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Transcript of Euro-Code 3 1).pdf · PDF file Euro-Code 3 Folder: _EC3 Bolted connections Euro-Code 3...

  • Euro-Code 3 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 eo = 30,00 mm Spacing of bolts b = 70,00 mm Spacing of bolts h = 220,00 mm Angle of tension force β β β β = 45,00 °

    Bolts: Bolt = SEL("steel/bolt"; BS; ) = M 20 SC = SEL("steel/bolt"; SC; ) = 8.8 fu,b = TAB("steel/bolt"; fubk; SC=SC) = 800,00 N/mm² Hole diameter dl= TAB("steel/bolt"; d; BS=Bolt) = 20,00 mm Shaft diameter dll= dl+2 = 22,00 mm Cross-section areas As = TAB("steel/bolt"; Asp; BS=Bolt) = 2,45 cm²

    Plate: steel = SEL("steel/EC"; Name; ) = Fe 510 fy = TAB("steel/EC"; fy; Name=steel) = 355,00 N/mm² fu = TAB("steel/EC"; fu; Name=steel) = 510,00 N/mm² γγγγM0= 1,10 γγγγMb= 1,25

    Loads: Ssd = 424,26 kN

    Nsd = COS(ββββ) * Ssd = 300,00 kN Vsd = SIN(ββββ) * Ssd = 300,00 kN

    Force per bolt: Ft,sd = Nsd / 4 = 75,00 kN Fv,sd = Vsd / 4 = 75,00 kN

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Limit tension force of bolts: Ft,Rd = 0,9 * fu,b * As / γγγγMb / 10 = 141,12 kN Ft,sd / Ft,Rd = 0,53 < 1

    Check limit shear force for bolts: Fv,Rd = 0,6 * fu,b * π π π π * dl² / 4000 / γγγγMb = 120,64 kN Fv,sd / Fv,Rd = 0,62 < 1

    Check combined: Ft,sd / (1,4 * Ft,Rd) + Fv,sd / Fv,Rd = 1,00 ≤≤≤≤ 1

    Analysis of bearing strength: as in 6.5.1.3: eo / dll = 1,36 > 1 as in 6.5.1.3: eo / dll = 1,36 < 1,5 as in 6.5.1.2(1): e / dll = 1,59 > 1,2 as in 6.5.1.2(3): b / dll = 3,18 > 3

    α α α α = MIN(e / (3 * dll); b / (3 * dll) - 0,25; fu,b / fu; 1) = 0,53 Tab.6.5.3 Fb1,Rd = 2,5 * α α α α * fu * dl * d / γγγγMb / 10³ = 162,18 kN 6.5.5.(10) Fb2,Rd = 2/3 * Fb1,Rd = 108,12 kN Fb,Rd = Fb2,Rd + (Fb1,Rd - Fb2,Rd) * (eo / dl - 1,2) / 0,3 = 162,18 kN

    Fv,sd / Fb,Rd = 0,46 < 1

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Bolted connection subject to bending

    Dimensions of connection: a = 80,00 mm a1 = 45,00 mm e = 80,00 mm e1 = 45,00 mm e2 = 50,00 mm e3 = 90,00 mm d1 = 20,00 mm d2 = 8,00 mm b1 = 160,00 mm

    h2 = 2 * (e2 + e3) = 280,00 mm

    Flansch-Bolts: Boltf = SEL("steel/bolt"; BS; ) = M 20 SC1 = SEL("steel/bolt"; SC; ) = 4.6 fu,bo = TAB("steel/bolt"; fubk; SC=SC1) = 400,00 N/mm² Hole diameter dlo = TAB("steel/bolt"; d; BS=Boltf) = 20,00 mm Shaft diameter dl1o = dlo + 2 = 22,00 mm Number of rows no = 3

    Steg-Bolts: BoltS = SEL("steel/bolt"; BS; ) = M 16 SC2 = SEL("steel/bolt"; SC; ) = 4.6 fu,bs = TAB("steel/bolt"; fubk; SC=SC2) = 400,00 N/mm² Hole diameter dls = TAB("steel/bolt"; d; BS=BoltS) = 16,00 mm Shaft diameter dl1s = dls + 2 = 18,00 mm Number of rows ns = 3 Number of columns ms = 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 Wy = TAB("steel/"Typ; Wy; Name=Profil) = 324,00 cm² Moment of resistance Wpl = 1,14 * Wy = 369,36 cm³

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Material and Partial safety factors: steel = SEL("steel/EC"; Name; ) = Fe 360 fy = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² fu = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γγγγM0 = 1,10 γγγγM2 = 1,25

    Loads: Msd = 157,95 kNm Vsd = 60,75 kN

    Check beam-web strength without holes: Mc,Rd = Wpl * fy / γM0 / 10³ = 78,91 kNm Msd / Mc,Rd = 2,00 < 1

    Av = 1,04 * h * s / 100 = 15,48 cm² Vpl,Rd = Av * fy / 10 / √√√√(3) / γM0 = 190,93 kN Vsd / Vpl,Rd = 0,32 < 1

    Check beam-web strength with holes: Az = 0,5 * A = 19,55 cm² Az,net = Az - (2 * dl1o * t + ((ns - 1) / 2) * dl1s * s) / 100 = 14,12 cm² (fy / fu * γγγγM2 / γγγγM0) / (0,9 * Az,net / Az) = 1,14 ≤≤≤≤ 1 Wpl,net = Wpl - 2 * dl1o * t * (h - t) / 2000 = 319,73 cm³ Mc,Rd,C = Wpl,net * fy / (γM0 * 10³) = 68,31 kNm

    Msd / Mc,Rd,C = 2,31 < 1

    Av,net = Av - ns * dl1s * s / 100 = 12,13 cm²

    fy / fu * Av / Av,net = 0,83 < 1 ⇒ Area of holes will be neglected.

    Analysis of bolts in flange: Iw = 2 / 12 * d2 * h2³ / 104 = 2926,93 cm4

    If = 2 * b1 * d1 * ((h + d1) / 2)² / 104 = 10816,00 cm4

    Mw = Msd * Iw / (Iw + If) = 33,64 kNm Mf = Msd * If / (Iw + If) = 124,31 kNm

    Effective tension force in flange: Nsd = Mf / (h + d1) * 10³ = 478,12 kN Limit shear force Fv,Rd = no * 2 * 0,6 * fu,bo * π/4 * dlo² / γM2 / 10³ = 361,91 kN Limit bearing force: α α α α = MIN(a1 / (3 * dl1o); a / (3 * dl1o) - 0,25; fu,bo / fu; 1) = 0,682 Fb,Rd = 2 * no * 2,5 * α α α α * fu * dlo * t / γγγγM2 / 10³ = 577,46 kN

    Nsd / MIN(Fv,Rd; Fb,Rd) = 1,32 < 1

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Analysis of bolts in web: ns1 = (ns - 1) / 2 + 0,49 = 1 ns2 = ns1 * 2 = 2 ms1 = (ms - 1) / 2 + 0,49 = 1 ms2 = ms1 * 2 = 2 Ip = (ns * ms2 * ((ms-1) / 2*e)² + ns2 * ms * ((ns-1) / 2*e3)²)/10² = 420,00 cm² Msw = Mw + Vsd * e3 / 10³ = 39,11 kNm Rsd = √√√√((10*Msw*e3/Ip)² + ((Vsd/(ms*ns)) + 10*Msw*(ms-1)/2*e/Ip)²) = 96,27 kN Fv,Rd = ms * 0,6 * fu,bs * π/4 * dls² / 10³ / γM2 = 77,21 kN α α α α = MIN(e1 / (3 * dl1s); e / (3 * dl1s) - 0,25; fu,bo / fu; 1) = 0,833 Fb,Rd = 2,5 * α α α α * fu * dls * s / γγγγM2 / 10³ = 59,50 kN

    Rsd / MIN(Fv,Rd; Fb,Rd) = 1,62 < 1

    Analysis of cover plates: A = d1 * b1 / 100 = 32,00 cm² Anet = A - (2 * dl1o * d1) / 100 = 23,20 cm² Limit tension force: Nt,Rd = MIN(A * fy / γM0; 0,9 * Anet * fu / γM2)/ 10 = 601,34 kN

    Nsd / Nt,Rd = 0,80 < 1

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Connection subject to moment load:

    7

    1 2 3

    54

    86

    e

    e

    e

    e

    e e

    e e

    2

    2

    3

    3

    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 fu,b1 = TAB("steel/bolt"; fubk; SC=SC1) = 500,00 N/mm² Hole diameter dl1 = TAB("steel/bolt"; d; BS=Bolt1) = 30,00 mm

    Bolt2 = SEL("steel/bolt"; BS; ) = M 12 SC2 = SEL("steel/bolt"; SC; ) = 5.6 fu,b2 = TAB("steel/bolt"; fubk; SC=SC2) = 500,00 N/mm² Hole diameter ds2 = TAB("steel/bolt"; d; BS=Bolt2) = 12,00 mm Shaft diameter dl2= ds2+1 = 13,00 mm

    IPE330 aus steel = SEL("steel/EC"; Name; ) = Fe 360 fu2 = TAB("steel/EC"; fu; Name=steel) = 360,00 N/mm² γγγγMb = 1,25 γγγγMo = 1,25

    Loads: Vsd = 58,70 kN Msd = 910,00 kNcm

    Analysis of the right bolt: Check limit shear force Fv,Rd = 0,6 * π π π π / 4 * (dl1 / 10)² * fu,b1 / γγγγMo / 10 = 169,65 kN Vsd / Fv,Rd = 0,35 < 1 Limit bearing strength Fb,Rd = 1,5 * dl1 * t * fu2 / γγγγMb / 10³ = 77,76 kN Vsd / Fb,Rd = 0,75 < 1

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Check bolts on left: Ip = (6 * e² + 6 * e3²) / 100 = 444,00 cm² Maximum horizontal force in bolt due to moment: Fh = Msd * e3 / 10 / Ip = 14,35 kN Maximum vertical force: Fv = Msd * e / 10 / Ip + Vsd / n = 17,59 kN Resulting force Rr = √√√√(Fh² + Fv²) = 22,70 kN Fv,Rd = 0,6 * fu,b2 * dl2² * π π π π / 4 / γγγγMb / 10³ = 31,86 kN

    Rr / Fv,Rd = 0,71 < 1

    Analysis of bearing strength α α α α = MIN(e1 / (3 * dl2); 2 * e / (3 * dl2) - 0,25; fu,b2 / fu2; 1) = 0,90 Fb,Rd = 2,5 * α α α α * fu2 * dl2 * t / γγγγMb / 10³ = 50,54 kN

    Fh / Fb,Rd = 0,28 < 1

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Bolted shear joint:

    Dimensions of connection: Spacing of bolts a = 45,00 mm Spacing of bolts a0 = 35,00 mm Spacing of bolts a1 = 30,00 mm Spacing of bolts a2 = 50,00 mm Spacing of bolts a3 = 90,00 mm Depth of cope a4 = 30,00 mm Plate projection as = 20,00 mm Lever-arm x = 45,00 mm Number of bolts n = 3

    Bolts: M16 4.6 Bolt = SEL("steel/bolt"; BS; ) = M 16 SC = SEL("steel/bolt"; SC; ) = 4.6 fu,b = TAB("steel/bolt"; fubk; SC=SC) = 400,00 N/mm² Hole diameter dl= TAB("steel/bolt"; d; BS=Bolt) = 16,00 mm Shaft diameter d0= dl+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 6.5.2..2(3): k = 0,5 for 1 group bolts; =2,5 for 2 rows

    steel = SEL("steel/EC"; Name; ) = Fe 360 fy = TAB("steel/EC"; fy; Name=steel) = 235,00 N/mm² fu = 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

    γγγγMb = 1,25 γγγγM2 = 1,25 γγγγM0 = 1,10

    Loads: Vsd = 60,00 kN

  • Euro-Code 3 Folder: _EC3 Bolted connections

    Check bolt spacing as in 6.5.1: 1,2 * d0 / a1 = 0,72 < 1 a1 / MAX(12 * t; 150) = 0,20 < 1 1,5 * d0 / a0 = 0,77 < 1 a0 / MAX(12 * t; 150) = 0,23 < 1 2,2 * d0 / a2 = 0,79 < 1 a2 / MIN(12 * s; 200) = 0,63 < 1

    Check bolts strength: Bolts in web of main beam Fv,sd = Vsd / (2 * n) = 10,00 kN Bolts in web of connecting beam Msd = x / 10 * Vsd