Calculations of the connection: Column base
General Information
Column: IPE 330
Material: S 235
Hb1 = 330 mm Column height
Wb1 = 160 mm Column width
twb1 = 7.5 mm Web thickness
tFb1 = 11.5 mm Flange thickness
Ab = 62.61 cm2 Section area
Iby = 11766.9 cm4 Moment of inertia
Wpl = 804.4 cm3 Plastic section modulus
W= 713.15 cm3 Elastic section modulus
fyb = 235 MPa Resistance
Endplate:
Material: S 235
hp = 450 mm Plate height
bp = 450 mm Plate width
tp = 22 mm Plate thickness
fyp = 235 MPa Resistance
Stiffeners:
Material: S 235
h= 150 mm Height of stiffener
h1 = 10 mm Lower height
l1 = 20 mm Length of upper part of the stiffener
es = 10 mm Shift
wst = 8 mm Thickness of web stiffeners
fst = 12 mm Thickness of flange stiffeners
Anchorage:
Class: 8.8
Type: Hook
d= 30 mm Diameter
h= 1000 mm Length of anchor bolt
heff = 800 mm Effective length of anchor bolt
nc = 2 Number of columns
nr = 1 Number of rows
n= 2 Number of anchor bolts
d1 = 90 mm Distance to upper and lower edge of column base
d2 = 90 mm Distance to left and right edge of column base
a1;b1;c1 = - mm Row spacing
a2;b2;c2 = 270; mm Column spacing
Welds:
aw = 6 mm Thickness of welds near web
af = 6 mm Thickness of welds near flanges
asv = 6 mm Thickness of welds between column and stiffeners
ash = 6 mm Thickness of welds between column base and stiffener
Foundation:
Hf = 1200 mm Foundation height
Wf = 1000 mm Foundation width
Lf = 1000 mm Foundation length
tg = 30 mm Thickness of leveling layer (grout)
fck.f = 25 MPa Characteristic resistance - concrete
fck.g = 30 MPa Characteristic resistance - grout
YC = 1.5 Partial safety factor
Cf.g = 0.5 Friction coefficient - grout
Safety factors:
M0 = 1
M1 = 1
M2 = 1.25
M3 = 1.25
Case: Case 1:
Nodal forces:
N= 251 kN Axial force
Mz = 0 kNm Bending moment along web
My = 0 kNm Bending moment along flange
Vz = 67 kN Shear force along web
Vy = -109 kN Shear force along flange
Capacity verification
Results of calculations
Resistances of components
Ft,Rd = 323.14 kN Tension resistance of a single anchor bolt [tab.3.4]
Ft,Rd,p = 203.06 kN Resistance for pulling out of concrete EN-1992-1-1 point 8.4.2
Fvj,Rd= 112.19 kN Total shear capacity of anchor bolt EN 1993-1-8 [6.2.2]
Mc,Rd = 191.95 kNm Design moment resistance of the section EN 1993-1-1 [6.2.5]
Class: 1 Section class EN 1993-1-1 [5.5.2]
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Tension resistance
Bending of endplate
= 1 Reduction coefficient [3.6.1.(3)]
leff = 0 mm Effective length for area near left flange of column
m= 0 mm Distance from bolt to stiffener edge [6.2.6.5]
Mpl,Rd,1 = 0 kNm Plastic capacity of endplate near left flange of
column
FT1-2,Rd1 = 0 kN Capacity of area near left flange of column [tab.6.2]
leff = 0 mm Effective length for area near web of column
m= 0 mm Distance from bolt to stiffener edge [6.2.6.5]
Mpl,Rd,2 = 0 kNm Plastic capacity of endplate near web of column
FT1-2,Rd2 = 0 kN Capacity of area near web of column [tab.6.2]
leff = 0 mm Effective length for area near right flange of
column
m= 0 mm Distance from bolt to stiffener edge [6.2.6.5]
Mpl,Rd,3 = 0 kNm Plastic capacity of endplate near right flange of
column
FT1-2,Rd3 = 0 kN Capacity of area near right flange of column [tab.6.2]
Resistances of anchor bolts
FT,Rd = 203.06 kN Resistance of a single anchor bolt
FT,Rd1 = 0 kN Sum of resistances of anchor bolts under left flange of column
FT,Rd2 = 0 kN Sum of resistances of anchor bolts under web of column
FT,Rd3 = 0 kN Sum of resistances of anchor bolts under right flange of column
Capacity of endplate
Ft.pl.1 = 0 kN Capacity of plate near left flange of column
Ft.pl.2 = 0 kN Capacity of plate near web of column
Ft.pl.3 = 0 kN Capacity of plate near right flange of column
Tension capacity of connection for axial force
Nj,Rd = Ft,pl,n
Nj,Rd = 0 kN
Verification of tension capacity :
N / Nj,Rd = 0 < 1.0 The condition is satisfied (0%)
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Shear verification
Shear in web plane
Fv,Rd = 112.19 kN Shear capacity of anchor bolt [6.2.2(7)]
Fb,Rd = 432 kN Bearing capacity of anchor bolt [tab.3.4]
Fvj,Rd = 112.19 kN Total shear capacity of anchor bolt
Ff,Rd = 0 kN Slip capacity of node [6.2.2(6)]
Shear capacity of connection:
Vj,Rdz = n*Fvj,Rd + Ff,Rd + Fv,Rd,wg,z
Vj,Rdz= 224.39 kN
Verification of shear capacity :
Vz / Vj,Rdz= 0.3 <1.0 The condition is satisfied (30%)
Shear in a plane of flanges
Fv,Rd = 112.19 kN Shear capacity of anchor bolt [6.2.2(7)]
Fb,Rd = 432 kN Bearing capacity of anchor bolt [tab.3.4]
Fvj,Rd = 112.19 kN Total shear capacity of anchor bolt
Ff,Rd = 0 kN Slip capacity of node [6.2.2(6)]
Shear capacity of connection:
Vj,Rdy = n*Fvj,Rd + Ff,Rd + Fv,Rd,wg,y
Vj,Rdy= 224.39 kN
Verification of shear capacity :
Vy / Vj,Rdy= 0.49 < 1.0 The condition is satisfied (49%)
Biaxial shear verification:
Vy / Vj,Rdy + Vz / Vj,Rdz= 0.78 < 1.0 The condition is satisfied (78%)
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Welds control
Horizontal weld check
Forces applied along flanges
Aw = 196.5 cm2 Total area of welds
Awz = 98.52 cm2 Area of horizontal welds
Iwy = 32382.78 cm4 Moment of inertia of welds about Y axis
perp = perp = 6.8 MPa Perpendicular stress in welds
par = 8.12 MPa Parallel stress in welds
w = 0.8 Appropriate correlation factor [tab.4.1]
Sqrt[(perp2 + 3(perp2 + par2)]<= fu/(w * M2); 19.57 MPa < 360 MPa The condition is satisfied (5%)
perp <= 0,9*fu / M2;6.8 MPa < 259.2 MPa The condition is satisfied (3%)
Forces applied along flanges
Aw = 196.5 cm2 Total area of welds
Awy = 97.98 cm2 Area of vertical welds
Iwz = 15916.82 cm4 Moment of inertia of welds about Z axis
perp = perp = 6.8 MPa Perpendicular stress in welds
par = 9.9 MPa Parallel stress in welds
w = 0.8 Appropriate correlation factor [tab.4.1]
Sqrt[(perp2 + 3(perp2 + par2)]<= fu/(w * M2); 21.89 MPa < 360 MPa The condition is satisfied (6%)
perp <= 0,9*fu / M2;6.8 MPa < 259.2 MPa The condition is satisfied (3%)
Vertical weld check
Forces applied along web
Averz = 54 cm2 Area of vertical welds
Nfz = 94.5 kN Force from column on vertical welds
perp = perp = 14.81 MPa Perpendicular stress in welds
par = 17.5 MPa Parallel stress in welds
Sqrt[(perp2 + 3(perp2 + par2)]<= fu/(w * M2); 42.39 MPa < 360 MPa The condition is satisfied (12%)
perp <= 0,9*fu / M2;14.81 MPa < 259.2 MPa The condition is satisfied (6%)
Forces applied along flages
Avery = 54 cm 2 Area of vertical welds
Nfy = 94.5 kN Force from column on vertical welds
perp = perp = 17.96 MPa Perpendicular stress in welds
par = 17.5 MPa Parallel stress in welds
Sqrt[(perp2 + 3(perp2 + par2)]<= fu/(w * M2); 47 MPa < 360 MPa The condition is satisfied (13%)
perp <= 0,9*fu / M2;17.96 MPa < 259.2 MPa The condition is satisfied (7%)
Additional condition
Nt,Rd = A * fy / M0
N / Nt,Rd = 0.09 < 1.0 The condition is satisfied
V / Vc,Rd = 0.13 < 1.0 The condition is satisfied
Final verification
Connection verification:
Verification of connection FEd force FRd - capacity Ratio FEd/FRd
Tension capacity N = 251 kN N j,Rd = 0 kN 0%
Shear capacity Vz = 67 kN Vj,Rdz = 224.39 kN 30 %
Vy = -109 kN Vj,Rdy = 224.39 kN 49 %
Horizontal welds - force in web plane 19.57 MPa 360 MPa 5%
Horizontal welds - force in flanges plane 21.89 MPa 360 MPa 6%
Vertical welds - force in web plane 42.39 MPa 360 MPa 12 %
Vertical welds - force in flanges plane 47 MPa 360 MPa 13 %
Tension capacity of column N = 251 kN Nt,Rd = 2674.45 kN 9%
Shear capacity of column V = 67 kN Vc,Rd = 526.55 kN 13 %
Biaxial shear Vz = 67 kN Vj,Rdz = 224.39 kN 78 %
Vy = -109 kN Vj,Rdy = 224.39 kN
The connection conforms to the (EN 1993-1-8:2005/AC:2009)
Additional remarks
