![Autodesk Robot Structural Analysis Professional 2015
Design of fixed beam-to-column connection
EN 1993-1-8:2005/AC:2009
Ratio
0.68
GENERAL
Connection no.: 30
Connection name: Узел рамы
Structure node: 127
Structure bars: 118, 122
GEOMETRY
COLUMN
Section: ДК 25х1
Bar no.: 118
= -90.0 [Deg] Inclination angle
hc = 246 [mm] Height of column section
bfc = 249 [mm] Width of column section
twc = 8 [mm] Thickness of the web of column section
tfc = 12 [mm] Thickness of the flange of column section
Ac = 77.52 [cm2] Cross-sectional area of a column
Ixc = 8917.12 [cm4] Moment of inertia of the column section
Material: С255
fyc = 250.00 [MPa] Resistance
BEAM
Section: ДК 26x2
Bar no.: 122
= -0.0 [Deg] Inclination angle
hb = 258 [mm] Height of beam section
bf = 260 [mm] Width of beam section
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![twb = 9 [mm] Thickness of the web of beam section
tfb = 14 [mm] Thickness of the flange of beam section
rb = 16 [mm] Radius of beam section fillet
rb = 16 [mm] Radius of beam section fillet
Ab = 93.19 [cm2] Cross-sectional area of a beam
Ixb = 11700.00 [cm4] Moment of inertia of the beam section
Material: С255
fyb = 250.00 [MPa] Resistance
BOLTS
The shear plane passes through the UNTHREADED portion of the bolt.
d = 20 [mm] Bolt diameter
Class = 8.8 Bolt class
FtRd = 141.12 [kN] Tensile resistance of a bolt
nh = 2 Number of bolt columns
nv = 7 Number of bolt rows
h1 = 50 [mm] Distance between first bolt and upper edge of front plate
Horizontal spacing ei = 125 [mm]
Vertical spacing pi = 135;55;51;125;55;70 [mm]
PLATE
hp = 643 [mm] Plate height
bp = 249 [mm] Plate width
tp = 20 [mm] Plate thickness
Material: С345
fyp = 320.00 [MPa] Resistance
LOWER STIFFENER
wd = 249 [mm] Plate width
tfd = 14 [mm] Flange thickness
hd = 275 [mm] Plate height
twd = 10 [mm] Web thickness
ld = 300 [mm] Plate length
= 42.5 [Deg] Inclination angle
Material: С255
fybu = 240.00 [MPa] Resistance
UPPER STIFFENER
hu = 50 [mm] Stiffener height
twu = 16 [mm] Thickness of vertical stiffener
lu = 300 [mm] Length of vertical stiffener
Material: С255
fyu = 240.00 [MPa] Resistance
COLUMN STIFFENER
Upper
hsu = 234 [mm] Stiffener height
bsu = 121 [mm] Stiffener width
thu = 10 [mm] Stiffener thickness
Material: С255
fysu = 240.00 [MPa] Resistance
Lower
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![hsd = 234 [mm] Stiffener height
bsd = 121 [mm] Stiffener width
thd = 10 [mm] Stiffener thickness
Material: С255
fysu = 240.00 [MPa] Resistance
PLATE STRENGTHENING COLUMN WEB
Typ: unilateral
ha = 480 [mm] Plate length
wa = 180 [mm] Plate width
ta = 12 [mm] Plate thickness
Material: С255
fya = 240.00 [MPa] Resistance
FILLET WELDS
aw = 8 [mm] Web weld
af = 10 [mm] Flange weld
as = 8 [mm] Stiffener weld
afd = 8 [mm] Horizontal weld
ap1 = 6 [mm] Horizontal weld
ap2 = 6 [mm] Vertical weld
MATERIAL FACTORS
M0 = 1.00 Partial safety factor [2.2]
M1 = 1.00 Partial safety factor [2.2]
M2 = 1.25 Partial safety factor [2.2]
M3 = 1.25 Partial safety factor [2.2]
LOADS
Ultimate limit state
Case: Manual calculations.
Mb1,Ed = 136.65 [kN*m] Bending moment in the right beam
Vb1,Ed = 148.53 [kN] Shear force in the right beam
Nb1,Ed = -26.80 [kN] Axial force in the right beam
Mc2,Ed = -50.07 [kN*m] Bending moment in the upper column
Vc2,Ed = -29.77 [kN] Shear force in the upper column
Nc2,Ed = -255.09 [kN] Axial force in the upper column
RESULTS
BEAM RESISTANCES
COMPRESSION
Ab = 93.19 [cm2] Area EN1993-1-1:[6.2.4]
Ncb,Rd = Ab fyb / M0
Ncb,Rd = 2329.75 [kN] Design compressive resistance of the section EN1993-1-1:[6.2.4]
SHEAR
Avb = 64.02 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
Vcb,Rd = Avb (fyb / 3) / M0
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![Vcb,Rd = 924.12 [kN] Design sectional resistance for shear EN1993-1-1:[6.2.6.(2)]
Vb1,Ed / Vcb,Rd ≤ 1,0 0.16 < 1.00 verified (0.16)
BENDING - PLASTIC MOMENT (WITHOUT BRACKETS)
Wplb = 978.26 [cm3] Plastic section modulus EN1993-1-1:[6.2.5.(2)]
Mb,pl,Rd = Wplb fyb / M0
Mb,pl,Rd = 244.56 [kN*m] Plastic resistance of the section for bending (without stiffeners) EN1993-1-1:[6.2.5.(2)]
BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT
Wpl = 2652.81 [cm3] Plastic section modulus EN1993-1-1:[6.2.5]
Mcb,Rd = Wpl fyb / M0
Mcb,Rd = 663.20 [kN*m] Design resistance of the section for bending EN1993-1-1:[6.2.5]
FLANGE AND WEB - COMPRESSION
Mcb,Rd = 663.20 [kN*m] Design resistance of the section for bending EN1993-1-1:[6.2.5]
hf = 517 [mm] Distance between the centroids of flanges [6.2.6.7.(1)]
Fc,fb,Rd = Mcb,Rd / hf
Fc,fb,Rd = 1283.40 [kN] Resistance of the compressed flange and web [6.2.6.7.(1)]
WEB OR BRACKET FLANGE - COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE
Bearing:
= 0.0 [Deg] Angle between the front plate and the beam
= 42.5 [Deg] Inclination angle of the bracket plate
beff,c,wb = 197 [mm] Effective width of the web for compression [6.2.6.2.(1)]
Avb = 28.52 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 0.82 Reduction factor for interaction with shear [6.2.6.2.(1)]
com,Ed = 119.09 [MPa] Maximum compressive stress in web [6.2.6.2.(2)]
kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)]
As = 18.91 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4]
Fc,wb,Rd1 = [ kwc beff,c,wb twb fyb / M0 + As fyb / M0] cos() / sin( - )
Fc,wb,Rd1 = 868.43 [kN] Beam web resistance [6.2.6.2.(1)]
Buckling:
dwb = 199 [mm] Height of compressed web [6.2.6.2.(1)]
p = 0.72 Plate slenderness of an element [6.2.6.2.(1)]
= 1.00 Reduction factor for element buckling [6.2.6.2.(1)]
s = 2.61 Stiffener slenderness EN1993-1-1:[6.3.1.2]
= 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2]
Fc,wb,Rd2 = [ kwc beff,c,wb twb fyb / M1 + As fyb / M1] cos() / sin( - )
Fc,wb,Rd2 = 868.30 [kN] Beam web resistance [6.2.6.2.(1)]
Resistance of the bracket flange
Fc,wb,Rd3 = bb tb fyb / (0.8*M0)
Fc,wb,Rd3 = 1137.50 [kN] Resistance of the bracket flange [6.2.6.7.(1)]
Final resistance:
Fc,wb,Rd,low = Min (Fc,wb,Rd1 , Fc,wb,Rd2 , Fc,wb,Rd3)
Fc,wb,Rd,low = 868.30 [kN] Beam web resistance [6.2.6.2.(1)]
COLUMN RESISTANCES
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![WEB PANEL - SHEAR
Mb1,Ed = 136.65 [kN*m] Bending moment (right beam) [5.3.(3)]
Mb2,Ed = 0.00 [kN*m] Bending moment (left beam) [5.3.(3)]
Vc1,Ed = 0.00 [kN] Shear force (lower column) [5.3.(3)]
Vc2,Ed = -29.77 [kN] Shear force (upper column) [5.3.(3)]
z = 486 [mm] Lever arm [6.2.5]
Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2
Vwp,Ed = 266.29 [kN] Shear force acting on the web panel [5.3.(3)]
Avs = 17.76 [cm2] Shear area of the column web EN1993-1-1:[6.2.6.(3)]
Avp = 14.40 [cm2] Area of the web stiffening plate EN1993-1-1:[6.2.6.(3)]
Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
ds = 523 [mm] Distance between the centroids of stiffeners [6.2.6.1.(4)]
Mpl,fc,Rd = 2.24 [kN*m] Plastic resistance of the column flange for bending [6.2.6.1.(4)]
Mpl,stu,Rd = 1.49 [kN*m] Plastic resistance of the upper transverse stiffener for bending [6.2.6.1.(4)]
Mpl,stl,Rd = 1.49 [kN*m] Plastic resistance of the lower transverse stiffener for bending [6.2.6.1.(4)]
Vwp,Rd = 0.9 ( Avs*fy,wc+Avp*fya ) / (3 M0) + Min(4 Mpl,fc,Rd / ds , (2 Mpl,fc,Rd + Mpl,stu,Rd + Mpl,stl,Rd) / ds)
Vwp,Rd = 424.57 [kN] Resistance of the column web panel for shear [6.2.6.1]
Vwp,Ed / Vwp,Rd ≤ 1,0 0.63 < 1.00 verified (0.63)
WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE
Bearing:
twc = 12 [mm] Effective thickness of the column web [6.2.6.2.(6)]
beff,c,wc = 187 [mm] Effective width of the web for compression [6.2.6.2.(1)]
Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 0.78 Reduction factor for interaction with shear [6.2.6.2.(1)]
com,Ed = 90.79 [MPa] Maximum compressive stress in web [6.2.6.2.(2)]
kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)]
As = 24.10 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4]
Fc,wc,Rd1 = kwc beff,c,wc twc fyc / M0 + As fys / M0
Fc,wc,Rd1 = 1017.23 [kN] Column web resistance [6.2.6.2.(1)]
Buckling:
dwc = 206 [mm] Height of compressed web [6.2.6.2.(1)]
p = 0.54 Plate slenderness of an element [6.2.6.2.(1)]
= 1.00 Reduction factor for element buckling [6.2.6.2.(1)]
s = 2.82 Stiffener slenderness EN1993-1-1:[6.3.1.2]
s = 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2]
Fc,wc,Rd2 = kwc beff,c,wc twc fyc / M1 + As s fys / M1
Fc,wc,Rd2 = 1017.23 [kN] Column web resistance [6.2.6.2.(1)]
Final resistance:
Fc,wc,Rd,low = Min (Fc,wc,Rd1 , Fc,wc,Rd2)
Fc,wc,Rd = 1017.23 [kN] Column web resistance [6.2.6.2.(1)]
WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM TOP FLANGE
Bearing:
twc = 12 [mm] Effective thickness of the column web [6.2.6.2.(6)]
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![beff,c,wc = 181 [mm] Effective width of the web for compression [6.2.6.2.(1)]
Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 0.79 Reduction factor for interaction with shear [6.2.6.2.(1)]
com,Ed = 90.79 [MPa] Maximum compressive stress in web [6.2.6.2.(2)]
kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)]
As = 24.10 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4]
Fc,wc,Rd1 = kwc beff,c,wc twc fyc / M0 + As fys / M0
Fc,wc,Rd1 = 1009.20 [kN] Column web resistance [6.2.6.2.(1)]
Buckling:
dwc = 206 [mm] Height of compressed web [6.2.6.2.(1)]
p = 0.53 Plate slenderness of an element [6.2.6.2.(1)]
= 1.00 Reduction factor for element buckling [6.2.6.2.(1)]
s = 2.82 Stiffener slenderness EN1993-1-1:[6.3.1.2]
s = 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2]
Fc,wc,Rd2 = kwc beff,c,wc twc fyc / M1 + As s fys / M1
Fc,wc,Rd2 = 1009.20 [kN] Column web resistance [6.2.6.2.(1)]
Final resistance:
Fc,wc,Rd,upp = Min (Fc,wc,Rd1 , Fc,wc,Rd2)
Fc,wc,Rd,upp = 1009.20 [kN] Column web resistance [6.2.6.2.(1)]
GEOMETRICAL PARAMETERS OF A CONNECTION
EFFECTIVE LENGTHS AND PARAMETERS - COLUMN FLANGE
Nr m mx e ex p leff,cp leff,nc leff,1 leff,2 leff,cp,g leff,nc,g leff,1,g leff,2,g
1 49 - 62 - 74 255 308 255 308 0 0 0 0
2 49 - 62 - 55 311 284 284 284 210 174 174 174
3 49 - 62 - 53 311 275 275 275 106 53 53 53
4 49 - 62 - 88 311 275 275 275 176 88 88 88
5 49 - 62 - 90 311 275 275 275 180 90 90 90
6 49 - 62 - 63 311 275 275 275 125 63 63 63
7 49 - 62 - 70 311 318 311 318 225 215 215 215
EFFECTIVE LENGTHS AND PARAMETERS - FRONT PLATE
Nr m mx e ex p leff,cp leff,nc leff,1 leff,2 leff,cp,g leff,nc,g leff,1,g leff,2,g
1 45 - 62 - 74 286 364 286 364 216 271 216 271
2 49 - 62 - 55 308 282 282 282 209 173 173 173
3 49 - 62 - 53 308 273 273 273 106 53 53 53
4 49 - 62 - 88 308 273 273 273 176 88 88 88
5 49 - 62 - 90 308 273 273 273 180 90 90 90
6 49 - 62 - 63 308 273 273 273 125 63 63 63
7 49 - 62 - 70 308 273 273 273 224 172 172 172
m – Bolt distance from the web
mx – Bolt distance from the beam flange
e – Bolt distance from the outer edge
ex – Bolt distance from the horizontal outer edge
p – Distance between bolts
leff,cp – Effective length for a single bolt in the circular failure mode
leff,nc – Effective length for a single bolt in the non-circular failure mode
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![leff,1 – Effective length for a single bolt for mode 1
leff,2 – Effective length for a single bolt for mode 2
leff,cp,g – Effective length for a group of bolts in the circular failure mode
leff,nc,g – Effective length for a group of bolts in the non-circular failure mode
leff,1,g – Effective length for a group of bolts for mode 1
leff,2,g – Effective length for a group of bolts for mode 2
CONNECTION RESISTANCE FOR COMPRESSION
Nj,Rd = Min ( Ncb,Rd2 Fc,wb,Rd,low , 2 Fc,wc,Rd,low , 2 Fc,wc,Rd,upp )
Nj,Rd = 1736.60 [kN] Connection resistance for compression [6.2]
Nb1,Ed / Nj,Rd ≤ 1,0 0.02 < 1.00 verified (0.02)
CONNECTION RESISTANCE FOR BENDING
Ft,Rd = 141.12 [kN] Bolt resistance for tension [Table 3.4]
Bp,Rd = 200.86 [kN] Punching shear resistance of a bolt [Table 3.4]
Ft,fc,Rd – column flange resistance due to bending
Ft,wc,Rd – column web resistance due to tension
Ft,ep,Rd – resistance of the front plate due to bending
Ft,wb,Rd – resistance of the web in tension
Ft,fc,Rd = Min (FT,1,fc,Rd , FT,2,fc,Rd , FT,3,fc,Rd) [6.2.6.4] , [Tab.6.2]
Ft,wc,Rd = beff,t,wc twc fyc / M0 [6.2.6.3.(1)]
Ft,ep,Rd = Min (FT,1,ep,Rd , FT,2,ep,Rd , FT,3,ep,Rd) [6.2.6.5] , [Tab.6.2]
Ft,wb,Rd = beff,t,wb twb fyb / M0 [6.2.6.8.(1)]
RESISTANCE OF THE BOLT ROW NO. 1
Ft1,Rd,comp - Formula Ft1,Rd,comp Component
Ft,fc,Rd(1) = 185.90 185.90 Column flange - tension
Ft,wc,Rd(1) = 579.06 579.06 Column web - tension
Ft,ep,Rd(1) = 282.24 282.24 Front plate - tension
Bp,Rd = 401.72 401.72 Bolts due to shear punching
Vwp,Rd/ = 424.57 424.57 Web panel - shear
Fc,wc,Rd = 1017.23 1017.23 Column web - compression
Fc,fb,Rd = 1283.40 1283.40 Beam flange - compression
Fc,wb,Rd = 868.30 868.30 Beam web - compression
Ft1,Rd = Min (Ft1,Rd,comp) 185.90 Bolt row resistance
RESISTANCE OF THE BOLT ROW NO. 2
Ft2,Rd,comp - Formula Ft2,Rd,comp Component
Ft,fc,Rd(2) = 202.82 202.82 Column flange - tension
Ft,wc,Rd(2) = 619.91 619.91 Column web - tension
Ft,ep,Rd(2) = 282.24 282.24 Front plate - tension
Ft,wb,Rd(2) = 635.39 635.39 Beam web - tension
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![Ft,wc,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 658.11 - 238.67 419.44 Column web - tension - group
Ft,fc,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 229.57 - 238.67 -9.10 Column flange - tension - group
Ft,wc,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 658.11 - 238.67 419.44 Column web - tension - group
Ft,ep,Rd(4 + 3) - ∑3
3 Ftj,Rd = 368.71 - 35.85 332.86 Front plate - tension - group
Ft,wb,Rd(4 + 3) - ∑3
3 Ftj,Rd = 317.25 - 35.85 281.40 Beam web - tension - group
Ft,ep,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 653.01 - 238.67 414.34 Front plate - tension - group
Ft,wb,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 707.05 - 238.67 468.38 Beam web - tension - group
Ft,ep,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 653.01 - 238.67 414.34 Front plate - tension - group
Ft,wb,Rd(4 + 3 + 2) - ∑3
2 Ftj,Rd = 707.05 - 238.67 468.38 Beam web - tension - group
Ft4,Rd = Min (Ft4,Rd,comp) 0.00 Bolt row resistance
The remaining bolts are inactive (they do not carry loads) because resistance of one of the connection components
has been used up or these bolts are positioned below the center of rotation.
SUMMARY TABLE OF FORCES
Nr hj Ftj,Rd Ft,fc,Rd Ft,wc,Rd Ft,ep,Rd Ft,wb,Rd Ft,Rd Bp,Rd
1 554 185.90 185.90 579.06 282.24 - 282.24 401.72
2 419 202.82 202.82 619.91 282.24 635.39 282.24 401.72
3 364 35.85 200.42 607.56 282.24 614.92 282.24 401.72
4 313 - 200.42 607.56 282.24 614.92 282.24 401.72
5 188 - 200.42 607.56 282.24 614.92 282.24 401.72
6 133 - 200.42 607.56 282.24 614.92 282.24 401.72
7 63 - 208.25 652.69 282.24 614.92 282.24 401.72
CONNECTION RESISTANCE FOR BENDING Mj,Rd
Mj,Rd = ∑ hj Ftj,Rd
Mj,Rd = 200.81 [kN*m] Connection resistance for bending [6.2]
Mb1,Ed / Mj,Rd ≤ 1,0 0.68 < 1.00 verified (0.68)
CONNECTION RESISTANCE FOR SHEAR
v = 0.60 Coefficient for calculation of Fv,Rd [Table 3.4]
Lf = 0.95 Reduction factor for long connections [3.8]
Fv,Rd = 114.88 [kN] Shear resistance of a single bolt [Table 3.4]
Ft,Rd,max = 141.12 [kN] Tensile resistance of a single bolt [Table 3.4]
Fb,Rd,int = 92.84 [kN] Bearing resistance of an intermediate bolt [Table 3.4]
Fb,Rd,ext = 177.60 [kN] Bearing resistance of an outermost bolt [Table 3.4]
Nr Ftj,Rd,N Ftj,Ed,N Ftj,Rd,M Ftj,Ed,M Ftj,Ed Fvj,Rd
1 282.24 -3.83 185.90 126.50 122.68 158.42
2 282.24 -3.83 202.82 138.02 134.19 151.73
3 282.24 -3.83 35.85 24.39 20.57 185.67
4 282.24 -3.83 0.00 0.00 -3.83 185.67
5 282.24 -3.83 0.00 0.00 -3.83 185.67
6 282.24 -3.83 0.00 0.00 -3.83 185.67
7 282.24 -3.83 0.00 0.00 -3.83 185.67
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![Ftj,Rd,N – Bolt row resistance for simple tension
Ftj,Ed,N – Force due to axial force in a bolt row
Ftj,Rd,M – Bolt row resistance for simple bending
Ftj,Ed,M – Force due to moment in a bolt row
Ftj,Ed – Maximum tensile force in a bolt row
Fvj,Rd – Reduced bolt row resistance
Ftj,Ed,N = Nj,Ed Ftj,Rd,N / Nj,Rd
Ftj,Ed,M = Mj,Ed Ftj,Rd,M / Mj,Rd
Ftj,Ed = Ftj,Ed,N + Ftj,Ed,M
Fvj,Rd = Min (nh Fv,Ed (1 - Ftj,Ed/ (1.4 nh Ft,Rd,max), nh Fv,Rd , nh Fb,Rd))
Vj,Rd = nh ∑1
n Fvj,Rd [Table 3.4]
Vj,Rd = 1238.51 [kN] Connection resistance for shear [Table 3.4]
Vb1,Ed / Vj,Rd ≤ 1,0 0.12 < 1.00 verified (0.12)
WELD RESISTANCE
Aw = 213.60 [cm2] Area of all welds [4.5.3.2(2)]
Awy = 132.80 [cm2] Area of horizontal welds [4.5.3.2(2)]
Awz = 80.80 [cm2] Area of vertical welds [4.5.3.2(2)]
Iwy = 82311.12 [cm4] Moment of inertia of the weld arrangement with respect to the hor. axis [4.5.3.2(5)]
max=max = 36.10 [MPa] Normal stress in a weld [4.5.3.2(5)]
= = 36.10 [MPa] Stress in a vertical weld [4.5.3.2(5)]
II = 18.38 [MPa] Tangent stress [4.5.3.2(5)]
w = 0.85 Correlation coefficient [4.5.3.2(7)]
[max
2 + 3*(max
2)] ≤ fu/(w*M2) 72.21 < 348.24 verified (0.21)
[
2 + 3*(
2+II
2)] ≤ fu/(w*M2) 78.91 < 348.24 verified (0.23)
≤ 0.9*fu/M2 36.10 < 266.40 verified (0.14)
CONNECTION STIFFNESS
twash = 4 [mm] Washer thickness [6.2.6.3.(2)]
hhead = 14 [mm] Bolt head height [6.2.6.3.(2)]
hnut = 20 [mm] Bolt nut height [6.2.6.3.(2)]
Lb = 57 [mm] Bolt length [6.2.6.3.(2)]
k10 = 7 [mm] Stiffness coefficient of bolts [6.3.2.(1)]
STIFFNESSES OF BOLT ROWS
Nr hj k3 k4 k5 keff,j keff,j hj
keff,j
hj
2
1 554 0 0 17 0 0.00 0.00
2 419 4 2 11 1 4.58 191.87
3 364 1 1 3 0 1.36 49.53
4 313 2 1 5 1 1.88 58.67
5 188 2 1 6 1 1.15 21.56
6 133 2 1 4 0 0.58 7.69
7 63 5 3 11 1 0.80 4.97
Sum 10.35 334.30
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![keff,j = 1 / (∑3
5 (1 / ki,j)) [6.3.3.1.(2)]
zeq = ∑j keff,j hj
2 / ∑j keff,j hj
zeq = 323 [mm] Equivalent force arm [6.3.3.1.(3)]
keq = ∑j keff,j hj / zeq
keq = 3 [mm] Equivalent stiffness coefficient of a bolt arrangement [6.3.3.1.(1)]
Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 1.00 Transformation parameter [5.3.(7)]
z = 323 [mm] Lever arm [6.2.5]
k1 = 4 [mm] Stiffness coefficient of the column web panel subjected to shear [6.3.2.(1)]
k2 = Stiffness coefficient of the compressed column web [6.3.2.(1)]
Sj,ini = E zeq
2 / ∑i (1 / k1 + 1 / k2 + 1 / keq) [6.3.1.(4)]
Sj,ini = 36199.63 [kN*m] Initial rotational stiffness [6.3.1.(4)]
= 1.06 Stiffness coefficient of a connection [6.3.1.(6)]
Sj = Sj,ini / [6.3.1.(4)]
Sj = 34247.54 [kN*m] Final rotational stiffness [6.3.1.(4)]
Connection classification due to stiffness.
Sj,rig = 31357.65 [kN*m] Stiffness of a rigid connection [5.2.2.5]
Sj,pin = 1959.85 [kN*m] Stiffness of a pinned connection [5.2.2.5]
Sj,ini Sj,rig RIGID
WEAKEST COMPONENT:
COLUMN WEB PANEL - SHEAR
Connection conforms to the code Ratio 0.68
Стр. 11 из 11
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Сalculation of the сentral node
- 1. Autodesk Robot Structural Analysis Professional 2015 Design of fixed beam-to-column connection EN 1993-1-8:2005/AC:2009 Ratio 0.68 GENERAL Connection no.: 30 Connection name: Узел рамы Structure node: 127 Structure bars: 118, 122 GEOMETRY COLUMN Section: ДК 25х1 Bar no.: 118 = -90.0 [Deg] Inclination angle hc = 246 [mm] Height of column section bfc = 249 [mm] Width of column section twc = 8 [mm] Thickness of the web of column section tfc = 12 [mm] Thickness of the flange of column section Ac = 77.52 [cm2] Cross-sectional area of a column Ixc = 8917.12 [cm4] Moment of inertia of the column section Material: С255 fyc = 250.00 [MPa] Resistance BEAM Section: ДК 26x2 Bar no.: 122 = -0.0 [Deg] Inclination angle hb = 258 [mm] Height of beam section bf = 260 [mm] Width of beam section Стр. 1 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 2. twb = 9 [mm] Thickness of the web of beam section tfb = 14 [mm] Thickness of the flange of beam section rb = 16 [mm] Radius of beam section fillet rb = 16 [mm] Radius of beam section fillet Ab = 93.19 [cm2] Cross-sectional area of a beam Ixb = 11700.00 [cm4] Moment of inertia of the beam section Material: С255 fyb = 250.00 [MPa] Resistance BOLTS The shear plane passes through the UNTHREADED portion of the bolt. d = 20 [mm] Bolt diameter Class = 8.8 Bolt class FtRd = 141.12 [kN] Tensile resistance of a bolt nh = 2 Number of bolt columns nv = 7 Number of bolt rows h1 = 50 [mm] Distance between first bolt and upper edge of front plate Horizontal spacing ei = 125 [mm] Vertical spacing pi = 135;55;51;125;55;70 [mm] PLATE hp = 643 [mm] Plate height bp = 249 [mm] Plate width tp = 20 [mm] Plate thickness Material: С345 fyp = 320.00 [MPa] Resistance LOWER STIFFENER wd = 249 [mm] Plate width tfd = 14 [mm] Flange thickness hd = 275 [mm] Plate height twd = 10 [mm] Web thickness ld = 300 [mm] Plate length = 42.5 [Deg] Inclination angle Material: С255 fybu = 240.00 [MPa] Resistance UPPER STIFFENER hu = 50 [mm] Stiffener height twu = 16 [mm] Thickness of vertical stiffener lu = 300 [mm] Length of vertical stiffener Material: С255 fyu = 240.00 [MPa] Resistance COLUMN STIFFENER Upper hsu = 234 [mm] Stiffener height bsu = 121 [mm] Stiffener width thu = 10 [mm] Stiffener thickness Material: С255 fysu = 240.00 [MPa] Resistance Lower Стр. 2 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 3. hsd = 234 [mm] Stiffener height bsd = 121 [mm] Stiffener width thd = 10 [mm] Stiffener thickness Material: С255 fysu = 240.00 [MPa] Resistance PLATE STRENGTHENING COLUMN WEB Typ: unilateral ha = 480 [mm] Plate length wa = 180 [mm] Plate width ta = 12 [mm] Plate thickness Material: С255 fya = 240.00 [MPa] Resistance FILLET WELDS aw = 8 [mm] Web weld af = 10 [mm] Flange weld as = 8 [mm] Stiffener weld afd = 8 [mm] Horizontal weld ap1 = 6 [mm] Horizontal weld ap2 = 6 [mm] Vertical weld MATERIAL FACTORS M0 = 1.00 Partial safety factor [2.2] M1 = 1.00 Partial safety factor [2.2] M2 = 1.25 Partial safety factor [2.2] M3 = 1.25 Partial safety factor [2.2] LOADS Ultimate limit state Case: Manual calculations. Mb1,Ed = 136.65 [kN*m] Bending moment in the right beam Vb1,Ed = 148.53 [kN] Shear force in the right beam Nb1,Ed = -26.80 [kN] Axial force in the right beam Mc2,Ed = -50.07 [kN*m] Bending moment in the upper column Vc2,Ed = -29.77 [kN] Shear force in the upper column Nc2,Ed = -255.09 [kN] Axial force in the upper column RESULTS BEAM RESISTANCES COMPRESSION Ab = 93.19 [cm2] Area EN1993-1-1:[6.2.4] Ncb,Rd = Ab fyb / M0 Ncb,Rd = 2329.75 [kN] Design compressive resistance of the section EN1993-1-1:[6.2.4] SHEAR Avb = 64.02 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] Vcb,Rd = Avb (fyb / 3) / M0 Стр. 3 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 4. Vcb,Rd = 924.12 [kN] Design sectional resistance for shear EN1993-1-1:[6.2.6.(2)] Vb1,Ed / Vcb,Rd ≤ 1,0 0.16 < 1.00 verified (0.16) BENDING - PLASTIC MOMENT (WITHOUT BRACKETS) Wplb = 978.26 [cm3] Plastic section modulus EN1993-1-1:[6.2.5.(2)] Mb,pl,Rd = Wplb fyb / M0 Mb,pl,Rd = 244.56 [kN*m] Plastic resistance of the section for bending (without stiffeners) EN1993-1-1:[6.2.5.(2)] BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT Wpl = 2652.81 [cm3] Plastic section modulus EN1993-1-1:[6.2.5] Mcb,Rd = Wpl fyb / M0 Mcb,Rd = 663.20 [kN*m] Design resistance of the section for bending EN1993-1-1:[6.2.5] FLANGE AND WEB - COMPRESSION Mcb,Rd = 663.20 [kN*m] Design resistance of the section for bending EN1993-1-1:[6.2.5] hf = 517 [mm] Distance between the centroids of flanges [6.2.6.7.(1)] Fc,fb,Rd = Mcb,Rd / hf Fc,fb,Rd = 1283.40 [kN] Resistance of the compressed flange and web [6.2.6.7.(1)] WEB OR BRACKET FLANGE - COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE Bearing: = 0.0 [Deg] Angle between the front plate and the beam = 42.5 [Deg] Inclination angle of the bracket plate beff,c,wb = 197 [mm] Effective width of the web for compression [6.2.6.2.(1)] Avb = 28.52 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] = 0.82 Reduction factor for interaction with shear [6.2.6.2.(1)] com,Ed = 119.09 [MPa] Maximum compressive stress in web [6.2.6.2.(2)] kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)] As = 18.91 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4] Fc,wb,Rd1 = [ kwc beff,c,wb twb fyb / M0 + As fyb / M0] cos() / sin( - ) Fc,wb,Rd1 = 868.43 [kN] Beam web resistance [6.2.6.2.(1)] Buckling: dwb = 199 [mm] Height of compressed web [6.2.6.2.(1)] p = 0.72 Plate slenderness of an element [6.2.6.2.(1)] = 1.00 Reduction factor for element buckling [6.2.6.2.(1)] s = 2.61 Stiffener slenderness EN1993-1-1:[6.3.1.2] = 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2] Fc,wb,Rd2 = [ kwc beff,c,wb twb fyb / M1 + As fyb / M1] cos() / sin( - ) Fc,wb,Rd2 = 868.30 [kN] Beam web resistance [6.2.6.2.(1)] Resistance of the bracket flange Fc,wb,Rd3 = bb tb fyb / (0.8*M0) Fc,wb,Rd3 = 1137.50 [kN] Resistance of the bracket flange [6.2.6.7.(1)] Final resistance: Fc,wb,Rd,low = Min (Fc,wb,Rd1 , Fc,wb,Rd2 , Fc,wb,Rd3) Fc,wb,Rd,low = 868.30 [kN] Beam web resistance [6.2.6.2.(1)] COLUMN RESISTANCES Стр. 4 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 5. WEB PANEL - SHEAR Mb1,Ed = 136.65 [kN*m] Bending moment (right beam) [5.3.(3)] Mb2,Ed = 0.00 [kN*m] Bending moment (left beam) [5.3.(3)] Vc1,Ed = 0.00 [kN] Shear force (lower column) [5.3.(3)] Vc2,Ed = -29.77 [kN] Shear force (upper column) [5.3.(3)] z = 486 [mm] Lever arm [6.2.5] Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2 Vwp,Ed = 266.29 [kN] Shear force acting on the web panel [5.3.(3)] Avs = 17.76 [cm2] Shear area of the column web EN1993-1-1:[6.2.6.(3)] Avp = 14.40 [cm2] Area of the web stiffening plate EN1993-1-1:[6.2.6.(3)] Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] ds = 523 [mm] Distance between the centroids of stiffeners [6.2.6.1.(4)] Mpl,fc,Rd = 2.24 [kN*m] Plastic resistance of the column flange for bending [6.2.6.1.(4)] Mpl,stu,Rd = 1.49 [kN*m] Plastic resistance of the upper transverse stiffener for bending [6.2.6.1.(4)] Mpl,stl,Rd = 1.49 [kN*m] Plastic resistance of the lower transverse stiffener for bending [6.2.6.1.(4)] Vwp,Rd = 0.9 ( Avs*fy,wc+Avp*fya ) / (3 M0) + Min(4 Mpl,fc,Rd / ds , (2 Mpl,fc,Rd + Mpl,stu,Rd + Mpl,stl,Rd) / ds) Vwp,Rd = 424.57 [kN] Resistance of the column web panel for shear [6.2.6.1] Vwp,Ed / Vwp,Rd ≤ 1,0 0.63 < 1.00 verified (0.63) WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE Bearing: twc = 12 [mm] Effective thickness of the column web [6.2.6.2.(6)] beff,c,wc = 187 [mm] Effective width of the web for compression [6.2.6.2.(1)] Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] = 0.78 Reduction factor for interaction with shear [6.2.6.2.(1)] com,Ed = 90.79 [MPa] Maximum compressive stress in web [6.2.6.2.(2)] kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)] As = 24.10 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4] Fc,wc,Rd1 = kwc beff,c,wc twc fyc / M0 + As fys / M0 Fc,wc,Rd1 = 1017.23 [kN] Column web resistance [6.2.6.2.(1)] Buckling: dwc = 206 [mm] Height of compressed web [6.2.6.2.(1)] p = 0.54 Plate slenderness of an element [6.2.6.2.(1)] = 1.00 Reduction factor for element buckling [6.2.6.2.(1)] s = 2.82 Stiffener slenderness EN1993-1-1:[6.3.1.2] s = 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2] Fc,wc,Rd2 = kwc beff,c,wc twc fyc / M1 + As s fys / M1 Fc,wc,Rd2 = 1017.23 [kN] Column web resistance [6.2.6.2.(1)] Final resistance: Fc,wc,Rd,low = Min (Fc,wc,Rd1 , Fc,wc,Rd2) Fc,wc,Rd = 1017.23 [kN] Column web resistance [6.2.6.2.(1)] WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM TOP FLANGE Bearing: twc = 12 [mm] Effective thickness of the column web [6.2.6.2.(6)] Стр. 5 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 6. beff,c,wc = 181 [mm] Effective width of the web for compression [6.2.6.2.(1)] Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] = 0.79 Reduction factor for interaction with shear [6.2.6.2.(1)] com,Ed = 90.79 [MPa] Maximum compressive stress in web [6.2.6.2.(2)] kwc = 1.00 Reduction factor conditioned by compressive stresses [6.2.6.2.(2)] As = 24.10 [cm2] Area of the web stiffener EN1993-1-1:[6.2.4] Fc,wc,Rd1 = kwc beff,c,wc twc fyc / M0 + As fys / M0 Fc,wc,Rd1 = 1009.20 [kN] Column web resistance [6.2.6.2.(1)] Buckling: dwc = 206 [mm] Height of compressed web [6.2.6.2.(1)] p = 0.53 Plate slenderness of an element [6.2.6.2.(1)] = 1.00 Reduction factor for element buckling [6.2.6.2.(1)] s = 2.82 Stiffener slenderness EN1993-1-1:[6.3.1.2] s = 1.00 Buckling coefficient of the stiffener EN1993-1-1:[6.3.1.2] Fc,wc,Rd2 = kwc beff,c,wc twc fyc / M1 + As s fys / M1 Fc,wc,Rd2 = 1009.20 [kN] Column web resistance [6.2.6.2.(1)] Final resistance: Fc,wc,Rd,upp = Min (Fc,wc,Rd1 , Fc,wc,Rd2) Fc,wc,Rd,upp = 1009.20 [kN] Column web resistance [6.2.6.2.(1)] GEOMETRICAL PARAMETERS OF A CONNECTION EFFECTIVE LENGTHS AND PARAMETERS - COLUMN FLANGE Nr m mx e ex p leff,cp leff,nc leff,1 leff,2 leff,cp,g leff,nc,g leff,1,g leff,2,g 1 49 - 62 - 74 255 308 255 308 0 0 0 0 2 49 - 62 - 55 311 284 284 284 210 174 174 174 3 49 - 62 - 53 311 275 275 275 106 53 53 53 4 49 - 62 - 88 311 275 275 275 176 88 88 88 5 49 - 62 - 90 311 275 275 275 180 90 90 90 6 49 - 62 - 63 311 275 275 275 125 63 63 63 7 49 - 62 - 70 311 318 311 318 225 215 215 215 EFFECTIVE LENGTHS AND PARAMETERS - FRONT PLATE Nr m mx e ex p leff,cp leff,nc leff,1 leff,2 leff,cp,g leff,nc,g leff,1,g leff,2,g 1 45 - 62 - 74 286 364 286 364 216 271 216 271 2 49 - 62 - 55 308 282 282 282 209 173 173 173 3 49 - 62 - 53 308 273 273 273 106 53 53 53 4 49 - 62 - 88 308 273 273 273 176 88 88 88 5 49 - 62 - 90 308 273 273 273 180 90 90 90 6 49 - 62 - 63 308 273 273 273 125 63 63 63 7 49 - 62 - 70 308 273 273 273 224 172 172 172 m – Bolt distance from the web mx – Bolt distance from the beam flange e – Bolt distance from the outer edge ex – Bolt distance from the horizontal outer edge p – Distance between bolts leff,cp – Effective length for a single bolt in the circular failure mode leff,nc – Effective length for a single bolt in the non-circular failure mode Стр. 6 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 7. leff,1 – Effective length for a single bolt for mode 1 leff,2 – Effective length for a single bolt for mode 2 leff,cp,g – Effective length for a group of bolts in the circular failure mode leff,nc,g – Effective length for a group of bolts in the non-circular failure mode leff,1,g – Effective length for a group of bolts for mode 1 leff,2,g – Effective length for a group of bolts for mode 2 CONNECTION RESISTANCE FOR COMPRESSION Nj,Rd = Min ( Ncb,Rd2 Fc,wb,Rd,low , 2 Fc,wc,Rd,low , 2 Fc,wc,Rd,upp ) Nj,Rd = 1736.60 [kN] Connection resistance for compression [6.2] Nb1,Ed / Nj,Rd ≤ 1,0 0.02 < 1.00 verified (0.02) CONNECTION RESISTANCE FOR BENDING Ft,Rd = 141.12 [kN] Bolt resistance for tension [Table 3.4] Bp,Rd = 200.86 [kN] Punching shear resistance of a bolt [Table 3.4] Ft,fc,Rd – column flange resistance due to bending Ft,wc,Rd – column web resistance due to tension Ft,ep,Rd – resistance of the front plate due to bending Ft,wb,Rd – resistance of the web in tension Ft,fc,Rd = Min (FT,1,fc,Rd , FT,2,fc,Rd , FT,3,fc,Rd) [6.2.6.4] , [Tab.6.2] Ft,wc,Rd = beff,t,wc twc fyc / M0 [6.2.6.3.(1)] Ft,ep,Rd = Min (FT,1,ep,Rd , FT,2,ep,Rd , FT,3,ep,Rd) [6.2.6.5] , [Tab.6.2] Ft,wb,Rd = beff,t,wb twb fyb / M0 [6.2.6.8.(1)] RESISTANCE OF THE BOLT ROW NO. 1 Ft1,Rd,comp - Formula Ft1,Rd,comp Component Ft,fc,Rd(1) = 185.90 185.90 Column flange - tension Ft,wc,Rd(1) = 579.06 579.06 Column web - tension Ft,ep,Rd(1) = 282.24 282.24 Front plate - tension Bp,Rd = 401.72 401.72 Bolts due to shear punching Vwp,Rd/ = 424.57 424.57 Web panel - shear Fc,wc,Rd = 1017.23 1017.23 Column web - compression Fc,fb,Rd = 1283.40 1283.40 Beam flange - compression Fc,wb,Rd = 868.30 868.30 Beam web - compression Ft1,Rd = Min (Ft1,Rd,comp) 185.90 Bolt row resistance RESISTANCE OF THE BOLT ROW NO. 2 Ft2,Rd,comp - Formula Ft2,Rd,comp Component Ft,fc,Rd(2) = 202.82 202.82 Column flange - tension Ft,wc,Rd(2) = 619.91 619.91 Column web - tension Ft,ep,Rd(2) = 282.24 282.24 Front plate - tension Ft,wb,Rd(2) = 635.39 635.39 Beam web - tension Стр. 7 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 8. Bp,Rd = 401.72 401.72 Bolts due to shear punching Vwp,Rd/ - ∑1 1 Fti,Rd = 424.57 - 185.90 238.67 Web panel - shear Fc,wc,Rd - ∑1 1 Ftj,Rd = 1017.23 - 185.90 831.33 Column web - compression Fc,fb,Rd - ∑1 1 Ftj,Rd = 1283.40 - 185.90 1097.50 Beam flange - compression Fc,wb,Rd - ∑1 1 Ftj,Rd = 868.30 - 185.90 682.40 Beam web - compression Ft2,Rd = Min (Ft2,Rd,comp) 202.82 Bolt row resistance RESISTANCE OF THE BOLT ROW NO. 3 Ft3,Rd,comp - Formula Ft3,Rd,comp Component Ft,fc,Rd(3) = 200.42 200.42 Column flange - tension Ft,wc,Rd(3) = 607.56 607.56 Column web - tension Ft,ep,Rd(3) = 282.24 282.24 Front plate - tension Ft,wb,Rd(3) = 614.92 614.92 Beam web - tension Bp,Rd = 401.72 401.72 Bolts due to shear punching Vwp,Rd/ - ∑1 2 Fti,Rd = 424.57 - 388.72 35.85 Web panel - shear Fc,wc,Rd - ∑1 2 Ftj,Rd = 1017.23 - 388.72 628.51 Column web - compression Fc,fb,Rd - ∑1 2 Ftj,Rd = 1283.40 - 388.72 894.68 Beam flange - compression Fc,wb,Rd - ∑1 2 Ftj,Rd = 868.30 - 388.72 479.58 Beam web - compression Ft,fc,Rd(3 + 2) - ∑2 2 Ftj,Rd = 165.50 - 202.82 -37.32 Column flange - tension - group Ft,wc,Rd(3 + 2) - ∑2 2 Ftj,Rd = 534.96 - 202.82 332.14 Column web - tension - group Ft,fc,Rd(3 + 2) - ∑2 2 Ftj,Rd = 165.50 - 202.82 -37.32 Column flange - tension - group Ft,wc,Rd(3 + 2) - ∑2 2 Ftj,Rd = 534.96 - 202.82 332.14 Column web - tension - group Ft,ep,Rd(3 + 2) - ∑2 2 Ftj,Rd = 445.07 - 202.82 242.25 Front plate - tension - group Ft,wb,Rd(3 + 2) - ∑2 2 Ftj,Rd = 509.05 - 202.82 306.23 Beam web - tension - group Ft,ep,Rd(3 + 2) - ∑2 2 Ftj,Rd = 445.07 - 202.82 242.25 Front plate - tension - group Ft,wb,Rd(3 + 2) - ∑2 2 Ftj,Rd = 509.05 - 202.82 306.23 Beam web - tension - group Ft3,Rd = Min (Ft3,Rd,comp) 35.85 Bolt row resistance RESISTANCE OF THE BOLT ROW NO. 4 Ft4,Rd,comp - Formula Ft4,Rd,comp Component Ft,fc,Rd(4) = 200.42 200.42 Column flange - tension Ft,wc,Rd(4) = 607.56 607.56 Column web - tension Ft,ep,Rd(4) = 282.24 282.24 Front plate - tension Ft,wb,Rd(4) = 614.92 614.92 Beam web - tension Bp,Rd = 401.72 401.72 Bolts due to shear punching Vwp,Rd/ - ∑1 3 Fti,Rd = 424.57 - 424.57 0.00 Web panel - shear Fc,wc,Rd - ∑1 3 Ftj,Rd = 1017.23 - 424.57 592.66 Column web - compression Fc,fb,Rd - ∑1 3 Ftj,Rd = 1283.40 - 424.57 858.83 Beam flange - compression Fc,wb,Rd - ∑1 3 Ftj,Rd = 868.30 - 424.57 443.73 Beam web - compression Ft,fc,Rd(4 + 3) - ∑3 3 Ftj,Rd = 102.65 - 35.85 66.80 Column flange - tension - group Ft,wc,Rd(4 + 3) - ∑3 3 Ftj,Rd = 366.57 - 35.85 330.73 Column web - tension - group Ft,fc,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 229.57 - 238.67 -9.10 Column flange - tension - group Стр. 8 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 9. Ft,wc,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 658.11 - 238.67 419.44 Column web - tension - group Ft,fc,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 229.57 - 238.67 -9.10 Column flange - tension - group Ft,wc,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 658.11 - 238.67 419.44 Column web - tension - group Ft,ep,Rd(4 + 3) - ∑3 3 Ftj,Rd = 368.71 - 35.85 332.86 Front plate - tension - group Ft,wb,Rd(4 + 3) - ∑3 3 Ftj,Rd = 317.25 - 35.85 281.40 Beam web - tension - group Ft,ep,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 653.01 - 238.67 414.34 Front plate - tension - group Ft,wb,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 707.05 - 238.67 468.38 Beam web - tension - group Ft,ep,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 653.01 - 238.67 414.34 Front plate - tension - group Ft,wb,Rd(4 + 3 + 2) - ∑3 2 Ftj,Rd = 707.05 - 238.67 468.38 Beam web - tension - group Ft4,Rd = Min (Ft4,Rd,comp) 0.00 Bolt row resistance The remaining bolts are inactive (they do not carry loads) because resistance of one of the connection components has been used up or these bolts are positioned below the center of rotation. SUMMARY TABLE OF FORCES Nr hj Ftj,Rd Ft,fc,Rd Ft,wc,Rd Ft,ep,Rd Ft,wb,Rd Ft,Rd Bp,Rd 1 554 185.90 185.90 579.06 282.24 - 282.24 401.72 2 419 202.82 202.82 619.91 282.24 635.39 282.24 401.72 3 364 35.85 200.42 607.56 282.24 614.92 282.24 401.72 4 313 - 200.42 607.56 282.24 614.92 282.24 401.72 5 188 - 200.42 607.56 282.24 614.92 282.24 401.72 6 133 - 200.42 607.56 282.24 614.92 282.24 401.72 7 63 - 208.25 652.69 282.24 614.92 282.24 401.72 CONNECTION RESISTANCE FOR BENDING Mj,Rd Mj,Rd = ∑ hj Ftj,Rd Mj,Rd = 200.81 [kN*m] Connection resistance for bending [6.2] Mb1,Ed / Mj,Rd ≤ 1,0 0.68 < 1.00 verified (0.68) CONNECTION RESISTANCE FOR SHEAR v = 0.60 Coefficient for calculation of Fv,Rd [Table 3.4] Lf = 0.95 Reduction factor for long connections [3.8] Fv,Rd = 114.88 [kN] Shear resistance of a single bolt [Table 3.4] Ft,Rd,max = 141.12 [kN] Tensile resistance of a single bolt [Table 3.4] Fb,Rd,int = 92.84 [kN] Bearing resistance of an intermediate bolt [Table 3.4] Fb,Rd,ext = 177.60 [kN] Bearing resistance of an outermost bolt [Table 3.4] Nr Ftj,Rd,N Ftj,Ed,N Ftj,Rd,M Ftj,Ed,M Ftj,Ed Fvj,Rd 1 282.24 -3.83 185.90 126.50 122.68 158.42 2 282.24 -3.83 202.82 138.02 134.19 151.73 3 282.24 -3.83 35.85 24.39 20.57 185.67 4 282.24 -3.83 0.00 0.00 -3.83 185.67 5 282.24 -3.83 0.00 0.00 -3.83 185.67 6 282.24 -3.83 0.00 0.00 -3.83 185.67 7 282.24 -3.83 0.00 0.00 -3.83 185.67 Стр. 9 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 10. Ftj,Rd,N – Bolt row resistance for simple tension Ftj,Ed,N – Force due to axial force in a bolt row Ftj,Rd,M – Bolt row resistance for simple bending Ftj,Ed,M – Force due to moment in a bolt row Ftj,Ed – Maximum tensile force in a bolt row Fvj,Rd – Reduced bolt row resistance Ftj,Ed,N = Nj,Ed Ftj,Rd,N / Nj,Rd Ftj,Ed,M = Mj,Ed Ftj,Rd,M / Mj,Rd Ftj,Ed = Ftj,Ed,N + Ftj,Ed,M Fvj,Rd = Min (nh Fv,Ed (1 - Ftj,Ed/ (1.4 nh Ft,Rd,max), nh Fv,Rd , nh Fb,Rd)) Vj,Rd = nh ∑1 n Fvj,Rd [Table 3.4] Vj,Rd = 1238.51 [kN] Connection resistance for shear [Table 3.4] Vb1,Ed / Vj,Rd ≤ 1,0 0.12 < 1.00 verified (0.12) WELD RESISTANCE Aw = 213.60 [cm2] Area of all welds [4.5.3.2(2)] Awy = 132.80 [cm2] Area of horizontal welds [4.5.3.2(2)] Awz = 80.80 [cm2] Area of vertical welds [4.5.3.2(2)] Iwy = 82311.12 [cm4] Moment of inertia of the weld arrangement with respect to the hor. axis [4.5.3.2(5)] max=max = 36.10 [MPa] Normal stress in a weld [4.5.3.2(5)] = = 36.10 [MPa] Stress in a vertical weld [4.5.3.2(5)] II = 18.38 [MPa] Tangent stress [4.5.3.2(5)] w = 0.85 Correlation coefficient [4.5.3.2(7)] [max 2 + 3*(max 2)] ≤ fu/(w*M2) 72.21 < 348.24 verified (0.21) [ 2 + 3*( 2+II 2)] ≤ fu/(w*M2) 78.91 < 348.24 verified (0.23) ≤ 0.9*fu/M2 36.10 < 266.40 verified (0.14) CONNECTION STIFFNESS twash = 4 [mm] Washer thickness [6.2.6.3.(2)] hhead = 14 [mm] Bolt head height [6.2.6.3.(2)] hnut = 20 [mm] Bolt nut height [6.2.6.3.(2)] Lb = 57 [mm] Bolt length [6.2.6.3.(2)] k10 = 7 [mm] Stiffness coefficient of bolts [6.3.2.(1)] STIFFNESSES OF BOLT ROWS Nr hj k3 k4 k5 keff,j keff,j hj keff,j hj 2 1 554 0 0 17 0 0.00 0.00 2 419 4 2 11 1 4.58 191.87 3 364 1 1 3 0 1.36 49.53 4 313 2 1 5 1 1.88 58.67 5 188 2 1 6 1 1.15 21.56 6 133 2 1 4 0 0.58 7.69 7 63 5 3 11 1 0.80 4.97 Sum 10.35 334.30 Стр. 10 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht
- 11. keff,j = 1 / (∑3 5 (1 / ki,j)) [6.3.3.1.(2)] zeq = ∑j keff,j hj 2 / ∑j keff,j hj zeq = 323 [mm] Equivalent force arm [6.3.3.1.(3)] keq = ∑j keff,j hj / zeq keq = 3 [mm] Equivalent stiffness coefficient of a bolt arrangement [6.3.3.1.(1)] Avc = 32.16 [cm2] Shear area EN1993-1-1:[6.2.6.(3)] = 1.00 Transformation parameter [5.3.(7)] z = 323 [mm] Lever arm [6.2.5] k1 = 4 [mm] Stiffness coefficient of the column web panel subjected to shear [6.3.2.(1)] k2 = Stiffness coefficient of the compressed column web [6.3.2.(1)] Sj,ini = E zeq 2 / ∑i (1 / k1 + 1 / k2 + 1 / keq) [6.3.1.(4)] Sj,ini = 36199.63 [kN*m] Initial rotational stiffness [6.3.1.(4)] = 1.06 Stiffness coefficient of a connection [6.3.1.(6)] Sj = Sj,ini / [6.3.1.(4)] Sj = 34247.54 [kN*m] Final rotational stiffness [6.3.1.(4)] Connection classification due to stiffness. Sj,rig = 31357.65 [kN*m] Stiffness of a rigid connection [5.2.2.5] Sj,pin = 1959.85 [kN*m] Stiffness of a pinned connection [5.2.2.5] Sj,ini Sj,rig RIGID WEAKEST COMPONENT: COLUMN WEB PANEL - SHEAR Connection conforms to the code Ratio 0.68 Стр. 11 из 11 03.12.2015mhtml:file://C:UsersTRISTANDocumentsAutodeskOutputra_res.mht