5.
WORKED EXAMPLE Fin plate connection Geometrical and mechanical data
5.2.1
e
M 20
p p
IPE 300 HEA 200
Main joint data
2b
Configuration Column Beam Type of connection Fin plate
Beam to column flange HEA 200 S 235 IPE 300 S 235 Fin plate connection 230 x 110 x 10, S 235
Detailed characteristics
Column HEA 200, S235
Depth Thickness of the web Width Thickness of the flange Root radius Area Inertia Yield strength Ultimate strength
Beam IPE 300, S235
h tcw bf tcf r A I
= 190,00 = 6,50 = 200,00 = 10,00 = 18,00 = 53,83 = 3692,16 235,00 360,00
mm mm mm mm mm cm cm4 N/mm N/mm
fyc = fuc =
Depth Thickness of the web Width Thickness of the flange Root radius
h tbw bf tbf r
= = = = =
300,00 7,10 150,00 10,70 15,00
mm mm mm mm mm
Area Inertia Yield strength Ultimate strength
Fin plate 230 x 110 x 10, S 235
A = 53,81 I = 8356,11 fyb = fub = 235,00 360,00
cm cm4 N/mm N/mm
Vertical gap gv Horizontal gap (end beam to column flange) Depth hp Width bp Thickness tp
Direction of load transfer (1)
= gh = = =
35,00 = 230,00 110,00 10,00
mm 10,00 mm mm mm mm
Number of bolts rows Edge to first bolt row distance Beam edge to first bolt row distance Pitch between bolt row 1 and 2 Pitch between bolt row 2 and 3 last bolt row to edge distance
Direction perpendicular to Load transfer (2)
n1 = 3 e11 = 45,00 e1b = 80,00 p1[1] = 70,00 p1[2] = 70,00 e1n = 45,00
mm mm mm mm mm
Number of bolts rows Edge to first bolt row distance last bolt row to beam edge distance Lever arm Yield strength Ultimate strength
Bolts M20, 8,8
n2 e21 e2b z
= = = =
1 50,00 50,00 60,00 235,00 360,00
mm mm mm N/mm N/mm
fyp = fup =
Resistant area Diameter of the shank Diameter of the holes Yield strength Ultimate strength
As d d0 fyb fub
= = = = =
245,00 20,00 22,00 640,00 800,00
mm mm mm N/mm N/mm
Welds
Throat thickness of the weld Length of the weld
Safety factors
aw = lw =
5,00 230,00
mm mm
M0 = M2 =
1,00 1,25
Applied shear force
VSd = 100 kN
5.2.2
Requirements to ensure sufficient rotation capacity
(1)
hp db
hp db
= = =
230,00 mm h 2 tbf 2 r 300,00 2 10,70 2 15,00 = 248,60 mm ok we suppose that this requirement is fulfilled,
(2)
available > required
5.2.3
Requirements to avoid premature weld failure
a > 0,4 tp w tp fyp fup w
f yp M 2 = 4,52 mm f up M 0 = 10,00 mm = 235,00 N/mm = 360,00 N/mm = 0,80 ok
a = 5,00 mm
5.2.4
Joint shear resistance
Bolts in shear
VRd 1 =
n Fv,Rd 6z 1 + (n + 1) p 1
2
= 173,28 kN
=3
z = 60,00 mm Fv,Rd = v A fub / M2 = 94,08 kN v = 0,6 A = As = 245,00 mm fub = 800,00 N/mm
Fin plate in bearing
VRd 2 =
1 1 + n Fb , ver ,Rd + F b ,hor ,Rd
2
= 192,59 kN
2
n =3 =0 1/n =1/3 6z = = 0,43 p1 n (n + 1)
Fb,Rd,ver = k1 b d tp fup / M2 = 98,18 kN b = min (1 , 2 , 3 , 1) = 0,68 1 = e1 / 3d0 = 0,68 2 = p1 / 3d0 1/4 = 0,81 3 = fub / fup = 2,22 k1 = min (2,8 e2 / d0 1,7 ; 2,5) = min (4,66 ; 2,5) = 2,5
Fb,Rd,hor = k1 b d tp fup / M2 = 109,09 kN b = min (1 , 2 , 1) = 0,75 1 2 k1 d tp fub fup = e2 / 3d0 = 0,75 = fub / fup = 2,22 = min (2,8 e1 / d0 1,7 ; 1,4 p1 / d0 1,7 ; 2,5) = min (4,03 ; 2,75 ; 2,5) = 2,5 = 20,00 mm = 10,00 mm = 800,00 N/mm = 360,00 N/mm
Gross section of the fin plate in shear
VRd 3 = Av fyp / (1,27
3 M0) = 245,72 kN
Av = hp tp = 23,00 cm fyp = 235,00 N/mm
Net section of the fin plate in shear
VRd 4 = Av,net fup / ( 3 M2 ) = 272,69 kN Av,net = ( hp n1 d0 ) tp = 16,40 cm hp = 230,00 mm n1 = 3 d0 = 22,00 mm tp = 10,00 mm fup = 360,00 N/mm
Shear block of the fin plate
VRd 5 = Feff,2,Rd = 232,54 kN Feff,2,Rd = 0,5 fup Ant / M2 + fyp Anv / ( 3 M0 ) = 232,54 kN Ant = tp ( e2 - d0/2 ) = 390,00 mm tp = 10,00 mm e2 = 50,00 mm d0 = 22,00 mm = tp ( hp e1 ( n1 0,5 ) d0 ) = 1300,00 mm n1 = 3 hp = 230,00 mm e1 = 45,00 mm = 235,00 N/mm = 360,00 N/mm
Anv
fyp fup
Fin plate in bending
hp = 230 mm 2,73 z = 163,8 mm VRd 6 =
Buckling of the fin plate
VRd 7 =
Wel z
M0
= 776,97 kN
Wel =
tp h2 p 6
= 88 166,67 mm
tp = 81 z
Beam web in bearing
235 = 528,75 N/mm
VRd 8 =
1 1 + n Fb , ver ,Rd + F b ,hor ,Rd
2
= 146,19 kN
2
n =3 =0 1/n =1/3 6z = = 0,43 p1 n (n + 1) Fb,Rd,ver = k1 b d tbw fubw / M2 = 82,88 kN b = min (1 , 2 , 1) = 0,81 1 = p1 / 3d0 1/4 = 0,81 3 = fub / fubw = 2,22 = min (2,8 e2b / d0 1,7 ; 2,5) = min (4,66 ; 2,5) = 2,5 Fb,Rd,hor = k1 b d tbw fubw / M2 = 77,45 kN b = min (1 , 2 , 1) = 0,75 1 = e2b / 3d0 = 0,75 2 = fub / fubw = 2,22 k1 d tbw fub fubw = min (1,4 p1 / d0 1,7 ; 2,5) = min (2,75 ; 2,5) = 2,5 = 20,00 mm = 7,10 mm = 800,00 N/mm = 360,00 N/mm k1
Gross section of the beam web in shear
VRd 9 = Ab,v fybw / ( 3 M0) = 348,42 kN Ab,v = 25,68 cm fybw = 235,00 N/mm
Net section of the beam web in shear
VRd10 = Av,net fubw / ( 3 M2 ) = 349,11 kN Ab,v,net = Ab,v n1 d0 tbw = 21,00 cm Ab,v = 25,68 cm n1 = 3 d0 = 22,00 mm tbw = 7,10 mm fubw = 360,00 N/mm
Shear block of the beam web
VRd11 = Feff,2,Rd = 198,82 kN Feff,2,Rd = 0,5 fubw Ant / M2 + fybw Anv / ( 3 M0 ) = 198,82 kN Ant = tbw ( e2b - d0/2 ) = 276,9 mm tbw = 7,10 mm e2b = 50,00 mm d0 = 22,00 mm Anv = tbw ( e1b + (n1 1 ) p1 (n1 0,5) d0 )= 1171,50 mm n1 = 3 p1 = 70,00 mm e1b = 45,00 + 35,00 = 80,00 mm fybw = 235,00 N/mm fubw = 360,00 N/mm
Joint shear resistance
Shear resistance of the joint VRd = 146,18 kN Failure Mode: Beam web in bearing
5.2.5
Requirements to ensure the safety of the shear design rules
(1)
VRd < min( VRd 1 ; VRd 7 ) VRd = 146,18 kN min( VRd 1 ; VRd 7 ) = 178,28 kN VRd 1 = 178,28 kN VRd 7 = 776,97 kN ok,
(2)
n2 = 1 :
Fb,hor,Rd min ( Fv,Rd ; VRd 7 )
VRd 7 = 776,97 kN Fv,Rd = 94,08 kN
for the beam web : Fb,hor,Rd = 77,45 kN = 0,43 min ( Fv,Rd ; VRd 7 ) = min ( 94,08 ; 334,09 ) = 94,08 kN ok,
One of the two inequalities is satisfied, ok, (3) VRd = VRd 8 ok,
5.2.6
Design check
Applied shear force: Shear resistance:
VSd VRd
= 100 kN = 146,18 kN
Design O,K,
5.2.7
Joint tying resistance
Bolts in shear
Nu 1 = n Fv,u = 352,80 kN
n=3
Fv ,u = v f ub A = 117,60 kN
A = As = 245,00 mm v = 0,6
Fin plate in bearing
Nu 2 = n Fb,u, hor = 409,09 kN n=3 Fb ,u ,hor = k 1 b f up d t p = 136,36 kN
b
= min (1 , 2 , 1) = 0,75
1 2
= e2 / 3d0 = 0,75 = fub / fup = 2,22 = min (2,8 e1 / d0 1,7 ; 1,4 p1 / d0 1,7 ; 2,5) = min (4,03 ; 2,75 ; 2,5) = 2,5
k1
d tp fub fup
= 20,00 mm = 10,00 mm = 800,00 N/mm = 360,00 N/mm
Fin plate in tension : gross section
Nu 3 = tp hp f up = 828,00 kN
Fin plate in tension : net section
Nu 4 = 0,9 Anet,p f up = 531,36 kN
Anet,p = tp hp d0 n1 tp = 1640,00 mm n1 = 3 hp = 230,00 mm tp = 10,00 mm d0 = 22,00 mm
Beam web in bearing
Nu 5 = n Fb,u, hor = 290,45 kN n=3 Fb ,u ,hor = k 1 b f ubw d t bw = 96,82 kN
b
= min (1 , 2 , 1) = 0,75 1 = e2b / 3d0 = 0,75 2 = fub / fubw = 2,22 = min (1,4 p1 / d0 1,7 ; 2,5) = min (2,75 ; 2,5) = 2,5 = 20,00 mm = 7,10 mm = 800,00 N/mm = 360,00 N/mm
k1 d tbw fub fubw
Beam web in tension : gross section
Nu 6 = tbw hbw f ubw = 587,88 kN
Beam web in tension : net section
Nu 7 = 0,9 Anet,bw f ubw = 377,27 kN
Anet,bw = tbw hbw d0 n1 tbw = 1164,40 mm tbw = 7,10 mm hbw = 230,00 mm n1 = 3 d0 = 22,00 mm
Supporting member in bending
,
Welds
Conditions for full-strength behaviour of the welds are fulfilled
Joint tying resistance
Tying resistance of the joint Nu = 290,45 kN Failure mode : Beam web in bearing Based on paper Jaspart J.P., Renkin S., Guillaume M.L.: European Recommendations for the Design of Simple Joints in Steel Structures, 1st draft of a forthcoming publication of the Technical Committee 10 Joints and Connections of the European Convention of Constructional Steelwork (ECCS TC10) prepared at the University of Lige, September 2003.
