Aufgabenstellung
HEB 300 Stütze (S355) auf Betonfundament (C30/37, f_cd=20 N/mm²). Bemessungsdruck N_Ed = 450 kN. Ankerbolzen: 4×M24 einbetoniert. Fußplatte: 400×400×25mm S355.
Berechnungsschritte — 4 Schritte
§6.2.5.2
Betonpressung
Herleitung
c = √((b_p - b) / 2)² + ((h_p - h) / 2)² = √(50² + 50²) = 71 mm
A_b = (b + 2c)(h + 2c) = (300+142)(300+142) = 195364 mm²
σ_c,Ed = N_Ed / A_b = 450000 / 195364 = 2.30 N/mm²
f_cd = f_ck / γ_C = 30/1.5 = 20 N/mm²
σ_c,Ed / f_cd = 2.30 / 20
Formel
\sigma_{c,Ed} = \frac{N_{Ed}}{(b+2c)(h+2c)}
Ergebnis
12% utilisation → PASS on concrete bearing
§6.2.5.3
Ankerbolzzug
Herleitung
e = (b - b_c) / 2 = 0 (centrally loaded)
M_Ed,plate = N_Ed × e = 0 → zero moment case
B_t,Rd (base plate in tension) = 0 kN (pinned, no moment)
Anchor bolt shear capacity:
F_v,Rd = 0.6·f_ub·A_s/γ_M2 = 0.6×800×353/1.25/1000
= 169.4 kN per bolt
V_Ed = 45 kN (from frame analysis)
4 × 169.4 × 0.6 = 406 kN > 45 kN
Formel
F_{v,Rd} = \frac{0.6 f_{ub} A_s}{\gamma_{M2}}
Ergebnis
11% utilisation → PASS
§6.2.8
Stütze-Fußplatte Schweißverbindung
Herleitung
F_w,Rd = f_vw,d · a / √3
f_vw,d = f_u / (√3·β_w·γ_M2) = 430/(1.732×0.9×1.25) = 196 N/mm²
a = 6mm fillet weld (minimum for S355)
F_w,Rd per mm = 196×6/√3 = 679 N/mm
Total weld length = 2(b+h) = 2(300+300) = 1200 mm
V_Ed = 45 kN < F_w,Rd total = 679 × 1200 / 1000 = 815 kN
Formel
F_{w,Rd} = \frac{f_{vw,d} \cdot a \cdot L}{\sqrt{3}}
Ergebnis
5.5% utilisation → PASS
§6.2.5.1
Fußplattendicke für Biegung
Herleitung
c_eff = (b - b_c)/2 - 0.8·a_w = (400-300)/2 - 0.8×6 = 45 mm
M_Ed, cantilever = σ_c,Ed × c_eff² / 2 = 2.30 × 45² / 2 / 10⁶
= 2.33 kNm/m
W_required = M_Ed / f_y = 2.33×10⁶ / 355 / (25²/6)
= 15.8 mm < 25 mm → OK
W_provided = t²/6 = 25²/6 = 104 mm³/mm
M_Rd = W_provided × f_y / γ_M0 = 104×355/1.0/10⁶
Formel
t_{min} = \sqrt{\frac{6 M_{Ed}}{b f_y}}
Ergebnis
21.5 mm < 25 mm provided → PASS