Folder: _EC3 Bolted connections

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1 Folder: _EC3 Bolted connections Euro-Code 3 Bolted connections Bolted angilar connection: Dimensions of connection: Plate thickness d = 15,00 mm Bolt spacing e = 35,00 mm Spacing of bolts e o = 30,00 mm Spacing of bolts b = 70,00 mm Spacing of bolts h = 220,00 mm Angle of tension force β = 45,00 Bolts: Plate: Bolt = SEL("steel/bolt"; BS; ) = M 20 SC = SEL("steel/bolt"; SC; ) = 8.8 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 800,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 20,00 mm Shaft diameter d ll = d l +2 = 22,00 mm Cross-section areas A s = TAB("steel/bolt"; Asp; BS=Bolt) = 2,45 cm² steel = SEL("steel/EC"; Name; ) = Fe 510 f y = TAB("steel/EC"; fy; Name=steel) = 355,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 510,00 N/mm² γ M0 = 1,10 γ Mb = 1,25 Loads: S sd = 424,26 kn N sd = COS(β) * S sd = 300,00 kn V sd = SIN(β) * S sd = 300,00 kn Force per bolt: F t,sd = N sd / 4 = 75,00 kn F v,sd = V sd / 4 = 75,00 kn

2 Folder: _EC3 Bolted connections Limit tension force of bolts: F t,rd = 0,9 * f u,b * A s / γ Mb / 10 = 141,12 kn F t,sd / F t,rd = 0,53 < 1 Check limit shear force for bolts: F v,rd = 0,6 * f u,b * π * d l ² / 4000 / γ Mb = 120,64 kn F v,sd / F v,rd = 0,62 < 1 Check combined: F t,sd / (1,4 * F t,rd ) + F v,sd / F v,rd = 1,00 1 Analysis of bearing strength: as in : e o / d ll = 1,36 > 1 as in : e o / d ll = 1,36 < 1,5 as in (1): e / d ll = 1,59 > 1,2 as in (3): b / d ll = 3,18 > 3 α = MIN(e / (3 * d ll ); b / (3 * d ll ) - 0,25; f u,b / f u ; 1) = 0,53 Tab F b1,rd = 2,5 * α * f u * d l * d / γ Mb / 10³ = 162,18 kn (10) F b2,rd = 2/3 * F b1,rd = 108,12 kn F b,rd = F b2,rd + (F b1,rd - F b2,rd ) * (e o / d l - 1,2) / 0,3 = 162,18 kn F v,sd / F b,rd = 0,46 < 1

3 Folder: _EC3 Bolted connections Bolted connection subject to bending Dimensions of connection: a = 80,00 mm a 1 = 45,00 mm e = 80,00 mm e 1 = 45,00 mm e 2 = 50,00 mm e 3 = 90,00 mm d 1 = 20,00 mm d 2 = 8,00 mm b 1 = 160,00 mm h 2 = 2 * (e 2 + e 3 ) = 280,00 mm Flansch-Bolts: Bolt f = SEL("steel/bolt"; BS; ) = M 20 SC1 = SEL("steel/bolt"; SC; ) = 4.6 f u,bo = TAB("steel/bolt"; fubk; SC=SC1) = 400,00 N/mm² Hole diameter d lo = TAB("steel/bolt"; d; BS=Bolt f ) = 20,00 mm Shaft diameter d l1o = d lo + 2 = 22,00 mm Number of rows n o = 3 Steg-Bolts: Bolt S = SEL("steel/bolt"; BS; ) = M 16 SC2 = SEL("steel/bolt"; SC; ) = 4.6 f u,bs = TAB("steel/bolt"; fubk; SC=SC2) = 400,00 N/mm² Hole diameter d ls = TAB("steel/bolt"; d; BS=Bolt S ) = 16,00 mm Shaft diameter d l1s = d ls + 2 = 18,00 mm Number of rows n s = 3 Number of columns m s = 2 Profil: Profil Typ = SEL("steel/Profils"; Name; ) = IPE Selected Profil = SEL("steel/"Typ; Name; ) = IPE 240 Column height h = TAB("steel/"Typ; h; Name=Profil) = 240,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 6,20 mm Flange thickness t = TAB("steel/"Typ; t; Name=Profil) = 9,80 mm Cross-sectional area A = TAB("steel/"Typ; A; Name=Profil) = 39,10 cm² Moment of resistance W y = TAB("steel/"Typ; Wy; Name=Profil) = 324,00 cm² Moment of resistance W pl = 1,14 * W y = 369,36 cm³

4 Folder: _EC3 Bolted connections Material and Partial safety factors: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γ M0 = 1,10 γ M2 = 1,25 Loads: M sd = 157,95 knm V sd = 60,75 kn Check beam-web strength without holes: M c,rd = W pl * f y / γ M0 / 10 ³ = 78,91 knm M sd / M c,rd = 2,00 < 1 A v = 1,04 * h * s / 100 = 15,48 cm² V pl,rd = A v * f y / 10 / (3) / γ M0 = 190,93 kn V sd / V pl,rd = 0,32 < 1 Check beam-web strength with holes: A z = 0,5 * A = 19,55 cm² A z,net = A z - (2 * d l1o * t + ((n s - 1) / 2) * d l1s * s) / 100 = 14,12 cm² (f y / f u * γ M2 / γ M0 ) / (0,9 * A z,net / A z ) = 1,14 1 W pl,net = W pl - 2 * d l1o * t * (h - t) / 2000 = 319,73 cm³ M c,rd,c =W pl,net * f y / (γ M0 * 10³) = 68,31 knm M sd / M c,rd,c = 2,31 < 1 A v,net = A v - n s * d l1s * s / 100 = 12,13 cm² f y / f u * A v / A v,net = 0,83 < 1 Area of holes will be neglected. Analysis of bolts in flange: I w = 2 / 12 * d 2 * h 2 ³ / 10 4 = 2926,93 cm 4 I f = 2 * b 1 * d 1 * ((h + d 1 ) / 2)² / 10 4 = 10816,00 cm 4 M w = M sd * I w / (I w + I f ) = 33,64 knm M f = M sd * I f / (I w + I f ) = 124,31 knm Effective tension force in flange: N sd = M f / (h + d 1 ) * 10³ = 478,12 kn Limit shear force F v,rd =n o * 2 * 0,6 * f u,bo * π/4 * d lo ² / γ M2 / 10³ = 361,91 kn Limit bearing force: α = MIN(a 1 / (3 * d l1o ); a / (3 * d l1o ) - 0,25; f u,bo / f u ; 1) = 0,682 F b,rd =2 * n o * 2,5 * α * f u * d lo * t / γ M2 / 10³ = 577,46 kn N sd / MIN(F v,rd ; F b,rd ) = 1,32 < 1

5 Folder: _EC3 Bolted connections Analysis of bolts in web: n s1 = (n s - 1) / 2 + 0,49 = 1 n s2 = n s1 * 2 = 2 m s1 = (m s - 1) / 2 + 0,49 = 1 m s2 = m s1 * 2 = 2 I p = (n s * m s2 * ((m s -1) / 2*e)² + n s2 * m s * ((n s -1) / 2*e 3 )²)/10² = 420,00 cm² M sw = M w + V sd * e 3 / 10³ = 39,11 knm R sd = ((10*M sw *e 3 /I p )² + ((V sd /(m s *n s )) + 10*M sw *(m s -1)/2*e/I p )²) = 96,27 kn F v,rd = m s * 0,6 * f u,bs * π/4 * d ls ² / 10³ / γ M2 = 77,21 kn α = MIN(e 1 / (3 * d l1s ); e / (3 * d l1s ) - 0,25; f u,bo / f u ; 1) = 0,833 F b,rd = 2,5 * α * f u * d ls * s / γ M2 / 10³ = 59,50 kn R sd / MIN(F v,rd ; F b,rd ) = 1,62 < 1 Analysis of cover plates: A = d 1 * b 1 / 100 = 32,00 cm² A net = A - (2 * d l1o * d 1 ) / 100 = 23,20 cm² Limit tension force: N t,rd = MIN(A * f y / γ M0 ; 0,9 * A net * f u / γ M2 )/ 10 = 601,34 kn N sd / N t,rd = 0,80 < 1

6 Folder: _EC3 Bolted connections Connection subject to moment load: e e e e e e e e 1 1 Dimensions of connection: Bolt spacing e = 50,00 mm Edge distance e1 = 35,00 mm Bolt spacing e3 = 70,00 mm Plate thickness t = 6,00 mm Number of bolts n = 8 Bolts: Bolt1 = SEL("steel/bolt"; BS; ) = M 30 SC1 = SEL("steel/bolt"; SC; ) = 5.6 f u,b1 = TAB("steel/bolt"; fubk; SC=SC1) = 500,00 N/mm² Hole diameter d l1 = TAB("steel/bolt"; d; BS=Bolt1) = 30,00 mm Bolt2 = SEL("steel/bolt"; BS; ) = M 12 SC2 = SEL("steel/bolt"; SC; ) = 5.6 f u,b2 = TAB("steel/bolt"; fubk; SC=SC2) = 500,00 N/mm² Hole diameter d s2 = TAB("steel/bolt"; d; BS=Bolt2) = 12,00 mm Shaft diameter d l2 = d s2 +1 = 13,00 mm IPE330 aus steel = SEL("steel/EC"; Name; ) = Fe 360 f u2 = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γ Mb = 1,25 γ Mo = 1,25 Loads: V sd = 58,70 kn M sd = 910,00 kncm Analysis of the right bolt: Check limit shear force F v,rd = 0,6 * π / 4 * (d l1 / 10)² * f u,b1 / γ Mo / 10 = 169,65 kn V sd / F v,rd = 0,35 < 1 Limit bearing strength F b,rd = 1,5 * d l1 * t * f u2 / γ Mb / 10³ = 77,76 kn V sd / F b,rd = 0,75 < 1

7 Folder: _EC3 Bolted connections Check bolts on left: I p = (6 * e² + 6 * e 3 ²) / 100 = 444,00 cm² Maximum horizontal force in bolt due to moment: F h = M sd * e 3 / 10 / I p = 14,35 kn Maximum vertical force: F v = M sd * e / 10 / I p + V sd / n = 17,59 kn Resulting force R r = (F h ² + F v ²) = 22,70 kn F v,rd = 0,6 * f u,b2 * d l2 ² * π / 4 / γ Mb / 10³ = 31,86 kn R r / F v,rd = 0,71 < 1 Analysis of bearing strength α = MIN(e 1 / (3 * d l2 ); 2 * e / (3 * d l2 ) - 0,25; f u,b2 / f u2 ; 1) = 0,90 F b,rd = 2,5 * α * f u2 * d l2 * t / γ Mb / 10³ = 50,54 kn F h / F b,rd = 0,28 < 1

8 Folder: _EC3 Bolted connections Bolted shear joint: Dimensions of connection: Spacing of bolts a = 45,00 mm Spacing of bolts a 0 = 35,00 mm Spacing of bolts a 1 = 30,00 mm Spacing of bolts a 2 = 50,00 mm Spacing of bolts a 3 = 90,00 mm Depth of cope a 4 = 30,00 mm Plate projection a s = 20,00 mm Lever-arm x = 45,00 mm Number of bolts n = 3 Bolts: M Bolt = SEL("steel/bolt"; BS; ) = M 16 SC = SEL("steel/bolt"; SC; ) = 4.6 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 400,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 16,00 mm Shaft diameter d 0 = d l +2 = 18,00 mm Angle section P = SEL("steel/WG"; Name; ) = L 80x8 Angle thickness t = TAB("steel/WG"; s; Name=P) = 8,00 mm Factor for group bolts as in (3): k = 0,5 for 1 group bolts; =2,5 for 2 rows steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² Profil Typ = SEL("steel/Profils"; Name; ) = IPE Selected Profil = SEL("steel/"Typ; Name; ) = IPE 270 Column height h = TAB("steel/"Typ; h; Name=Profil) = 270,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 6,60 mm γ Mb = 1,25 γ M2 = 1,25 γ M0 = 1,10 Loads: V sd = 60,00 kn

9 Folder: _EC3 Bolted connections Check bolt spacing as in 6.5.1: 1,2 * d 0 / a 1 = 0,72 < 1 a 1 / MAX(12 * t; 150) = 0,20 < 1 1,5 * d 0 / a 0 = 0,77 < 1 a 0 / MAX(12 * t; 150) = 0,23 < 1 2,2 * d 0 / a 2 = 0,79 < 1 a 2 / MIN(12 * s; 200) = 0,63 < 1 Check bolts strength: Bolts in web of main beam F v,sd = V sd / (2 * n) = 10,00 kn Bolts in web of connecting beam M sd = x / 10 * V sd = 270,00 kncm Horizontal force due to M sd F h,sd = M sd / ((n - 1) * a 2 / 10) = 27,00 kn Distributed shearing force on bolts F v,sd = V sd / n = 20,00 kn Maximum bolt strength F sd = (F h,sd ² + F v,sd ²) = 33,60 kn Limit strength and analysis of bolts: Bolts in web of main beam: Plain...in the shear plane F v,rd = 0,6 * f u,b * π * d l ² / 4 / γ Mb / 10³ = 38,60 kn Limit bearing strength α = MIN(a 1 / (3 * d 0 ); a 2 / (3 * d 0 ) - 0,25; f u,b / f u ; 1) = 0,556 F b,rd = 2,5 * α * f u * d l * t / γ Mb / 10³ = 51,24 kn Analysis: F sd / F b,rd = 0,66 < 1 Bolts in web of connecting beam: F v,rd = 2 * 0,6 * f u,b * π * d l ² / 4 / γ Mb / 10³ = 77,21 kn Limit bearing strength α = MIN(a 1 / (3 * d 0 ); a 2 / (3 * d 0 ) - 0,25; f u,b / f u ; 1) = 0,556 F b,rd = 2,5 * α * f u * d l * s / γ Mb / 10³ = 42,27 kn Analysis: F sd / F b,rd = 0,79 < 1 Check angle section strength Design loads: V sdw = V sd / 2 = 30,00 kn M sdw = M sd / 2 = 135,00 knm A = (2 * a * a 1 ) * t / 200 = 6,40 cm² A net = (2 * a * a 1 - n * d 0 ) * t / 200 = 4,24 cm² (f y / f u * γ M2 / γ M0 ) / (0,9 * A net / A) = 1,24 > 1 Subtract bottom bolt holes. A = A * 2 = 12,80 cm² A net = A net * 2 = 8,48 cm² f y / f u * A / A net = 0,99 < 1 Bolt holes should not be subtracted W pl = (t * (2 * a * a 1 )² / 4 - d 0 * t * a 2 ) / 1000 = 44,00 cm³ M pl,rd = W pl * f y / 10 / γ M0 = 940,00 kncm M sd / M pl,rd = 0,29 < 1 V pl,rd = A * f y / 10 / ( (3) * γ M0 ) = 157,88 kn V sd / V pl,rd = 0,38 < 1 Also: V sd / (V pl,rd / 2) = 0,76 < 1 No interaction.

10 Folder: _EC3 Bolted connections Check shear failure: L v = (n - 1) * a 2 = 100,00 mm L 1 = a 2 = 50,00 mm L 1 / (5 * d 0 ) = 0,56 < 1 L 2 = (a - k * d 0 ) * f u / f y = 55,15 mm L 3 = L v + a 2 + a 3 = 240,00 mm L v,eff = L v + L 1 + L 2 = 205,15 mm L v,eff / L 3 = 0,85 < 1 L 3 / ((L v + a 2 + a 3 - n * d 0 ) * f u / f y ) = 0,84 < 1 Effective shear area: A v,eff = L v,eff * t / 100 = 16,41 cm² V eff,rd = A v,eff * f y / 10 / (3) / γ M0 = 202,41 kn V sd / V eff,rd = 0,30 < 1

11 Folder: _EC3 Bolted connections Double shear joint with bolts: Dimensions of connection: Plate thickness d 1 = 6,00 mm Number of plates n 1 = 2 Plate thickness d 2 = 7,10 mm Number of plates n 2 = 1 Plate width b = 210,00 mm Bolt spacing e = 40,00 mm Edge distance e1 = 60,00 mm Edge distance e2 = 40,00 mm Bolt spacing e3 = 65,00 mm Bolts: Plate : Loads: Bolt = SEL("steel/bolt"; BS; ) = M 20 SC = SEL("steel/bolt"; SC; ) = 10.9 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 1000,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 20,00 mm Cross-section areas A s = TAB("steel/bolt"; Asp; BS=Bolt) = 2,45 cm² Number of bolts n= 5 steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γ M0 = 1,10 γ M2 = 1,25 N sd = 100,00 kn Joint with tension and shear: Limit tension force of plate links A = b * d 1 * n 1 / 100 = 25,20 cm² d = d l + 2 = 22,00 mm Cross-section area 1: A net,1 = A - 2 * d * d 1 * n 1 / 100 = 19,92 cm²

12 Folder: _EC3 Bolted connections Cross-section area 2: A net,2 = A-3 *d *d 1 *n 1 /10² + 2 * e² / (4*e 3 ) * d 1 * n 1 / 10² = 18,76 cm² A net = MIN(A net,1 ; A net,2 ) = 18,76 cm² N t,rd1 =MIN(A * f y / γ M0 ; 0,9 * A net * f u / γ M2 )/10 = 486,26 kn Limit tension force of plate rechts A = b * d 2 * n 2 / 100 = 14,91 cm² d = d l + 2 = 22,00 mm A net,1 = A - 2 * d * d 2 * n 2 / 100 = 11,79 cm² A net,2 = A - 3 * d * d 2 * n 2 / 10² + 2 * e² / (4*e 3 ) * d 2 * n 2 / 10² = 11,10 cm² A net = MIN(A net,1 ; A net,2 ) = 11,10 cm² N t,rd2 =MIN(A * f y / γ M0 ; 0,9 * A net * f u / γ M2 )/10 = 287,71 kn N t,rd = MIN(N t,rd2 ; N t,rd1 ) = 287,71 kn Limit tension force of boltsn: A s = π * (d l /10)² / 4 = 3,14 cm² Thread in the shearing plane: F v,rd = 0,6 * n * (n 1 + n 2-1) * f u,b / 10* A s / γ M2 = 1507,20 kn Limit bearing strength α = MIN(e 1 / (3 * d); 2 * e / (3 * d) - 0,25; f u,b / f u ; 1) = 0,91 F b,rd1 =n 1 * n * 2,5 * α * f u * d l * d 1 / γ M2 / 10³ = 786,24 kn α = MIN(e 1 / (3 * d); 2 * e / (3 * d) - 0,25; f u,b / f u ; 1) = 0,91 F b,rd2 =n 2 * n * 2,5 * α * f u * d l * d 2 / γ M2 / 10³ = 465,19 kn F b,rd = MIN(F b,rd1 ; F b,rd2 ) = 465,19 kn Maximum allowed force: N l,rd = MIN(N t,rd ; F v,rd ; F b,rd ) = 287,71 kn Analysis: N sd / N l,rd = 0,35 < 1

13 Folder: _EC3 Bolted connections High strength friction-grip bolt connection: Dimensions of connection: Plate thickness 1 d 1 = 10,00 mm Plate thickness 2 d 2 = 8,00 mm Bolt spacing e = 65,00 mm Edge distance e1 = 55,00 mm Edge distance e2 = 50,00 mm Bolt spacing e3 = 70,00 mm Plate width b= 240,00 mm Bolts: Bolt = SEL("steel/bolt"; BS; ) = M 22 SC = SEL("steel/bolt"; SC; ) = 10.9 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 1000,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 22,00 mm Cross-section areas A s = TAB("steel/bolt"; Asp; BS=Bolt) = 3,03 cm² Number of bolts n= 5 Löcher mit normalem Lochspiel as in (2) K s = 1,00 Anzahl der Gleitfugen as in (1) η = 1,00 Reibungszahl as in µ = 0,40 as in (3) γ Ms = 1,25 Plate: Loads: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γ M0 = 1,10 γ M2 = 1,25 Tension force N sd = 100,00 kn Limit tension force of plate: A = b * MIN(d 1 ; d 2 ) / 100 = 19,20 cm² as in d = d l + 2 = 24,00 mm Cross-section area 1: A net,1 = A - 2 * d * MIN(d 1 ; d 2 ) / 10² = 15,36 cm² Cross-section area 2: A net,2 = A - 3 * d * MIN(d 1 ; d 2 )/10² + 2 * e² / (4*e 3 ) * MIN(d 1 ; d 2 )/10² = 15,85 cm² A net = MIN(A net,1 ; A net,2 ) = 15,36 cm²

14 Folder: _EC3 Bolted connections Friction-grip connection: Plate N net,rd = A net * f y / 10 / γ M0 = 328,15 kn Limit tension force of bolts Limit shank tension F p,cd = 0,7 * f u,b / 10 * A s = 212,10 kn Limit slip resistance force F s,rd = n * K s * η * µ * F p,cd / γ Ms =339,36 kn Limit bearing force: α = MIN(e 1 / (3 * d); 2 * e /(3 * d) - 0,25; f u,b / f u ; 1) = 0,76 F b,rd = n * 2,5 * α * f u / 10 * d l *MIN(d 1 ; d 2 ) / γ M2 / 100 = 481,54 kn Maximum allowed force: N g,rd = MIN(N net,rd ; F b,rd ; F s,rd ) = 328,15 kn Analysis: N sd / N g,rd = 0,30 < 1

15 Folder: _EC3 Bolted connections Joint with tension and shear: Dimensions of connection: Plate thickness d 1 = 10,00 mm Plate thickness d 2 = 8,00 mm Bolt spacing e = 65,00 mm Edge distance e1 = 55,00 mm Edge distance e2 = 50,00 mm Bolt spacing e3 = 70,00 mm Plate width b = 240,00 mm Bolts: Plate: Loads: Bolt = SEL("steel/bolt"; BS; ) = M 22 SC = SEL("steel/bolt"; SC; ) = 4.6 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 400,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 22,00 mm Cross-section areas A s = TAB("steel/bolt"; Asp; BS=Bolt) = 3,03 cm² Number of bolts n = 5 steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γ M0 = 1,10 γ M2 = 1,25 N sd = 100,00 kn Joint with tension and shear: Limit tension force of plate: A = b * MIN(d 1 ; d 2 ) / 100 = 19,20 cm² d = d l + 2 = 24,00 mm Cross-section area 1: A net,1 = A - 2 * d * MIN(d 1 ; d 2 ) / 100 = 15,36 cm² Cross-section area 2: A net,2 = A-3*d*MIN(d 1 ;d 2 )/10² + 2*e²/(4*e 3 )*MIN(d 1 ;d 2 )/10² = 15,85 cm² A net = MIN(A net,1 ; A net,2 ) = 15,36 cm² N t,rd = MIN(A * f y / γ M0 ; 0,9 * A net * f u / γ M2 )/ 10 = 398,13 kn

16 Folder: _EC3 Bolted connections Limit tension force of boltsn: A s = π * (d / 10)² / 4 = 4,52 cm² Thread in the shearing plane: F v,rd = 0,6 * n * f u,b / 10 * A s / γ M2 = 433,92 kn/cm² Limit bearing strength α = MIN(e 1 / (3 * d); 2 * e / (3 * d) - 0,25;f u,b / f u ; 1) = 0,76 F b,rd = n * 2,5 * α * f u * d * MIN(d 1 ; d 2 ) / γ M2 / 10³ = 525,31 kn Maximum allowed force: N l,rd = MIN(N t,rd ; F v,rd ; F b,rd ) = 398,13 kn Analysis: N sd / N l,rd = 0,25 < 1

17 Folder: _EC3 Bolted connections Check shear failure: Dimensions of connection: Spacing of bolts a = 50,00 mm Spacing of bolts a 1 = 43,00 mm Spacing of bolts a 2 = 70,00 mm Spacing of bolts a 3 = 75,00 mm Number of bolts n = 4 Bolts: Bolt = SEL("steel/bolt"; BS; ) = M 20 SC = SEL("steel/bolt"; SC; ) = 5.6 f u,b = TAB("steel/bolt"; fubk; SC=SC) = 500,00 N/mm² Hole diameter d l = TAB("steel/bolt"; d; BS=Bolt) = 20,00 mm Shaft diameter d l2 = d l +2 = 22,00 mm k = 0,5 for 1 group bolts; =2,5 for 2 rows steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² f u = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² Profil Typ = SEL("steel/Profils"; Name; ) = IPE Selected Profil = SEL("steel/"Typ; Name; ) = IPE 360 Column height h = TAB("steel/"Typ; h; Name=Profil) = 360,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 8,00 mm γ Mb = 1,25 γ M0 = 1,10 Loads: V sd = 58,70 kn Limit shear force of section: A v = 1,04 * h * s / 100 = 29,95 cm² V pl,rdp = A v * f y / 10 / (3) / γ M0 = 369,41 kn A v,net = A v - (n * s * d l2 ) / 100 = 22,91 f y / f u * A v / A v,net = 0,85 < 1 Holes can be neglected.

18 Folder: _EC3 Bolted connections Joint with shear failure as in Bild 6.5.5: L v = (n - 1) * a 2 = 210,00 mm L 1 = a 1 = 43,00 mm L 1 / (5 * d l2 ) = 0,39 < 1 L 2 = (a - k * d l2 ) * f u / f y = 59,74 mm L 3 = L v + a 1 + a 3 = 328,00 mm L v,eff = L v + L 1 + L 2 = 312,74 mm L v,eff / L 3 = 0,95 < 1 L 3 / (L v + a 1 + a 3 - n + d l2 ) = 0,95 < 1 Effective shear area: A v,eff = L v,eff * s / 100 = 25,02 cm² V pl,rd = A v,eff * f y / 10 / (3) / γ M0 = 308,60 kn Maximum design force for shear: V Rd = MIN(V pl,rdp ; V pl,rd ) = 308,60 kn

19 Folder: _EC3 Columns Columns Column of section class 4: F h A t1 b t 2 B h F C D Load diagram: Column height H = 6,50 m Beam width b = 50,00 cm Column height h = 100,00 cm Web thickness t 1 = 1,00 cm Flange thickness t 2 = 1,00 cm Loads: N d = 3500,00 kn Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 1,00 Partial safety factors: γ M = 1,10 γ g = 1,35 Section classification: As in Table b' = b - 2 * t 1 = 48,00 cm b' / t 2 / (42 * ε) = 1,14 > 1 Section class 4 h' = h - 2 * t 2 = 98,00 cm h' / t 1 / (42 * ε) = 2,33 > 1 Section class 4

20 Folder: _EC3 Columns Effective web area: Part A-B; C-D As in Table 5.3.2: ψ = 1,00 k σ = 4,00 as in 5.3.5(3) λ trans,p =b' / t 2 / (28,4 * ε * (k σ )) = 0,85 >0,673 ρ = (λ trans,p - 0,22) / λ trans,p ² = 0,872 b eff = ρ * b' = 41,86 cm Part A-C; B-D As in Table 5.3.2: ψ = 1,00 cm k σ = 4,00 as in 5.3.5(3) λ trans,p =h' / t 1 / (28,4 * ε * (k σ )) = 1,73 >0,673 ρ = (λ trans,p - 0,22) / λ trans,p ² = 0,505 h eff = ρ * h' = 49,49 cm Check buckling: A eff = 2 * (h eff * t 1 + b eff * t 2 ) + 4 * t 1 * t 2 = 186,70 cm² A = b * h - (b - 2 * t 1 ) * (h - 2 * t 2 ) = 296,00 cm² β A = A eff / A = 0,631 I b = (b * h³ - (b - 2 * t 1 ) * (h - 2 * t 2 )³) / 12 = ,67 cm 4 I h = (b³ * h - (b - 2 * t 1 )³ * (h - 2 * t 2 )) / 12 = ,67 cm 4 I = MIN(I b ; I h ) = ,67 cm 4 N cr = π² * E/10 * I / (H * 100)² = 67941,82 kn λ trans = (β A * A * f y /10 / N cr ) = 0,25 Apply strut curve b α = 0,34 ϕ = 0,5 * (1 + α * (λ trans - 0,2) + λ trans ²) = 0,540 χ = 1 / (ϕ + (ϕ² - λ trans ²) 0,5 ) = 0,9817 N b,rd = χ * β A * A * f y / 10 / γ M = 3917,19 kn N d / N b,rd = 0,893 < 1

21 Folder: _EC3 Columns Column subject to compression force: Nd H Column heigth H = 7,50 m l y = H/2 = 3,75 m l z = H/3 = 2,50 m Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 430 f y = TAB("steel/EC"; fy; Name=steel) = 275,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 0,92 Profil: Profil Typ = SEL("steel/Profils"; Name; ) = IPE Selected Profil = SEL("steel/"Typ; Name; ) = IPE 300 Cross-sectional area A = TAB("steel/"Typ; A; Name=Profil) = 53,80 cm² Column height h = TAB("steel/"Typ; h; Name=Profil) = 300,00 mm Depth of web h 1 = TAB("steel/"Typ; h1; Name=Profil) = 248,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 7,10 mm Flange width b = TAB("steel/"Typ; b; Name=Profil) = 150,00 mm Flange thickness t = TAB("steel/"Typ; t; Name=Profil) = 10,70 mm Radius of gyration i y = TAB("steel/"Typ; iy; Name=Profil) = 12,50 cm Radius of gyration i z = TAB("steel/"Typ; iz; Name=Profil) = 3,35 cm Section classification As in Table 5.3.1: Web: ( h 1 / s ) / ( 33 * ε ) = 1,15 < 1 ( h 1 / s ) / ( 38 * ε ) = 1,00 < 1 Section class 2. Flange: ( b / 2 / t ) / ( 10 * ε ) = 0,76 < 1 Section class 1. Section will be classified as class 2.

22 Folder: _EC3 Columns Analysis: nach (1) β A = 1,00 Cross-section class 2 nach (2) γ M1 = 1,10 Cross-section class 2 Check buckling In Y-Y Axis: h / b = 2,00 > 1,2 t /10 = 1,07 cm < 4 cm as in Tab : λ y = l y * 100 / i y = 30,00 λ 1 = 93,9 * ε = 86,39 λ trans,y = λ y / λ 1 * (β A ) = 0,347 Apply strut curve a As in Table α = 0,21 ϕ = 0,5 * (1 + α * (λ trans,y - 0,2) + λ trans,y ²) = 0,576 χ = 1 / (ϕ + (ϕ² - λ trans,y ²) 0,5 ) = 0,9655 N b,y,rd = χ * β A * A * f y /10/ γ M1 = 1298,60 kn Check buckling In Z-Z Axis: h / b = 2,00 > 1,2 t / 10 = 1,07 cm < 4cm as in Tab : λ z = l z * 100 / i z = 74,63 λ trans,z = λ z / λ 1 * (β A ) = 0,864 Apply strut curve b As in Table α = 0,34 ϕ = 0,5 * (1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 0,986 χ = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,6844 N b,z,rd = χ * β A * A * f y /10/ γ M1 = 920,52 kn max_n d = MIN(N b,y,rd ; N b,z,rd ) = 920,52 kn

23 Folder: _EC3 Columns Column of section class 4: b F t 2 h y h t 1 F Load diagram: Column heigth H = 4,00 kn Flange width b = 20,00 cm Depth of web h = 30,00 cm Web thickness t 1 = 1,20 cm Flange thickness t 2 = 1,20 cm z Loads: N d = 700,00 kn Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 1,00 λ 1 = 93,90 * ε = 93,90 Partial safety factors: γ M = 1,10 Section classification As in Table 5.3.1: b / t 2 / (14 * ε) = 1,19 > 1 Section class 4 h / t 1 / (33 * ε) = 0,76 > 1 Section class 1

24 Folder: _EC3 Columns Effective web area: Flangee: As in Table 5.3.3: ψ = 1,00 k σ = 0,43 as in 5.3.5(3) λ trans,p = b / t 2 / (28,4 * ε * (k σ )) = 0,89 >0,673 ρ = (λ trans,p - 0,22) / λ trans,p ² = 0,846 b eff = ρ * b = 16,92 cm A eff = 2 * (b eff * t 2 ) + (h + 2 * t 2 ) * t 1 = 79,49 cm² Location of shear centre: y s,eff = (b eff * (2 * t 2 ) * (b eff + t 2 ) / 2) / A eff = 4,628 cm b eff ³ / 12 * (2 * t 2 ) + b eff * (2 * t 2 ) * ((b eff + t 1 ) / 2 - y s,eff )² = 1766,44 cm 4 (h + 2 * t 2 ) * t 1 ³ / 12 + (h + 2 * t 2 ) * t 1 * y s,eff ² = 837,41 cm 4 Iz,eff= 2603,85 cm 4 W z,eff = I z,eff / ((b eff + t 1 ) - y s,eff - (t 1 / 2)) = 201,97 cm³ Gross area: A = b * 2 * t 2 + (h + 2 * t 2 ) * t 1 = 86,88 cm² Location of center of gravity: y s = (b * 2 * t 2 * (b + t 1 ) / 2) / A = 5,856 cm I z = b³/12*2*t 2 +b*2*t 2 *((b+t 1 )/2-y s )²+(h+2*t 2 )*t 1 ³/12+(h+2*t 2 )*t 1 *y s ² = 4018,23 cm 4 e Nz = y s - y s,eff = 1,228 cm Check buckling: N cr = π² * E/10 * I z / (H * 100)² = 5205,15 kn β A = A eff / A = 0,915 λ trans,z = (β A * A * f y /10 / N cr ) = 0,60 Apply strut curve c As in Table α = 0,49 ϕ = 0,5 * (1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 0,778 χ = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,7854 M z = N d * e Nz / 100 = 8,60 knm ψ = 1,00 β Mψ = 1,8-0,7 * ψ = 1,10 µ z = λ trans,z * (2 * β Mψ - 4) = -1,080 < 0,9 k z1 = 1 - (µ z * N d ) / (χ * A eff * f y /10) = 1,515 ~ 1,5 k z2 = 1,500 k z = MIN(k z1 ; k z2 ) = 1,500 N d / (χ * A eff * f y /10 / γ M ) * k z *M z / (W z,eff * f y /10 / γ M ) = 0,824 < 1

25 Folder: _EC3 Columns Column with compression and moment: Nsd Msd H Load diagram: Column heigth H = 5,00 m Loads: N sd = 200,00 kn M y,sd = 10,00 kn Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² G = TAB("steel/EC"; G; Name=steel) = 81000,00 N/mm² ε = (235 / f y ) = 1,00 Partial safety factors: γ M = 1,10 γ g = 1,35 platischer Formbeiwert α ply = 1,14 platischer Formbeiwert α plz = 1,25 Profil: Profil Typ = SEL("steel/Profils"; Name; ) = HEA Selected Profil = SEL("steel/"Typ; Name; ) = HEA 160 Cross-sectional area A = TAB("steel/"Typ; A; Name=Profil) = 38,80 cm² Column height h = TAB("steel/"Typ; h; Name=Profil) = 152,00 mm Depth of web h 1 = TAB("steel/"Typ; h1; Name=Profil) = 104,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 6,00 mm Flange width b = TAB("steel/"Typ; b; Name=Profil) = 160,00 mm Flange thickness t = TAB("steel/"Typ; t; Name=Profil) = 9,00 mm Radius of gyration i y = TAB("steel/"Typ; iy; Name=Profil) = 6,57 cm Radius of gyration i z = TAB("steel/"Typ; iz; Name=Profil) = 3,98 cm W ely = TAB("steel/"Typ; Wy; Name=Profil) = 220,00 cm³ W ply = α ply * W ely = 250,80 cm³ W elz = TAB("steel/"Typ; Wz; Name=Profil) = 76,90 cm³ W plz = α plz * W elz = 96,13 cm³ Section classification As in Table5.3.1: Web will be assumed as pressed in ( h 1 / s ) / ( 33 * ε ) = 0,53 < 1 Section class 1. Flange: ( b / 2 / t ) / ( 10 * ε ) = 0,89 < 1 Section class 1.

26 Folder: _EC3 Columns Check bending and buckling: as in (1) β A = 1,00 Cross-section class 1 as in (2) γ M1 = 1,10 Cross-section class 1 λ y = H * 100 / i y = 76,10 λ 1 = 93,9 * ε = 93,90 λ trans,y = λ y / λ 1 * (β A ) = 0,810 λ z = 100 * H / i z = 125,63 λ trans,z = λ z / (π * (E / f y )) = 1,34 As in Table h / b = 0,95 < 1,2 t / 10 = 0,90 cm < 10cm As in Table:5.5.1 Strut curve b for Y-Y axis α = 0,34 ϕ = 0,5 * (1 + α * (λ trans,y - 0,2) + λ trans,y ²) = 0,932 χ y = 1 / (ϕ + (ϕ² - λ trans,y ²) 0,5 ) = 0,7179 Apply strut curve c for z-achse α = 0,49 ϕ = 0,5 * (1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 1,677 χ z = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,3724 ψ = 0,00 β My = 1,8-0,7 * ψ = 1,80 µ y = λ trans,y * (2 * β My - 4) + (W ply - W ely ) / W ely = -0,184 < 0,9 k y = 1 - (µ y * N sd ) / (χ y * A * f y ) = 1,006 < 1,5 χ = MIN(χ y ; χ z ) = 0,372 N sd / (χ * A * f y / 10 / γ M ) * k y * M y,sd / (W ply * f y / 10 / γ M ) = 0,836 < 1 Check torsional-flexural buckling: β w = 1,00 Cross-section class 1 As in Table: F.1.1 ψ = 0,00 k = 1,00 C 1 = 1,879 λ LT = 90 * H / i z / ((C 1 ) 0,5 * (1 + 1 / 20 * ((100 * H / i z ) / (h / t))²) 0,25 ) = 59,208 λ trans,lt = λ LT / λ 1 * (β w ) = 0,631 For rolled sections strut curve a α = 0,21 ϕ = 0,5 * (1 + α * (λ trans,lt - 0,2) + λ trans,lt ²) = 0,74 χ LT = 1 / (ϕ + (ϕ² - λ trans,lt ²) 0,5 ) = 0,89 β M,LT = 1,8-0,7 * ψ = 1,80 λ trans,z = λ z / λ 1 * (β A ) = 1,338 µ LT = 0,15 * λ trans,z * β M,LT - 0,15 = 0,211 < 0,9 h / b = 0,95 < 1,2 t / 10 = 0,90 cm < 10cm Z-Z axis Strut curve c α = 0,49 ϕ = 0,5 * (1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 1,674 χ z = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,3731 k LT = 1 - (µ LT * N sd ) / (χ z * A * f y ) = 0,988 < 1,0 N sd / (χ z * A * f y / 10 / γ M ) * k LT * M y,sd / (χ LT *W ply * f y / 10 / γ M )= 0,854 < 1

27 Folder: _EC3 Columns Column subject to compression force: Nd H Column base is pinned. For buckling, column head is pinned about the Y-Y axis, and fixed about the Z-Z axis. Load diagram: Column heigth H = 8,00 m Loads: N d = 2000,00 kn Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 1,00 Effective length factor: k y = 1,00 For simply supported ends k z = 0,70 fixed ends Profil: Profil Typ = SEL("steel/Profils"; Name; ) = HEB Selected Profil = SEL("steel/"Typ; Name; ) = HEB 300 Cross-sectional area A = TAB("steel/"Typ; A; Name=Profil) = 149,00 cm² Column height h = TAB("steel/"Typ; h; Name=Profil) = 300,00 mm Depth of web h 1 = TAB("steel/"Typ; h1; Name=Profil) = 208,00 mm Web thickness s = TAB("steel/"Typ; s; Name=Profil) = 11,00 mm Flange width b = TAB("steel/"Typ; b; Name=Profil) = 300,00 mm Flange thickness t = TAB("steel/"Typ; t; Name=Profil) = 19,00 mm Moment of inertia I = TAB("steel/"Typ; Iy; Name=Profil) = 25170,00 cm 4 Radius of gyration i y = TAB("steel/"Typ; iy; Name=Profil) = 13,00 cm Radius of gyration i z = TAB("steel/"Typ; iz; Name=Profil) = 7,58 cm Section classification: Web: ( h 1 / s ) / ( 33 * ε ) = 0,57 < 1 Flange: ( b / 2 / t ) / ( 10 * ε ) = 0,79 < 1 Section class 1.

28 Folder: _EC3 Columns Analysis: β A = 1,00 Cross-section class 1 γ M1 = 1,10 Cross-section class 1 Check buckling In Y-Y Axis: h / b = 1,00 < 1,2 t / 10 = 1,90 cm < 10cm λ y = k y * H * 100 / i y = 61,54 λ 1 = 93,9 * ε = 93,90 λ trans,y = λ y / λ 1 * (β A ) = 0,655 Apply strut curve b As in Table α = 0,34 ϕ = 0,5 * (1 + α * (λ trans,y - 0,2) + λ trans,y ²) = 0,792 χ = 1 / (ϕ + (ϕ² - λ trans,y ²) 0,5 ) = 0,8083 N b,rd = χ * β A * A * f y / 10 / γ M1 = 2572,97 kn N d / N b,rd = 0,78 < 1 Check buckling In Z-Z Axis: h / b = 1,00 < 1,2 t / 10 = 1,90 cm < 10cm λ z = k z * H * 100 / i z = 73,88 m λ trans,z = λ z / λ 1 * (β A ) = 0,787 Apply strut curve c As in Table α = 0,49 ϕ = 0,5 * (1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 0,953 χ = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,6709 N b,rd = χ * β A * A * f y / 10 / γ M1 = 2135,60 kn N d /N b,rd = 0,94 < 1

29 Folder: _EC3 Columns Column of channel section with compression and transverse loads: q d Pd b t 2 H t 1 y h z Load diagram: Column height H = 4,00 m Beam width b = 9,50 cm Depth of web h = 29,40 cm Web thickness t 1 = 1,00 cm Flange width t 2 = 0,60 cm Loads: q d = 15,00 kn/m N d = 90,00 kn Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 1,00 λ 1 = 93,90 * ε = 93,90 Partial safety factors: γ M = 1,10 Section classification: As in Table b / t 2 / (14 * ε) = 1,13 > 1 Section class 4 As in Table h / t 1 / (33 * ε) = 0,89 > 1 Section class 1 A = b * 2 * t 2 + (h + 2 * t 2 ) * t 1 = 42,00 cm² Location of center of gravity: y s = (b * 2 * t 2 * (b + t 1 ) / 2) / A = 1,425 cm b³ / 12 * 2 * t 2 + b * 2 * t 2 * ((b + t 1 ) / 2 - y s )² = 252,53 cm 4 (h + 2 * t 2 ) * t 1 ³ / 12 + (h + 2 * t 2 ) * t 1 * y s ² = 64,69 cm 4 Iz= 317,22 cm 4 I y = h³ / 12 * t * (b * t 2 ³ / 12 + b * t 2 * ((h + t 2 ) / 2)²) = 4683,02 cm 4 W el,z = I z / (b + t 1 / 2 - y s ) = 36,99 cm³ W el,y = I y / ((h + t 1 ) / 2) = 308,09 cm³

30 Folder: _EC3 Columns Effective web area: Flangee: As in Table 5.3.3: ψ = 1,00 k σ = 0,43 as in 5.3.5(3) λ trans,p = b / t 2 / (28,4 * ε * (k σ )) = 0,85 >0,673 ρ = (λ trans,p - 0,22) / λ trans,p ² = 0,872 b eff = ρ * b = 8,28 cm A eff = 2 * (b eff * t 2 ) + (h + 2 * t 2 ) * t 1 = 40,54 cm² Location of shear centre: y s,eff = (b eff * (2 * t 2 ) * (b eff + t 2 ) / 2) / A eff = 1,088 cm e Nz = y s - y s,eff = 0,337 cm β A = A eff / A = 0,965 Slenderness and reductions: In Z-Z Axis: N cr,z = π² * E * I z / (H * 100)² = 4109,22 kn λ trans,z = (β A * A * f y / N cr,z ) = 1,52 Apply strut curve c α = 0,49 ϕ = 0,5 *(1 + α * (λ trans,z - 0,2) + λ trans,z ²) = 1,979 χ z = 1 / (ϕ + (ϕ² - λ trans,z ²) 0,5 ) = 0,3080 In Y-Y Axis: N cr,y = π² * E * I y / (H * 100)² = 60663,06 kn λ trans,y = (β A * A * f y / N cr,y ) = 0,40 Apply strut curve c α = 0,49 ϕ = 0,5 * (1 + α * (λ trans,y - 0,2) + λ trans,y ²) = 0,629 χ y = 1 / (ϕ + (ϕ² - λ trans,y ²) 0,5 ) = 0,8973 χ = MIN(χ z ; χ y ) = 0,3080 N b,rd = χ * A eff * f y / γ M = 2667,53 kn

31 Folder: _EC3 Columns Limit bending moment about the Y-Y axis: Cross-section class 4 z' s = (-b eff * t 2 * (h + t 2 ) / 2 + (b + (t 1 / 2)) * t 2 * (h + t 2 ) / 2) / A eff = 0,382 cm (h + t 2 )³ / 12 * t 1 + (h + t 2 ) * t 1 * z' s = 2261,46 cm 4 b eff * t 2 * ((h + t 2 ) / 2 + z' s )² + (b + (t 1 / 2)) * t 2 * ((h + t 2 ) / 2 - z' s )² = 2457,57 cm 4 Ieff,y= 4719,03 cm 4 W eff,y = I eff,y / ((h + t 2 ) / 2 + z' s ) = 306,79 cm³ M c,rd,y =W eff,y * f y / γ M = 65541,50 knm Limit bending moment about the Z-Z axis: Cross-section class 4 Tab ψ = -ys / (b + (t 1 / 2) - y s ) = -0,17 k σ = 0,57-0,21 * ψ + 0,07 * ψ² = 0,61 (b + (t 1 / 2)) / t 2 / (21 * ε * (k σ )) = 1,02 > 1 As in Table:5.3.5 (3) λ trans,p = (b + (t 1 / 2)) / t 2 / (28,4 * ε * (k σ )) = 0,75 > 0,673 ρ = (λ trans,p - 0,22) / λ trans,p ² = 0,942 b eff = ρ * (b + (t 1 / 2)) / (1 - ψ) = 8,05 cm b t = -(b + (t 1 / 2)) * ψ / (1 - ψ) = 1,45 cm c eff = b eff + b t = 9,50 cm A eff = (h + t 2 ) * t * c eff * t 2 = 41,40 cm² y' = 2 * c eff ² * t 2 / 2 / A eff = 1,31 cm I eff,z = (h + t 2 ) * t 1 * y'² + 2 * c eff ³ / 12 * t * c eff * t 2 * (c eff / 2 - y')² = 272,12 cm 4 W eff,z = I eff,z / (c eff / 2 - y') = 79,10 cm³ M c,rd,z =W eff,z * f y / γ M = 16898,64 knm Check buckling: N sd = N d = 90,00 kn M y,sd = q d * H² / 8 = 30,00 knm M z,sd = N d * e Nz / 100 = 0,30 knm Hilfsbeiwerte: β My = 1,30 µ y = λ trans,y * (2 * β My - 4) = -0,560 < 0,9 k y = 1 - (µ y * N sd ) / (χ y * A eff * f y ) = 1,006 < 1,5 ψ = 1,000 β Mψ = 1,8-0,7 * ψ = 1,10 < 1,5 µ z = λ trans,z * (2 * β Mψ - 4) = -2,736 < 0,9 k z1 = 1 - (µ z * N sd ) / (χ * A eff * f y ) = 1,082 k z2 = 1,500 k z = MIN(k z1 ; k z2 ) = 1,082 N sd /(χ*a eff *f y /γ M )+k y *100*M y,sd /(W eff,y *f y /γ M )+k z *100*M z,sd /(W eff,z *f y /γ M ) = 0,081 < 1

32 l Euro-Code 3 Folder: _EC3 Columns Laced column made up of channel and angle sections: H sd N d b l y h Loads: N sd = 300,00 kn H sd = 45,00 kn Plan and elevation values: Span length l y = 69,20 cm Column height l = 10*l y /100 = 6,92 m Width b = 40,00 cm Winkel ϕ 1 = 45,00 U-Profil U = SEL("steel/U"; Name; ) = U 300 A f = TAB("steel/U"; A; Name=U) = 58,80 cm² e z = TAB("steel/U"; ez; Name=U) = 2,70 cm i z = TAB("steel/U"; iz; Name=U) = 2,90 cm Winkel W = SEL("steel/WG"; Name; ) = L 50x5 Angle thickness A D = TAB("steel/WG"; A; Name=W) = 4,80 cm² Angle thickness i ζ = TAB("steel/WG"; iζ; Name=W) = 0,98 cm steel = SEL("steel/EC"; Name; ) = Fe 360 f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² E = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² ε = (235 / f y ) = 1,00 λ 1 = 93,90 * ε = 93,90 Partial safety factors: γ M = 1,10

33 Folder: _EC3 Columns Maximal tension force in chord: Effective length ratio k = 2,00 Imperfection: w o = 2 * l / 5 = 2,77 cm Effective moment of inertia: h o = b - 2 * e z = 34,60 cm I eff = 0,5 * h o ² * A f = 35196,50 cm 4 Shear strength: S v = 2 * E/10 * A D * l y * h o ² / (2 * (2 * h o ²)³) = 71276,36 kn N cr = 1 / ((4 * (100 * l)²/(π² * E/10 * I eff )) + (1 / S v )) = 3615,26 kn max_m s =H sd * l + N sd / (1 - N sd / N cr ) * w o / 100 = 320,46 knm N f,sd = 0,5 * N sd * max_m s / h o = 1076,18 kn Analysis of channels: λ = l y / i z = 23,86 λ trans = λ / (λ 1 * ε) = 0,254 Apply strut curve c α = 0,49 ϕ = 0,5 * (1 + α * (λ trans - 0,2) + λ trans ²) = 0,545 χ = 1 / (ϕ + (ϕ² - λ trans ²) 0,5 ) = 0,9735 N b,rd = χ * A f * f y / 10 / γ M = 1222,89 kn N f,sd / N b,rd = 0,88 < 1 Analysis of lacing angles: max_v s = H sd + N sd / (1 - N sd / N cr ) * w o * π / (200 * l) = 47,06 kn Design force for a diagonal: N ds = max_v s / (2 * COS(ϕ 1 )) = 33,28 kn λ = (2 * h o ²) / i ζ = 49,93 λ trans = λ / (λ 1 * ε) = 0,532 Apply strut curve c α = 0,49 ϕ = 0,5 * (1 + α * (λ trans - 0,2) + λ trans ²) = 0,723 χ = 1 / (ϕ + (ϕ² - λ trans ²) 0,5 ) = 0,8247 N b,rd = χ * A D * f y / 10 / γ M = 84,57 kn N ds /N b,rd = 0,39 < 1

34 Folder: _EC3 Continuous Beam Continuous Beam Purlin / Strut with biaxial bending and torsional-flexural buckling: q sd q sd l l ϕ Plan and elevation values: Span length l= 720,00 cm Angle of slope ϕ= 10,00 Spacing of purlin l'= 4,00 m platischer Formbeiwert α ply = 1,14 platischer Formbeiwert α plz = 1,25 Loads: From dead load g= 0,20 kn/m² From snow load s= 0,40 kn/m² Section classification for: IPE 200 Profil Typ = SEL("steel/Profils"; Name; ) = IPE Selected Profil = SEL("steel/"Typ; Name; ) = IPE 200 Column height h = TAB("steel/"Typ; h; Name=Profil) = 200,00 mm Flange width b f = TAB("steel/"Typ; b; Name=Profil) = 100,00 mm Flange thickness t f = TAB("steel/"Typ; t; Name=Profil) = 8,50 mm Flange thickness t w = TAB("steel/"Typ; s; Name=Profil) = 5,60 mm Moment of inertia I y = TAB("steel/"Typ; Iy; Name=Profil) = 1940,00 cm 4 Moment of inertia I z = TAB("steel/"Typ; Iz; Name=Profil) = 142,00 cm 4 Moment of inertia I y = TAB("steel/"Typ; IT; Name=Profil) = 6,98 cm 4 I ω = t f * b f ³ * (h - t f )² / (24*106 ) = 12988,09 cm 6 i z = TAB("steel/"Typ; iz; Name=Profil) = 2,24 cm W ely = TAB("steel/"Typ; Wy; Name=Profil) = 194,00 cm³ W ply = α ply * W ely = 221,16 cm³ W elz = TAB("steel/"Typ; Wz; Name=Profil) = 28,50 cm³ Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 E s = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² G = TAB("steel/EC"; G; Name=steel) = 81000,00 N/mm² f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² ε = (235/f y ) = 1,00 Partial safety factors: γ M = 1,10 γ g = 1,35 γ p = 1,50

35 Folder: _EC3 Continuous Beam Design calculations: Factored load p d = γ g * g + γ p * s = 0,87 kn/m² Effective load q d = p d * 4 = 3,48 kn/m Vertical load component q zd = q d * COS(ϕ) = 3,43 kn/m Horizontal load component q yd = q d * SIN(ϕ) = 0,60 kn/m Forces at 2nd support: M bysd = 0,105 * q zd * (l / 100)² = 18,67 knm M bzsd = 0,105 * q yd * (l / 100)² = 3,27 knm V bzsd = 0,606 * q zd * l / 100 = 14,97 kn V bysd = 0,606 * q yd * l / 100 = 2,62 kn Check biaxial bending strength: About Y-Y axis A v = 1,04 * h * t w / 10² = 11,65 cm² V pl,z,rd = A v * fy / (γ M * (3) * 10) = 143,69 kn V bzsd / V pl,z,rd = 0,10 < 1 V bzsd / V pl,z,rd = 0,10 < 0,5 No reduction in moment strength necessary due to shear. M pl,y,rd = W ply * f y / γ M / 10 = 4724,78 kncm About Z-Z axis A v = 2 * b f * t f / 10² = 17,00 cm² V pl,y,rd = A v * fy / (γ M * (3) * 10) = 209,68 kn V bysd / V pl,y,rd = 0,01 < 1 V bysd / V pl,y,rd = 0,01 < 0,5 No reduction in moment strength necessary due to shear M pl,z,rd = 1,5 * W elz * f y / γ M / 10 = 913,30 kncm Analysis: as in 5.35: for I- and H- sections: α= 2,00 β= 1,00 Or else: (11) ABS((M bysd /(M pl,y,rd /10²)) (α) +(M bzsd /(M pl,z,rd /10²)) (β) ) = 0,514 < 1 Check flexural-torsional buckling strength: i LT = (I z * I ω / W ply ²)0,25 = 2,48 cm Load is applied in top flange. z a = 10,00 cm z s = 0,00 cm z g = z a - z s = 10,00 cm As in Table F.1.2, Werte interpoliert. C 1 = 1,00 C 2 = 0,80 C 3 = 0,70 For simply supported ends fixed ends k = 0,70 No measures taken toward bending k w = 1,00

36 Folder: _EC3 Continuous Beam h s = (h - t f ) / 10 = 19,15 cm 5.5.2; Section class 1+2 β w = 1,00 λ 1 = π * (E s / f y ) = 93,91 Auxilliary value v =((k / k w )²+1/20*(k*l/i LT /(h/t f ))²+(2*C 2 *z g /h s )²) = 4,92 λ LT = k*l/i LT /((C 1 ) 0,5 *(v 0,5-2*C 2 *z g /h s ) 0,5 ) = 172,83 λ trans,lt = λ LT / λ 1 * (β w ) = 1,840 Apply strut curve a: As in Table α = 0,21 ϕ = 0,5 * (1 + α * (λ trans,lt -0,2) + λ trans,lt ²) = 2,37 χ LT = 1 / (ϕ + (ϕ² - λ trans,lt ²) 0,5 ) = 0,26 No longitudinal forces k z = 1,00 No longitudinal forces k LT = 1,00 k LT * M bysd / (χ LT * M pl,y,rd / 10²) + k z * M bzsd / (M pl,z,rd / 10²) = 1,88 < 1 Section is not adequate: Restrain section in quarterly points: l = l / 4 = 180,00 cm Auxilliary value v =((k/k w )²+1/20*(k*l/i LT /(h/t f ))²+(2*C 2 *z g /h s )²) = 1,42 λ LT = k*l/i LT /((C 1 ) 0,5 *(v 0,5-2*C 2 *z g /h s ) 0,5 ) = 85,14 λ trans,lt = λ LT / λ 1 * (β w ) = 0,907 Apply strut curve a: ϕ = 0,5 * (1 + α * (λ trans,lt -0,2) + λ trans,lt ²) = 0,99 χ LT = 1 / (ϕ + (ϕ² -λ trans,lt ²) 0,5 ) = 0,72 k LT * M bysd / (χ LT * M pl,y,rd / 10²) + k z * M bzsd / (M pl,z,rd / 10²) = 0,91 < 1

37 Folder: _EC3 foot and support foot and support Concentrated point load of a beam in another beam: Design loads and properties P sd = 68,00 kn M sd1 = 70,00 knm M sd2 = -22,00 knm Top beam (IPE180) Profil TypO = SEL("steel/Profils"; Name; ) = IPE Selected ProfilO = SEL("steel/"TypO; Name; ) = IPE 180 Web thickness s o = TAB("steel/"TypO; s; Name=ProfilO) = 5,30 mm Flange thickness t o = TAB("steel/"TypO; t; Name=ProfilO) = 8,00 mm Radius r o = TAB("steel/"TypO; r; Name=ProfilO) = 9,00 mm Flange width b o = TAB("steel/"TypO; b; Name=ProfilO) = 91,00 mm Web depth h o = TAB("steel/"TypO; h; Name=ProfilO) = 180,00 mm Web depth h 1o = TAB("steel/"TypO; h1; Name=ProfilO) = 146,00 mm W elo = TAB("steel/"TypO; W y ; Name=ProfilO) = 146,00 cm³ W plo = 1,14 * W elo = 166,44 cm 3 I yo = TAB("steel/"TypO; Iy; Name=ProfilO) = 1320,00 cm 4 Bottom beam (HEA200) Profil TypO = SEL("steel/Profils"; Name; ) = HEA Selected ProfilO = SEL("steel/"TypO; Name; ) = HEA 200 Web thickness of beam s u = TAB("steel/"TypO; s; Name=ProfilO) = 6,50 mm Flange thickness t u = TAB("steel/"TypO; t; Name=ProfilO) = 10,00 mm Radius r u = TAB("steel/"TypO; r; Name=ProfilO) = 18,00 mm Flange width bu = TAB("steel/"TypO; b; Name=ProfilO) = 200,00 mm Web depth h u = TAB("steel/"TypO; h; Name=ProfilO) = 190,00 mm Web depth h 1u = TAB("steel/"TypO; h1; Name=ProfilO) = 134,00 mm W elu = TAB("steel/"TypO; W y ; Name=ProfilO) = 389,00 cm³ W plu = 1,14 * W elu = 443,46 cm 3 I yu = TAB("steel/"TypO; Iy; Name=ProfilO) = 3690,00 cm 4

38 Folder: _EC3 foot and support Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 360 E s = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² G = TAB("steel/EC"; G; Name=steel) = 81000,00 N/mm² f y = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² ε = (235 / f y ) = 1,00 γ M = 1,10 λ 1 = 93,90 * ε = 93,90 f yd = f y /γ M = 213,64 kn/cm² Limit plastic bearing: Stiff bearing length of top, bottom beam: s s1 = s o + 2 * t o + 4 * r o * (1 - (2) / 2) = 31,84 mm σ f,ed1 = 100 * M sd1 / W elu = 17,99 kn/cm² b f1 = t u * 25 = 250,00 mm b f1 = MIN(b f1 ; b u ) = 200,00 mm s y1 = 2 * t u * (b u / s u ) 0,5 * (1 - (γ M * σ f,ed1 / f y * 10 )²) 0,5 = 59,83 mm R y,rd1 = (s s1 + s y1 ) * s u * f y / γ M / 10 ³ = 127,30 kn P sd / R y,rd1 = 0,53 < 1 Stiff bearing length of bottom beam: s s2 = s u + 2 * t u + 4 * r u * (1 - (2) / 2) = 47,59 mm σ f,ed2 = 100 * M sd2 / W elo = -15,07 kn/cm² b f = t o * 25 = 200,00 mm b f2 = MIN(b f ; b o ) = 91,00 mm s y2 = 2 * t o * (b o / s o ) 0,5 * ( 1 - (γ M * σ f,ed2 / f y * 10)²) 0,5 = 46,99 mm R y,rd2 = (s s2 + s y2 ) * s o * f y / γ M / 10³ = 107,09 kn P sd / R y,rd2 = 0,63 < 1 Check web crushing: Bottom beam: m 1 = s s1 / h 1u = 0,238 m 2 = 0,200 m u = MIN(m 1 ; m 2 ) = 0,200 R a,rd1 = 0,5 * s u ² * (E s * f y ) 0,5 * ((t u / s u ) 0,5 + 3 *(s u / t u ) * m u ) / γ M / 10³ = 219,95 kn P sd / R a,rd1 = 0,31 < 1 M c,rd1 = W plu * f y / γ M / 10³ = 94,74 knm M sd1 / M c,rd1 = 0,74 < 1 Top beam: m 1 = s s2 / h 1o = 0,326 m 2 = 0,200 m o = MIN(m 1 ; m 2 ) = 0,200 R a,rd2 = 0,5 * s o ² * (E s * f y ) 0,5 * ((t o / s o ) 0,5 + 3 * (s o / t o ) * m o ) / γ M / 10³ = 145,85 kn P sd / R a,rd2 = 0,47 < 1 M c,rd2 = W plo * f y / γ M / 10³ = 35,56 knm ABS(M sd2 ) / M c,rd2 = 0,62 < 1

39 Folder: _EC3 foot and support Check web buckling for whole web: Bottom beam: Effective web width b eff2 = (h u ² + s s1 ²) 0,5 = 192,65 mm Effective web area A 2 = b eff2 * s u / 100 = 12,52 cm² Moment of inertia I 2 = b eff2 / 10 * (s u / 10)³ / 12 = 0,441 cm 4 Radius of gyration i 2 = (I 2 / A 2 ) 0,5 = 0,188 cm Effective slenderness λ trans2 = h u / (i 2 * λ 1 * 10) = 1,076 Apply strut curve c: α = 0,49 ϕ = 0,5 * (1 + α * (λ trans2-0,2) + λ trans2 ²) = 1,294 χ 2 = 1 / (ϕ + (ϕ² - λ trans2 ²) 0,5 ) = 0,4968 R b,rd2 = χ 2 * A 2 * f y / 10 / γ M = 132,88 kn P sd / R b,rd2 = 0,51 < 1 Top beam: Effective web width b eff1 = (h o ² + s s1 ²) 0,5 = 182,79 mm Effective web area A 1 = b eff1 * s o / 100 = 9,69 cm² Moment of inertia I 1 = b eff1 / 10 * (s o / 10)³ / 12 = 0,227 cm 4 Radius of gyration i 1 = (I 1 / A 1 ) 0,5 = 0,153 cm Effective slenderness λ trans1 = h o / (i 1 * λ 1 * 10) = 1,253 Apply strut curve c: α = 0,49 ϕ = 0,5 * (1 + α * (λ trans1-0,2) + λ trans1 ²) = 1,543 χ 1 = 1 / (ϕ + (ϕ² - λ trans1 ²) 0,5 ) = 0,4093 R b,rd1 = χ 1 * A 1 * f y / 10 / γ M = 84,73 kn P sd / R b,rd1 = 0,80 < 1 Check web yield at load points: Bottom beam: σ x,ed2 = M sd1 * 10² * (h u / 2 - t u ) / I yu = 161,25 kn/cm² σ z,ed2 = 10³ * P sd / ((s s1 + 2 * t u ) * s u ) = 201,80 kn/cm² (σ x,ed2 / f yd )² + (σ z,ed2 / f yd )² - (σ x,ed2 / f yd )*(σ z,ed2 / f yd )= 0,75 < 1 Top beam: σ x,ed1 = -M sd2 * 10² * (h o / 2 - t o ) / I yo = 136,67 kn/cm² σ z,ed1 = 10³ * P sd / ((s s2 + 2 * t o ) * s o ) = 201,76 kn/cm² (σ x,ed1 / f yd )² + (σ z,ed1 / f yd )² - (σ x,ed1 / f yd ) * (σ z,ed1 / f yd ) = 0,70 < 1

40 Folder: _EC3 foot and support Column base subject to compression und bending: Msd Nsd l d e1 p e1 e a Plan and elevation values: Distance to edge of baseplate e = 45,00 mm Distance to edge of baseplate e 1 = 100,00 mm Spacing of bolts p = 300,00 mm Width of baseplate b = 500,00 mm Length of baseplate a = 500,00 mm Plate thickness d = 30,00 mm Projection of plate l = 100,00 mm Weld thickness a w = 10,00 mm Projection of pad footing a r = 1000,00 mm Depth of pad footing h = 1400,00 mm as in L.3 (idr) Bearing plane factor β j = 2/3 = 0,67 b Profil Typ = SEL("steel/Profils"; Name; ) = HEB Selected Profil = SEL("steel/"Typ; Name; ) = HEB 300 Moment of inertia I y1 = TAB("steel/"Typ; Iy; Name=Profil) = 25170,00 cm 4 Flange width b f = TAB("steel/"Typ; b; Name=Profil) = 300,00 mm Flange thickness t f = TAB("steel/"Typ; t; Name=Profil) = 19,00 mm Column height h t = TAB("steel/"Typ; h; Name=Profil) = 300,00 mm M pl,y,rd = TAB("steel/"Typ; Mplyd; Name=Profil) = 418,00 knm N pl,rd = TAB("steel/"Typ; Npld; Name=Profil) = 3250,00 kn Loads: N sd = 1000,00 kn M sd = 221,75 knm

41 Folder: _EC3 foot and support Materials and stresses: steel = SEL("steel/EC"; Name; ) = Fe 430 E s = TAB("steel/EC"; E; Name=steel) = ,00 N/mm² f y = TAB("steel/EC"; fy; Name=steel) = 275,00 N/mm² Concrete = SEL("Concrete/EC"; Name; ) = C30/37 f ck = TAB("Concrete/EC"; f ck ; Name=Concrete) = 30,00 N/mm² SC = SEL("steel/bolt"; SC; ) = 4.6 Bolt = SEL("steel/bolt"; BS; ) = M 24 f u = TAB("steel/bolt"; fubk; SC=SC) = 400,00 N/mm² A s = TAB("steel/bolt"; Asp; BS=Bolt) = 3,53 cm² γ Mb = 1,25 γ c = 1,50 γ M0 = 1,10 Design: m = l - e - 0,8 * a w * (2) = 43,69 mm l eff1a = MIN(4 * m + 1,25 * e; 2 * m + 0,625 * e + e 1 ) = 215,51 mm l eff1b = MIN(2 * m + 0,625 * e + 0,5 * p; e 1 + 0,5 * p; b / 2) = 250,00 mm l eff1 = MIN(l eff1a ; l eff1b ) = 215,51 mm l eff2a = MIN(π * 2 * m; π * m + 2 * e 1 ) = 274,51 mm l eff2b = MIN(π * m + p; p + 2 * e 1 ) = 437,26 mm l eff = MIN(l eff2a ; l eff2b ; l eff1 ) = 215,51 mm Maximum stress of base plate at the centre of tension bolt: M pl,1,rd = 0,25 * l eff * (d / 10)² * f y / 10/ γ M0 = 12,12*10 3 knmm n = e = 45,00 mm n / (1,25 * m) = 0,82 < 1 B t,rd = 0,9 * f u * A s / 10 / γ Mb = 101,66 kn Full flange yield: F T,Rd1 = 4 * M pl,1,rd / m = 1109,64 kn Bolt failure with flange yielding: F T,Rd2 = (2 * M pl,1,rd + n * 2 * B t,rd ) / ( m + n ) = 376,47 kn Bolt failure without flange yielding: F T,Rd3 = 2 * B t,rd = 203,32 kn F T,Rd = MIN(F T,Rd1 ; F T,Rd2 ; F T,Rd3 ) = 203,32 kn Effective compression area: Limit pressure in the base plate: a 1 = MIN(a + 2 * a r ; 5 * a; a + h) = 1900,00 mm k j = (a 1 ² / (a * b)) 0,5 = 3,80 f j = β j * k j * f ck / γ c = 50,92 N/mm² A eff = 10 * (N sd + F T,Rd ) / f j = 236,32 cm² c = d * (f y *10/ ( 3 * f j * γ M0 )) 0,5 = 121,36 mm x 0 = 100 * A eff / ( 2 * c + b f ) = 43,54 mm x 0 /(t f + 2 * c) = 0,17 < 1

42 Folder: _EC3 foot and support Limit moment at column base: r c = h t / 2 + c - x 0 / 2 = 249,59 mm M Rd = (F T,Rd * 10³ *(h t / e) + A eff * 100 * f j * r c ) / 10 6 = 342,02 knm Check permissible strength of column to bending and compression.: M Ny,Rd = 1,1 * M pl,y,rd * (1- N sd / N pl,rd ) = 318,32 knm Analysis: M sd / MIN(M Ny,Rd ; M Rd ) = 0,70 < 1

43 Folder: _EC3 Frames Frames Sway frame with bracing out of plane of frame, plastic theory: q d H d B D h A C l Plan and elevation values: Frame width l = 8,00 m Frame depth h = 6,00 m Number of column n c = 2 Number of storeys n s = 1 Beam: Profil Typ1 = SEL("steel/Profils"; Name; ) = IPE Selected Profil1= SEL("steel/"Typ1; Name; ) = IPE 240 Column height h 1 = TAB("steel/"Typ1; h; Name=Profil1) = 240,00 mm Web thickness s 1 = TAB("steel/"Typ1; s; Name=Profil1) = 6,20 mm Moment of inertia I y1 = TAB("steel/"Typ1; Iy; Name=Profil1) = 3890,00 cm 4 Cross-sectional area A 1 = TAB("steel/"Typ1; A; Name=Profil1) = 39,10 cm² Moment of resistance W y1 = TAB("steel/"Typ1; Wy; Name=Profil1) = 324,00 cm² Moment of resistance Wpl y1 = 1,14 * W y1 = 369,36 cm³ Column section: Profil Typ2 = SEL("steel/Profils"; Name; ) = HEB Selected Profil2 = SEL("steel/"Typ2; Name; ) = HEB 240 Flange width b 2 = TAB("steel/"Typ2; b; Name=Profil2) = 240,00 mm Column height h 2 = TAB("steel/"Typ2; h; Name=Profil2) = 240,00 mm Web thickness s 2 = TAB("steel/"Typ2; s; Name=Profil2) = 10,00 mm Moment of inertia I y2 = TAB("steel/"Typ2; Iy; Name=Profil2) = 11260,00 cm 4 Moment of inertia I z2 = TAB("steel/"Typ2; Iz; Name=Profil2) = 3920,00 cm 4 Moment of inertia I t2 = TAB("steel/"Typ2; IT; Name=Profil2) = 103,00 cm 4 Moment of inertia I ω2 = 10³*TAB("steel/"Typ2; Iω; Name=Profil2) =486900,00 cm 6 Cross-sectional area A 2 = TAB("steel/"Typ2; A; Name=Profil2) = 106,000 cm² i y = TAB("steel/"Typ2; iy; Name=Profil2) = 10,30 cm i z = TAB("steel/"Typ2; iz; Name=Profil2) = 6,08 cm Moment of resistance W ely2 = TAB("steel/"Typ2;Wy; Name=Profil2) = 938,00 cm³ Moment of resistance W ply2 = 1,25 * W ely2 = 1172,50 cm³ Loads: H d = 9,00 kn q d = 9,00 kn/m

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