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1 C:\Users\joc\Documents\IT\Robot EC3 6 1 (5)\Eurocode (5) Concentrated Load - Rev 1_0.mcdx Page 1 of 01/03/016 Section sec HEB500 with steel grade gr S355 I x Iy_sec (sec) cm 4 = cm 4 A V Avz_sec (sec) cm = 89.8 cm h h_sec (sec) mm = 500 mm b b_sec (sec) mm = 300 mm t f tf_sec (sec) mm = 8 mm t w tw_sec (sec) mm = 14.5 mm r r_sec (sec) mm = 7 mm Safety factors according to Eurocode S-E 1993 γ M γ M γ M 1.5 Yield Stress f y fy_sec ( sec, gr) = 355, Design Stress f, mm mm d = 355 γ M0 mm f y E metal 10 k mm EC (5) Total Stress (as per eq 6.1) σ σ x, σ z, τ σ x + σ z σ x σ z + 3 τ Load spreading length ss 0 mm ROBOT k m, V Ed 0 k, 185 k y h t f = 0. m, σ x.ed y = 4.701, I x mm τ Ed 0 mm l t f + ss = 76 mm, width t w = 14.5 mm, σ z.ed = mm = 165.6, (eq 6.1) mm float, ACTUAL Point 1 - Bottom level of wing or begining of radius (going downwards) y h t f = 0. m, σ x.ed y = 4.701, as a simplification I x mm τ Ed 0 mm l t f + ss = 76 mm, width r+ t w = 68.5 mm, σ z.ed = mm = 33.4, (eq 6.1) mm float, Point Simplified - End of radius (going downwards) y h t f r = m, σ x.ed y = 4.19 I x mm (eq 6.1) τ Ed V Ed = 0, A,, (>0.6?) A V mm w h t f t w = 6438 mm A f b t f = 8400 mm A f = A w l t f + ss = 76 mm, width t w = 14.5 mm, σ z.ed = mm

2 C:\Users\joc\Documents\IT\Robot EC3 6 1 (5)\Eurocode (5) Concentrated Load - Rev 1_0.mcdx Page of 01/03/016 = 165.9, (eq 6.1) mm float, Point - End of radius (going downwards) y h t f r = m, σ x.ed y = 4.19 I x mm Static moment at point : S x b t f h t f + t w r h t f r + r 1 π h t f 0.3 r = cm 3 4 τ Ed V Ed S x = 0 I x t w mm l t f + ss = 76 mm, width t w = 14.5 mm, σ z.ed = mm = 165.9, (eq 6.1) mm float,

4 DETAILED AALYSIS according to Eurocode 3 (E :005) for member no. Beam_ SECTIO PARAMETERS: HEB 500 ht=500 mm bf=300 mm Ay=16800 mm Az=750 mm Ax=3860 mm tw=15 mm Iy= mm4 Iz= mm4 Ix= mm4 tf=8 mm Wely= mm3 Welz= mm3 TRASVERSE STIFFEERS Stiffener positions: Translation: a = 0.00 m; b = 0.00 m COCETRATED FORCES Force positions: 1.0; 3.0; 4.40; 5.95; 7.15; 9.15; Force 1 F1 = k ss1 = 0 mm Force F = k ss = 0 mm Force 3 F3 = k ss3 = 0 mm Force 4 F4 = k ss4 = 0 mm Force 5 F5 = k ss5 = 0 mm Force 6 F6 = k ss6 = 0 mm real coordinates real coordinates SHEAR BUCKLIG RESISTACE (EC3 art. 5) Lam_w - relative web slenderness [5..(5)] kt - local buckling coefficient for shear [A.3.(1)] Xw - Influence factor for shear resistance (web) [5.3.(1)] Xf - Influence factor for shear resistance (flange) [5.4.(1)] Xv - Instability factor for shear [5..(1)] Mf,Rd - Design resistance of section flanges [5.4.(1)]

5 VEd - Maximum shear force in a panel [5..(1)] Vb,Rd - Design shear buckling resistance [5..(1)] Panel A Panel coordinates A x = (0.00 ; 1.00) Point x = 7.4 m According to paragraph 5.1.(), it is not necessary to check resistance to local shear buckling. RESISTACE OF WEBS TO TRASVERSE FORCES (EC3 art.5.7) ss - Length of stiff bearing [Figure 6.] m1 - Reduction factor Leff [6.5.(1)] m - Reduction factor Leff [6.5.(1)] kf - Web buckling coefficient [Figure 6.1] Xf - Reduction factor Leff [6.4.(1)] Leff - Effective length of web [6..(1)] FRd - Web resistance for local buckling [6..(1)] Sigx.Ed - Local stresses due to moment and axial force [E &6..1.(5)] Sigz.Ed - Local stresses due to transversal load [E &6..1.(5)] Tau.Ed - Shear stress under a concentrated force [E &6..1.(5)] Web stability under force FEd,1 Point x = 1.0 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,1 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.13 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 0.5 < 1.0 Web stability under force FEd, Point x =.67 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd, = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.57 < 1.4 Web stability under force FEd,3 Point x = 3.0 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,3 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.)

6 = 0.6 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 0.97 < 1.0 Web stability under force FEd,4 Point x = 4.40 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,4 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.6 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 1.18 > 1.0 ICORRECT Web stability under force FEd,5 Point x = 5.95 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,5 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.6 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 1.18 > 1.0 ICORRECT Web stability under force FEd,6 Point x = 7.15 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,6 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.6 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 0.97 < 1.0 Web stability under force FEd,7 Point x = 7.67 m

7 ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,7 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.57 < 1.4 Web stability under force FEd,8 Point x = 9.15 m ss = 0 mm m1 = 0.69 m = 0.00 kf = 6.00 LamF = 0.47 Xf = 1.00 Leff = 331 mm Frd = k FEd,8 = k < FRd = k Interaction of transversal force, moment and axial force (EC3 section 7..(1)) Check condition: (7.) = 0.13 < 1.4 Web in plane stress (EC3 art (5)) Sigx,Ed = MPa Sigx,Ed = MPa Tau,Ed = 0.00 MPa Check condition: (E &6..1.(5)) (Sigx.Ed/(fy/g0))^ + (Sigz.Ed/(fy/g0))^ - (Sigx.Ed/(fy/g0))*(Sigz.Ed/(fy/g0)) + 3.0*(Tau,Ed/(fy/g0))^ = 0.5 < 1.0 ITERACTIO SHEAR/BEDIG/AXIAL FORCE (EC3 art. 7.1) My,Ed - Design bending moment Mz,Ed - Design bending moment Ed - Design axial force VEd - Design shear force Mf.Rd - Design plastic moment resistance of a section consisting of flanges [7.1.(1)] My,pl.Rd - Design beam resistance at bending [7.1.(1)] Vb.Rd - Design shear buckling resistance [5..(1)] Panel A Panel coordinates A x = (0.00 ; 1.00) Point x = 7.4 m According to [7.1.(1)] checking of TM interaction is not necessary (VEd/Vb,Rd < 0.5 ); STABILITY OF COMPRESSIVE FLAGE (EC3 art. 8.1) k - Factor depending on section class [8.(1)] Aw - Area of stiffener [8.(1)] Afc - Area of compressive flange [8.(1)] k = 0.30 Aw = 6438 mm Afc = 8400 mm Check condition: (8.1) D/tw = 30.6 < k(e/fyf)*[aw/afc]^0.5 = Analyzed beam does not meet the Eurocode 3 requirements

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