Calculations of the connection: Column base / Circular
tube
General Information
Column: C 323.9x12.5
Material: S 355
Db1 = 323.9 mm Column diameter
tp1 = 12.5 mm Section thickness
Ab = 122.3 cm2 Section area
Iby = 14847 cm4 Moment of inertia
Wpl = 1212.74 cm3 Plastic section modulus
W= 916.48 cm3 Elastic section modulus
fyb = 355 MPa Resistance
Wedge: HEB 200
Material: S 235
Hb1 = 200 mm Wedge height
Wb1 = 200 mm Wedge width
twb1 = 9 mm Web thickness
tFb1 = 15 mm Flange thickness
Ab = 78.1 cm2 Section area
Iby = 5696 cm4 Moment of inertia
fyb = 235 MPa Resistance
Endplate:
Material: S 235
dp = 624 mm Plate diameter
tp = 40 mm Plate thickness
fyp = 235 MPa Resistance
Stiffeners:
Material: S 235
h= 350 mm Height of stiffener
h1 = 150 mm Lower height
l1 = 50 mm Length of upper part of the stiffener
es = 19 mm Shift
ts 20 mm Thicknes of stiffeners
Anchorage:
Class: 5.6
Type: Plate
d= 36 mm Diameter
h= 1000 mm Length of anchor bolt
heff = 900 mm Effective length of an anchor bolt
n= 6 Number of anchor bolts
e1 = 75.02 mm Distance from profile to bolts
e2 = 75.02 mm Distance from bolts to edge of endplate
p2 = 60 Deg Angle between bolts
Welds:
a= 6 mm Weld thickness
asv = 6 mm Thickness of weld between column and stiffeners
ash = 6 mm Thickness of weld between column base plate and stiffener
asd = 4 mm Thickness of weld between column base and wedge
Foundation:
Hf = 1750 mm Foundation height
Wf = 1500 mm Foundation width
Lf = 1500 mm Foundation length
tg = 50 mm Thickness of leveling layer (grout)
fck.f = 25 MPa Characteristic resistance - concrete
fck.g = 100 MPa Characteristic resistance - grout
YC = 1.5 Partial safety factor
Cf.g = 0.5 Friction coefficient - grout
Safety factors:
γM0 = 1
γM1 = 1
γM2 = 1.25
γM3 = 1.25
Case: Case 4:
Nodal forces:
N= -710 kN Axial force
M= 7 kNm Bending moment
V= 60 kN Shear force
Capacity verification
Results of calculations
Resistances of components
Ft,Rd = 294.12 kN Tension resistance of single anchor bolt [tab.3.4]
Ft,Rd,p = 349.04 kN Resistance for pulling out of concrete EN 1993-1-8 [6.2.6.12]
Fvj,Rd= 142.5 kN Total shear capacity of anchor bolt EN 1993-1-8 [6.2.2(7)]
Mc,Rd = 500.79 kNm Design resistance of the section for EN 1993-1-1 [6.2.5]
bending
Class: 1 Section class EN 1993-1-1 [5.5.2]
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Compression resistance
fcd = 66.67 MPa Compression capacity EN 1992-1-1 [3.1.6]
c= 34.25 mm Additional bearing width [6.2.5(4)]
βj = 0.67 Reduction coefficient [6.2.5(7)]
fy = 235 MPa Resistance endplate
fj = 106.84 MPa Bearing resistance under endplate [6.2.5(7)]
Frdu = 6357.04 kN Concentrated design resistance force [6.2.5(7)]
fjd = 133.33 MPa Capacity of node [6.2.5(7)]
Acn = 1190.29 cm2 Bearing area under column [6.2.8.2(1)]
Compression capacity of node:
Nc,Rd = Fc = Acn* fjd
Nc,Rd = 15870.5 kN
Verification of compression capacity :
N / Nc,Rd = 0.04 < 1.0 The condition is satisfied (4%)
Bending resistance
Calculation case:
Case 4: Compression under both side
e= -9.86 mm Eccentricity
Z= 311.4 mm Internal forces level arm [tab. 6.7]
beff = 236.98 mm Effective length determined for external row of
bolts
omega = 1 Reduction coefficient [6.2.6.2]
Ft,wc,Rd = 1050.55 kN Tension capacity of web [6.2.6.3]
FC,fc,Rd = 1964.86 kN Compression capacity of flange and web [6.2.6.7]
FT,l,Rd = 588.24 kN Tension capacity of left side of node [6.2.8.3]
FTr,Rd = 588.24 kN Tension capacity of right side of node [6.2.8.3]
FCl,Rd = 1964.86 kN Compression capacity of left side of node [6.2.8.3]
FCr,Rd = 1964.86 kN Compression capacity of right side of node [6.2.8.3]
MRd1 = 41.36 kNm Bending resistance of left side of node [tab. 6.7]
MRd2 = 36.44 kNm Bending resistance of right side of node [tab. 6.7]
MRd = 36.44 kNm Bending resistance of node
Verification of bending capacity :
N / Ft,wc,Rd = 0.68 < 1.0 The condition is satisfied (68%)
M / MRd = 0.19 < 1.0 The condition is satisfied (19%)
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Shear verification
Fv,Rd = 142.5 kN Shear capacity of anchor bolt [6.2.2(7)]
Fb,Rd = 664.84 kN Bearing capacity of anchor bolt [tab.3.4]
Fvj,Rd = 142.5 kN Total shear capacity of anchor bolt
Ff,Rd = 355 kN Slip capacity of node [6.2.2(6)]
Fv,Rd1,wg,y = 700 kN Shear resistance of wedge - bearing capacity of
concrete
Fv,Rd2,wg,y = 246.09 kN Shear resistance of welds joining wedge to
endplate
Fv,Rd,wg,y = 246.09 kN Wedge capacity
Fv,Rd,wg,y = min(Fv,Rd1,wg,y ,Fv,Rd2,wg,y )
Fv,Rd,wg,y = 246.09 kN
Shear capacity of connection:
Vj,Rd = n*Fvj,Rd + Ff,Rd + Fv,Rd,wg,y
Vj,Rd = 1456.11 kN
Verification of shear capacity :
V/Vj,Rd = 0.04 < 1.0 The condition is satisfied (4%)
Welds control
Aw = 76.15 cm2 Total area of welds
Awy = 51.99 cm2 Area of vertical welds
Iwy = 11010.61 cm4 Moment of inertia of welds about Y axis
σperp = τperp 73.48 MPa Perpendicular stress in welds
=
τpar = 11.54 MPa Parallel stress in welds
β w = 0.8 Appropriate correlation factor [tab.4.1]
Sqrt [(σperp2 + 3(τperp2 + τ par2)] <= fu / (βw * γM2); 148.31 MPa < 510 MPa The condition is satisfied (29%)
σperp <= 0,9*fu / γM2; 73.48 MPa < 367.2 MPa The condition is satisfied (20%)
Additional condition
N/Nc,Rd = 0.07 < 1.0 The condition is satisfied
M/Mc,Rd = 0.01 < 1.0 The condition is satisfied
V/Vc,Rd = 0.02 < 1.0 The condition is satisfied
Final verification
Connection verification:
Verification of connection FEd – force FRd - capacity Ratio FEd/FRd
Compression capacity N = -710 kN N c,Rd = 15870.5 kN 4%
Bending capacity M = 7 kNm Mj,Rd = 36.44 kNm 19%
Shear capacity V = 60 kN Vj,Rd = 1456.11 kN 4%
Welds 148.31 MPa 510 MPa 29%
Compression capacity of column N = -710 kN Nc,Rd = 9924.38 kN 7%
Bending capacity of column M = 7 kNm Mc,Rd = 500.79 kNm 1%
Tension resistance of column web N = -710 kN Ft,wc,Rd = 1050.55 kN 68%
Shear capacity of column V = 60 kN Vc,Rd = 2670.18 kN 2%
The connection conforms to the (EN 1993-1-8:2005/AC:2009)
