the same bolt grade and size, at the cost of more complex fabrication and weld detailing at the extension.
How do I size the endplate thickness?
The T-stub plastic moment M_pl,Rd = 0.25 × l_eff × t_p² × f_y / γ_M0 drives Mode 1 and Mode 2 resistance. A thicker plate raises M_pl,Rd → shifts governing mode from Mode 1 toward Mode 3 (bolt failure) → more ductile behaviour. As a rule of thumb, match t_ep to roughly 0.9–1.1 × t_f (beam flange thickness). For full-strength joints (M_j,Rd ≥ M_pl,b), the plate typically needs t_ep ≈ 1.5–2 × bolt diameter divided by a factor depending on m. This tool's default 20 mm plate is a good starting point for IPE 300–500 beams.
What do the national annexes change for NL / DE / BE?
The key difference is γ_M2 (partial factor for bolt resistance): EN default = 1.25; NL = 1.25; BE = 1.25; DE = 1.10 (less conservative for bolts). This means DE designs show ~13% higher bolt F_t,Rd per bolt for identical inputs, which can shift governing mode from Mode 3 to Mode 2. γ_M0 = 1.0 in all four annexes. For full comparison use the National Annex toggle on this page.