Probleemomschrijving
Een uitgebreide kopplaatverbinding verbindt HEA 300 (S355) ligger aan HEB 300 kolom (S355). Ontwerpmoment M_Ed = 220 kNm, schuif V_Ed = 85 kN. Kopplaat: 300×350×20mm S355. 8×M24 10.9 bouten, 4-rij configuratie.
Berekening Stappen — 4 stappen
§6.2.6.1
Boutrij op trek — T-stomp model
Afleiding
l_eff = 164 mm (for S355 20mm end plate)
m = (350 - tw_col)/2 - 0.8·a_weld = 146 mm
e = 40 mm, n = min(e, 1.25·m) = min(40, 183) = 40 mm
A_s = 353 mm², f_ub = 1000 N/mm²
F_t,Rd = (0.9·f_ub·A_s) / γ_M2 = (0.9×1000×353)/1.25/1000
Formule
F_{t,Rd} = \frac{0.9 f_{ub} A_s}{\gamma_{M2}}
Resultaat
254 kN per bolt
§6.2.4
Pryingkracht B — Mode 1/2
Afleiding
M_pl,Rd = (b·t²·f_y)/(4·γ_M0) = (300×20²×355)/(4×1.0)/10⁶
= 107 kNm
Mode 1: L_b = (330×353)/(2×353+2×330) = 82 mm
Mode 2: L_b = 82 mm
B_Mode1 = (8·M_pl,Rd - n·F_t,Rd)/(8·m + n) = (857-160)/(1168+40) = 0.57 kN → negligible
Mode 2 governs: F_T,Rd = B + F_t,Rd = 254.6 kN/bolt row
Formule
B = \frac{8 M_{pl,Rd} - n F_{t,Rd}}{8m + n}
Resultaat
254.6 kN per bolt row
§6.2.7
Verbindingsmomentweerstand M_j,Rd
Afleiding
z_eq = Σh_i·F_T,Rd / ΣF_T,Rd = (280+220+160+100)/4 = 190 mm
M_j,Rd = Σ(F_T,Rd · h_i) = 4 × 254.6 × 0.190
= 193.5 kNm
Utilization = 220 / 193.5
Formule
M_{j,Rd} = \sum F_{T,Rd} \cdot h_i
Resultaat
88% utilisation → FAIL — increase plate or bolt grade
§6.2.7
Herzien met M30 10.9 bouten
Afleiding
A_s(M30) = 561 mm², F_t,Rd = (0.9×1000×561)/1.25/1000 = 404 kN
F_T,Rd = 404.2 kN (prying negligible with 30mm bolts)
M_j,Rd = 4 × 404.2 × 0.190 = 307.2 kNm
Utilization = 220 / 307.2
Formule
M_{j,Rd} = \sum F_{T,Rd} \cdot h_i
Resultaat
72% utilisation → PASS