5.1 WORKED EXAMPLE Header plate connection Geometrical and mechanical data e 1. p 1. e 2 p 2 e 2

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1 5.1 WORKED EXAMPLE Header late coectio Geoetrical ad echaical data e 1 M20 1 HEA200 IPE300 1 e 1 e 2 2 e 2 Mai joit data Coiguratio Bea to colu lage Colu HEA 200 S 235 Bea IPE 300 S 235 Tye o coectio Header late coectio Header late 230 x 200 x 10, S 235 Detailed characteristics Colu HEA 200, S235 Deth h = 190,00 Thickess o the eb t c = 6,50 Width b c = 200,00 Thickess o the lage t = 10,00 Root radius r = 18,00 Area A = 53,83 c² Iertia I = 3692,16 c 4 Yield stregth yc = 235,00 N/² Ultiate stregth uc = 360,00 N/² Bea IPE 300, S235 Deth h = 300,00 Thickess o the eb t b = 7,10 Width b b = 150,00 Thickess o the lage t b = 10,70 Root radius r = 15,00 Area A = 53,81 c² Iertia I = 8356,11 c 4

2 Yield stregth yb = 235,00 N/² Ultiate stregth ub = 360,00 N/² Header late 230 x 200 x 10, S 235 Vertical ga g v = 35,00 Deth h = 230,00 Width b = 200,00 Thickess t = 10,00 Directio o load traser (1) Nuber o bolts ros 1 = 3 Edge to irst bolt ro distace e 11 = 45,00 Pitch betee bolt ro 1 ad 2 1[1] = 70,00 Pitch betee bolt ro 2 ad 3 1[2] = 70,00 last bolt ro to edge distace e 1 = 45,00 Directio eredicular to Load traser (2) Nuber o bolts ros 2 = 2 Edge to irst bolt ro distace e 21 = 50,00 Pitch betee bolt ro 1 ad 2 2 ' = 100,00 last bolt ro to edge distace e 2 = 50,00 last bolt ro to edge distace (colu lage) e 2s = 50,00 Yield stregth y = 235,00 N/² Ultiate stregth u = 360,00 N/² Bolts M20, 8.8 Resistat area A s = 245,00 ² Diaeter o the shak d = 20,00 Diaeter o the holes d 0 = 22,00 Yield stregth yb = 640,00 N/² Ultiate stregth ub = 800,00 N/² Welds Throat thickess o the eld a = 4,00 Legth o the eld l = 230,00 Saety actors γ M0 = 1,00 γ M2 = 1,25 Alied shear orce

3 V Sd = 200 kn Ductility ad rotatio requireets Rotatio requireets (1) h d b h = 230,00 d b = h 2 t b 2 r = 300, , ,00 = 248,60 ok (2) φ available > φ required e suose that this requireet is ulilled, Ductility requireets (1) d 2,8 t y ub d / t = 2,00 y / ub = 0,29 2,00 1,52 ok yb γ M2 (2) a 0,4 t b β 3 = 3,21 ub γ M0 t b = 7,1 yb = 235,00 N/² ub = 360,00 N/² β = 0, Joit shear resistace a = 4,00 ok Bolts i shear V Rd 1 = 0,8 F v,rd = 451,58 kn F v,rd = α v A ub / γ M2 = 94,08 kn α v = 0,6 A = A s = 245,00 ²

4 ub = 800,00 N/² Header late i bearig V Rd 2 = F b,rd = 589,09 kn F b,rd = k 1 α b d t u / γ M2 = 98,18 kn α b = i(α 1, α 2, α 3, 1) = 0,68 α 1 = e 1 / 3d 0 = 0,68 α 2 = 1 / 3d 0-1/4 = 0,81 α 3 = ub / u = 2,22 k 1 = i(2,8 e 2 / d 0 1,7 ; 2,5) = i(4,66 ; 2,5) = 2,5 d t ub u = 20,00 = 10,00 = 800,00 N/² = 360,00 N/² Colu lage i bearig V Rd 3 = F b,rd = 700,36 kn F b,rd = k 1 α b d t u / γ M2 = 116,73 kn α = i(α 1, α 2, 1) = 0,81 α 1 = 1 / 3d 0-1/4 = 0,81 α 2 = ub / u = 2,22 k 1 = i(2,8 e 2s / d 0 1,7 ; 2,5) = i(4,66 ; 2,5) = 2,5 d t ub u = 20,00 = 10,00 = 800,00 N/² = 360,00 N/² Gross sectio o the header late i shear V Rd 4 = 2 F v,rd = 491,44 kn F v,rd = A v y / (1,27 3 γ M0 ) = 245,72 kn A v = h t = 23,00 c² y = 235,00 N/²

5 Net sectio o the header late i shear V Rd 5 = 2 F v,rd = 545,39 kn F v,rd = A v,et u / ( 3 γ M2 ) = 272,69 kn A v,et = ( h - 1 d 0 ) t = 16,40 c² h = 230,00 1 = 6 d 0 = 22,00 t = 10,00 u = 360,00 N/² Shear block o the header late V Rd 6 = 2 F e,rd = 577,40 kn 1,36 2 ' = 136,00 h > 1,36 2 ' 1 = 3 1 > 1 F e,rd = F e,1,rd = u A t / γ M2 + y A v / ( 3 γ M0 ) = 288,70 kn A t = t ( e 2 - d 0/2 ) = 390,00 ² t = 10,00 e 2 = 50,00 d 0 = 22,00 A v = t ( h e 1 ( 1 0,5 ) d 0 ) = 1300,00 ² 1 = 3 h = 230,00 e 1 = 45,00 y u = 235,00 N/² = 360,00 N/² Header late i bedig V Rd 7 = h = 230,00 1,36 2 ' = 136,4 h > 1,36 2 ' Bea eb i shear V Rd 8 = F v,rd = 221,56 kn F v,rd = A v yb / ( 3 γ M0 ) = 221,56 kn A v = h t b = 16,33 c² yb = 235,00 N/²

6 Joit shear resistace Shear resistace o the joit V Rd = 221,56 kn Failure Mode: Bea eb i shear Desig check Alied shear orce: V Sd = 200 kn Shear resistace: V Rd = 221,56 kn Desig ok Joit tyig resistace Bolts i tesio N u 1 = B t,u = 1176,00 kn B t,u = ub A s = 196,00 kn A s = 245,00 ² F ub = 800,00 N/² Header late i bedig N u 2 = i ( F h,u,1 ; F h,u,2 ) = 684,69 kn F h,u,1 = F h,u,2 = (8 2 2 l 2 e e..t,2 e ) l u. + e..t,1 ( + B + t.u u. ) = 852,83 kn = 684,69 kn = ( 2 ' t 2 x 0,8 a 2-0,5 ) / 2 = 41,925 = i ( e 2 ; 1,25 ) = i ( 50 ; 52,4 ) = 50,00 2 t u u, = = 9000,00 N / 4 l e,1 = l e,2 = h = 230,00 e = 37,00

7 Suortig eber i bedig (colu lage) N u 2 = i ( F,u,1 ; F,u,2 ) = F,u,1 = F,u,2 = (8 2 2 l 2 e e..t,2 e ) l u. + e..t,1 ( + B + t.u u. ) = = = ( 2 ' t c 2 x 0,8 r c ) / 2 = 32,35 = i ( e 2s ; 1,25 ) = i ( 50 ; 40,438 ) = 40,438 2 t u u, = = 9000,00 N / 4 l e,1 = l e,2 = e = 37,00 Coet : More resistace tha or the header late (higher l e values ad saller values o ad ). Bea eb i tesio N u 4 = t h ub = 587,88 kn t = 7,10 h = 230,00 ub = 360,00 N/² Welds Coditios or ull-stregth behaviour o the elds are ulilled Joit tyig resistace Tyig resistace o the joit N u = 587,88 kn Failure ode : Bea eb i tesio Based o aer Jasart J.P., Reki S., Guillaue M.L.: Euroea Recoedatios or the Desig o Sile Joits i Steel Structures, 1st drat o a orthcoig ublicatio o the Techical Coittee 10 Joits ad Coectios o the Euroea Covetio o Costructioal Steelork (ECCS TC10) reared at the Uiversity o Liège, Seteber 2003.