Post on 25-Jan-2016
description
CALCULATION NOTE FOR T8-INTERDIKE STAIRCASE
Loads Cases
Result
Member
Section
Material
Lay
Laz
Ratio
Case
1 Simple
bar_1
IPE 200 S275 11.73 43.34 0.19 3 COMB1
2 Simple
bar_2
IPE 200 S275 11.73 43.34 0.19 3 COMB1
3 Simple
bar_3
IPE 200 S275 43.10 159.24 0.27 3 COMB1
4 Simple
bar_4
IPE 200 S275 43.10 159.24 0.08 3 COMB1
5 Simple
bar_5
HEA 140 S275 43.42 70.73 0.27 3 COMB1
6 Simple
bar_6
HEA 140 S275 43.42 70.73 0.27 3 COMB1
9 Simple
bar_9
UPN 200 S275 49.25 177.08 0.10 3 COMB1
10 Simple
bar_10
UPN 200 S275 49.25 177.08 0.18 3 COMB1
12 Simple
bar_12
UPN 200 S275 49.25 177.08 0.18 3 COMB1
13 Simple
bar_13
UPN 200 S275 49.25 177.08 0.10 3 COMB1
Case
Label
Case name
1 DL1 Dead load
2 LL1 Live load
3 COMB1 Combination 1
Autodesk Robot Structural Analysis Professional 2012
Design of fixed beam-to-column connection
EN 1993-1-8:2005/AC:2009
Ratio 0.14
GENERAL
Connection no.: 1
Connection name: Column-Beam
Structure node: 12
Structure bars: 5, 4
GEOMETRY
COLUMN
Section: HEA 140
Bar no.: 5
= -90.0 [Deg] Inclination angle
hc = 133.000 [mm] Height of column section
bfc = 140.000 [mm] Width of column section
twc = 5.500 [mm] Thickness of the web of column section
tfc = 8.500 [mm] Thickness of the flange of column section
rc = 12.000 [mm] Radius of column section fillet
Ac = 3141.610 [mm2] Cross-sectional area of a column
Ixc = 10331300.000 [mm
4] Moment of inertia of the column section
Material: S275
fyc = 0.28 [kN/mm2] Resistance
BEAM
Section: IPE 200
Section: IPE 200
Bar no.: 4
= -0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bf = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Ixb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Resistance
BOLTS
d = 16.000 [mm] Bolt diameter
Class = 8.8
Bolt class
FtRd = 90.43 [kN] Tensile resistance of a bolt
nh = 2
Number of bolt columns
nv = 3
Number of bolt rows
h1 = 60.000 [mm] Distance between first bolt and upper edge of front plate
Horizontal spacing ei = 50.000 [mm]
Vertical spacing pi = 50.000;50.000 [mm]
PLATE
hp = 220.000 [mm] Plate height
bp = 100.000 [mm] Plate width
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Resistance
FILLET WELDS
aw = 4.000 [mm] Web weld
af = 6.000 [mm] Flange 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: 3: COMB1 1*1.20+2*1.60
Mb1,Ed = 1672.26 [kN*mm] Bending moment in the right beam
Vb1,Ed = -4.61 [kN] Shear force in the right beam
Nb1,Ed = 0.05 [kN] Axial force in the right beam
Mc1,Ed = -1682.26 [kN*mm] Bending moment in the lower column
Vc1,Ed = 1.06 [kN] Shear force in the lower column
Nc1,Ed = -15.09 [kN] Axial force in the lower column
Nc2,Ed = -0.03 [kN] Axial force in the upper column
RESULTS
BEAM RESISTANCES
TENSION
Ab = 2848.410 [mm2] Area EN1993-1-1:[6.2.3]
Ntb,Rd = Ab fyb / M0 Ntb,Rd = 783.31 [kN] Design tensile resistance of the section EN1993-1-1:[6.2.3]
SHEAR
Avb = 1400.010 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
Vcb,Rd = Avb (fyb / 3) / M0 Vcb,Rd = 222.28 [kN] Design sectional resistance for shear EN1993-1-1:[6.2.6.(2)]
Vb1,Ed / Vcb,Rd 1,0 0.02 < 1.00 verified (0.02)
BENDING - PLASTIC MOMENT (WITHOUT BRACKETS)
Wplb = 220657.000 [mm3] Plastic section modulus EN1993-1-1:[6.2.5.(2)]
Mb,pl,Rd = Wplb fyb / M0 Mb,pl,Rd =
60680.6
8
[kN*mm]
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 = 220657.000 [mm3] Plastic section modulus EN1993-1-1:[6.2.5]
Mcb,Rd = Wpl fyb / M0 Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending EN1993-1-1:[6.2.5]
FLANGE AND WEB - COMPRESSION
Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending EN1993-1-1:[6.2.5]
hf = 191.500 [mm] Distance between the centroids of flanges [6.2.6.7.(1)]
Fc,fb,Rd = Mcb,Rd / hf Fc,fb,Rd = 316.87 [kN] Resistance of the compressed flange and web [6.2.6.7.(1)]
COLUMN RESISTANCES
WEB PANEL - SHEAR
Mb1,Ed = 1672.26 [kN*mm] Bending moment (right beam) [5.3.(3)]
Mb2,Ed = 0.00 [kN*mm] Bending moment (left beam) [5.3.(3)]
Vc1,Ed = 1.06 [kN] Shear force (lower column) [5.3.(3)]
Vc2,Ed = 0.00 [kN] Shear force (upper column) [5.3.(3)]
z = 120.750 [mm] Lever arm [6.2.5]
Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2
Vwp,Ed = 13.32 [kN] Shear force acting on the web panel [5.3.(3)]
Avs = 1012.360 [mm2] Shear area of the column web EN1993-1-1:[6.2.6.(3)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
Vwp,Rd = 0.9*( fy,wc*Avc+fy,wp*Avp+fys*Avd ) / (3 M0) Vwp,Rd = 144.66 [kN] Resistance of the column web panel for shear [6.2.6.1]
Vwp,Ed / Vwp,Rd 1,0 0.09 < 1.00 verified (0.09)
WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE
Bearing:
twc = 5.500 [mm] Effective thickness of the column web [6.2.6.2.(6)]
beff,c,wc = 139.971 [mm] Effective width of the web for compression [6.2.6.2.(1)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 0.76
Reduction factor for interaction with shear [6.2.6.2.(1)]
com,Ed = 0.01 [kN/mm2] Maximum compressive stress in web [6.2.6.2.(2)]
kwc = 1.00
Reduction factor conditioned by compressive stresses [6.2.6.2.(2)]
Fc,wc,Rd1 = kwc beff,c,wbc twc fyc / M0 Fc,wc,Rd1 = 159.95 [kN] Column web resistance [6.2.6.2.(1)]
Buckling:
dwc = 92.000 [mm] Height of compressed web [6.2.6.2.(1)]
p = 0.70
Plate slenderness of an element [6.2.6.2.(1)]
= 1.00
Reduction factor for element buckling [6.2.6.2.(1)]
Fc,wb,Rd2 = kwc beff,c,wc twc fyc / M1
Fc,wc,Rd2 = 159.95 [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 = 159.95 [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 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 89.741
78.42
5 78.42
5 78.42
5
2 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 100.00
0 50.00
0 50.00
0 50.00
0
3 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 89.741
78.42
5 78.42
5 78.42
5
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 17.67
5 -
25.00
0 -
50.00
0 111.05
2 104.48
2 104.48
2 104.48
2 105.52
6 78.50
8 78.50
8 78.50
8
2 17.67
5 -
25.00
0 -
50.00
0 111.05
2 101.94
8 101.94
8 101.94
8 100.00
0 50.00
0 50.00
0 50.00
0
3 17.67
5 -
25.00
0 -
50.00
0 111.05
2 101.94
8 101.94
8 101.94
8 105.52
6 75.97
4 75.97
4 75.97
4
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
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 TENSION
Ft,Rd = 90.43 [kN] Bolt resistance for tension [Table 3.4]
Bp,Rd = 93.37 [kN] Punching shear resistance of a bolt [Table 3.4]
Nj,Rd = Min (Ntb,Rd , nv nh Ft,Rd , nv nh Bp,Rd) Nj,Rd = 542.59 [kN] Connection resistance for tension [6.2]
Nb1,Ed / Nj,Rd 1,0 0.00 < 1.00 verified (0.00)
CONNECTION RESISTANCE FOR BENDING
Ft,Rd = 90.43 [kN] Bolt resistance for tension [Table 3.4]
Bp,Rd = 93.37 [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
Ft1,Rd = Min (Ft1,Rd,comp) 58.52 Bolt row resistance
Ft,fc,Rd(1) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(1) = 107.85 107.85 Column web - tension
Ft,ep,Rd(1) = 58.52 58.52 Front plate - tension
Ft,wb,Rd(1) = 160.90 160.90 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ = 144.66 144.66 Web panel - shear
Fc,wc,Rd = 159.95 159.95 Column web - compression
Fc,fb,Rd = 316.87 316.87 Beam flange - compression
RESISTANCE OF THE BOLT ROW NO. 2
Ft2,Rd,comp - Formula Ft2,Rd,comp Component
Ft2,Rd = Min (Ft2,Rd,comp) 13.46 Bolt row resistance
Ft,fc,Rd(2) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(2) = 107.85 107.85 Column web - tension
Ft,ep,Rd(2) = 57.10 57.10 Front plate - tension
Ft,wb,Rd(2) = 157.00 157.00 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ - 11 Fti,Rd = 144.66 - 58.52 86.14 Web panel - shear
Fc,wc,Rd - 11 Ftj,Rd = 159.95 - 58.52 101.43 Column web - compression
Fc,fb,Rd - 11 Ftj,Rd = 316.87 - 58.52 258.35 Beam flange - compression
Ft,fc,Rd(2 + 1) - 11 Ftj,Rd = 201.71 - 58.52 143.19 Column flange - tension - group
Ft,wc,Rd(2 + 1) - 11 Ftj,Rd = 152.01 - 58.52 93.49 Column web - tension - group
Ft,ep,Rd(2 + 1) - 11 Ftj,Rd = 71.98 - 58.52 13.46 Front plate - tension - group
Ft,wb,Rd(2 + 1) - 11 Ftj,Rd = 197.90 - 58.52 139.38 Beam web - tension - group
RESISTANCE OF THE BOLT ROW NO. 3
Ft3,Rd,comp - Formula Ft3,Rd,comp Component
Ft3,Rd = Min (Ft3,Rd,comp) 42.56 Bolt row resistance
Ft,fc,Rd(3) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(3) = 107.85 107.85 Column web - tension
Ft,ep,Rd(3) = 57.10 57.10 Front plate - tension
Ft,wb,Rd(3) = 157.00 157.00 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ - 12 Fti,Rd = 144.66 - 71.98 72.68 Web panel - shear
Fc,wc,Rd - 12 Ftj,Rd = 159.95 - 71.98 87.97 Column web - compression
Fc,fb,Rd - 12 Ftj,Rd = 316.87 - 71.98 244.89 Beam flange - compression
Ft,fc,Rd(3 + 2) - 22 Ftj,Rd = 201.71 - 13.46 188.25 Column flange - tension - group
Ft,wc,Rd(3 + 2) - 22 Ftj,Rd = 152.01 - 13.46 138.55 Column web - tension - group
Ft,fc,Rd(3 + 2 + 1) - 21 Ftj,Rd = 324.89 - 71.98 252.91 Column flange - tension - group
Ft,wc,Rd(3 + 2 + 1) - 21 Ftj,Rd = 192.49 - 71.98 120.51 Column web - tension - group
Ft,ep,Rd(3 + 2) - 22 Ftj,Rd = 70.56 - 13.46 57.10 Front plate - tension - group
Ft,wb,Rd(3 + 2) - 22 Ftj,Rd = 194.00 - 13.46 180.54 Beam web - tension - group
Ft,ep,Rd(3 + 2 + 1) - 21 Ftj,Rd = 114.54 - 71.98 42.56 Front plate - tension - group
Ft,wb,Rd(3 + 2 + 1) - 21 Ftj,Rd = 314.90 - 71.98 242.92 Beam web - tension - group
SUMMARY TABLE OF FORCES
Nr hj Ftj,Rd Ft,fc,Rd Ft,wc,Rd Ft,ep,Rd Ft,wb,Rd Ft,Rd Bp,Rd
1 145.750 58.52 124.84 107.85 58.52 160.90 180.86 186.75
2 95.750 13.46 124.84 107.85 57.10 157.00 180.86 186.75
3 45.750 42.56 124.84 107.85 57.10 157.00 180.86 186.75
CONNECTION RESISTANCE FOR BENDING Mj,Rd
Mj,Rd = hj Ftj,Rd Mj,Rd = 11765.23 [kN*mm] Connection resistance for bending [6.2]
Mb1,Ed / Mj,Rd 1,0 0.14 < 1.00 verified (0.14)
CONNECTION RESISTANCE FOR SHEAR
v = 0.60
Coefficient for calculation of Fv,Rd [Table 3.4]
Fv,Rd = 77.21 [kN] Shear resistance of a single bolt [Table 3.4]
Ft,Rd,max = 90.43 [kN] Tensile resistance of a single bolt [Table 3.4]
Fb,Rd,int = 48.86 [kN] Bearing resistance of an intermediate bolt [Table 3.4]
Fb,Rd,ext = 72.29 [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
1 180.86 0.02 58.52 8.32 8.34 97.72
2 180.86 0.02 13.46 1.91 1.93 97.72
3 180.86 0.02 42.56 6.05 6.07 97.72
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,Rd (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 = 293.16 [kN] Connection resistance for shear [Table 3.4]
Vb1,Ed / Vj,Rd 1,0 0.02 < 1.00 verified (0.02)
WELD RESISTANCE
Aw = 3196.800 [mm2] Area of all welds
[4.5.3.2(2)]
Awy = 1924.800 [mm2] Area of horizontal welds
[4.5.3.2(2)]
Awz = 1272.000 [mm2] Area of vertical welds
[4.5.3.2(2)]
Iwy = 20726644.20
0 [mm
4]
Moment of inertia of the weld arrangement with respect to the hor. axis
[4.5.3.2(5)]
max=max =
0.01 [kN/mm
2
] Normal stress in a weld
[4.5.3.2(5)]
= = 0.00 [kN/mm
2
] Stress in a vertical weld
[4.5.3.2(5)]
II = -0.00 [kN/mm
2
] Tangent stress
[4.5.3.2(5)]
w = 0.85
Correlation coefficient [4.5.3.2(7
)]
[max2 + 3*(max
2)] fu/(w*M2) 0.01 < 0.40 verified (0.03)
[2 + 3*(
2+II
2)] fu/(w*M2) 0.01 < 0.40 verified (0.03)
0.9*fu/M2 0.01 < 0.31 verified (0.02)
CONNECTION STIFFNESS
twash = 4.000 [mm] Washer thickness [6.2.6.3.(2)]
hhead = 12.000 [mm] Bolt head height [6.2.6.3.(2)]
hnut = 16.000 [mm] Bolt nut height [6.2.6.3.(2)]
Lb = 36.500 [mm] Bolt length [6.2.6.3.(2)]
k10 = 6.882 [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 hj2
Sum 272.472 31450.892
Nr hj k3 k4 k5 keff,j keff,j hj keff,j hj2
1 145.750 2.603 21.413 2.764 1.066 155.390 22648.134
2 95.750 1.659 13.652 1.760 0.720 68.925 6599.595
3 45.750 2.603 21.413 2.675 1.053 48.157 2203.164
keff,j = 1 / (35 (1 / ki,j)) [6.3.3.1.(2)]
zeq = j keff,j hj2 / j keff,j hj
zeq = 115.428 [mm] Equivalent force arm [6.3.3.1.(3)]
keq = j keff,j hj / zeq keq = 2.361 [mm] Equivalent stiffness coefficient of a bolt arrangement [6.3.3.1.(1)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 1.00
Transformation parameter [5.3.(7)]
z = 115.428 [mm] Lever arm [6.2.5]
k1 = 3.333 [mm] Stiffness coefficient of the column web panel subjected to shear [6.3.2.(1)]
beff,c,wc = 135.485 [mm] Effective width of the web for compression [6.2.6.2.(1)]
twc = 5.500 [mm] Effective thickness of the column web [6.2.6.2.(6)]
dc = 116.000 [mm] Height of compressed web [6.2.6.2.(1)]
k2 = 4.497 [mm] Stiffness coefficient of the compressed column web [6.3.2.(1)]
Sj,ini = E zeq2 / i (1 / k1 + 1 / k2 + 1 / keq) [6.3.1.(4)]
Sj,ini = 2887049.32 [kN*mm] Initial rotational stiffness [6.3.1.(4)]
= 1.00
Stiffness coefficient of a connection [6.3.1.(6)]
Sj = Sj,ini / [6.3.1.(4)]
Sj = 2887049.32 [kN*mm] Final rotational stiffness [6.3.1.(4)]
Connection classification due to stiffness.
Sj,rig = 8951682.02 [kN*mm] Stiffness of a rigid connection [5.2.2.5]
Sj,pin = 559480.13 [kN*mm] Stiffness of a pinned connection [5.2.2.5]
Sj,pin Sj,ini < Sj,rig SEMI-RIGID
Connection conforms to the code Ratio 0.14
Autodesk Robot Structural Analysis Professional 2012
Calculation of the beam-column (web) connection
EN 1993-1-8:2005/AC:2009
Ratio 0.40
GENERAL
Connection no.: 7
Connection name: Beam-column (web)
Structure node: 12
Structure bars: 5, 1
GEOMETRY
COLUMN
Section: HEA 140
Bar no.: 5
= -90.0 [Deg] Inclination angle
hc = 133.000 [mm] Height of column section
bfc = 140.000 [mm] Width of column section
twc = 5.500 [mm] Thickness of the web of column section
tfc = 8.500 [mm] Thickness of the flange of column section
rc = 12.000 [mm] Radius of column section fillet
Ac = 3141.610 [mm2] Cross-sectional area of a column
Iyc = 10331300.000 [mm
4] Moment of inertia of the column section
Material: S275
fyc = 0.28 [kN/mm2] Design resistance
fuc = 0.43 [kN/mm
2] Tensile resistance
BEAM
Section: IPE 200
Bar no.: 1
= 0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bb = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Iyb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Design resistance
fub = 0.43 [kN/mm
2] Tensile resistance
PLATE
Type: unilateral
lp = 85.000 [mm] Plate length
hp = 130.000 [mm] Plate height
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Design resistance
fup = 0.43 [kN/mm
2] Tensile resistance
UPPER BRACKET OF A BEAM
lbu = 85.000 [mm] Bracket length
hbu = 130.000 [mm] Bracket height
tbu = 6.000 [mm] Bracket thickness
Material: S275
fybu = 0.28 [kN/mm2] Design resistance
fubu = 0.43 [kN/mm
2] Tensile resistance
LOWER BRACKET OF A BEAM
lbd = 85.000 [mm] Bracket length
hbd = 130.000 [mm] Bracket height
tbd = 6.000 [mm] Bracket thickness
Material: S275
fybd = 0.28 [kN/mm2] Design resistance
fubd = 0.43 [kN/mm
2] Tensile resistance
BOLTS
BOLTS CONNECTING BEAM WITH PLATE
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
BOLTS CONNECTING UPPER BRACKET WITH BEAM
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
Class = 8.8
Bolt class
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
BOLTS CONNECTING LOWER BRACKET WITH BEAM
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
WELDS
acp = 5.000 [mm] Fillet welds connecting plate with column
aswu = 5.000 [mm] Fillet welds connecting upper bracket with column
aswd = 5.000 [mm] Fillet welds connecting lower bracket with column
MATERIAL FACTORS
M0 = 1.00
Partial safety factor [2.2]
M2 = 1.25
Partial safety factor [2.2]
LOADS
Case: 3: COMB1 1*1.20+2*1.60
Nb,Ed = -3.18 [kN] Axial force
Vb,Ed = -10.46 [kN] Shear force
Mb,Ed = 4547.38 [kN*mm] Bending moment
RESULTS
BOLTS CONNECTING BEAM WITH PLATE
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd1x = 49.94 [kN] Bearing resistance of a single bolt Fb,Rd1x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.86
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.86 > 0.00 verified
Fb,Rd1z = 66.35 [kN] Bearing resistance of a single bolt Fb,Rd1z=k1z*bz*fu*d*ti/M2
Bolt bearing on the plate
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd2x = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.65
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.65 > 0.00 verified
Fb,Rd2z = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2z=k1z*bz*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION
Bolt shear
e = 52.750 [mm] Distance between centroid of a bolt group and center of column web
M0 = -
551.57
[kN*mm]
Real bending moment M0=Vb,Ed*e
FNx = 1.59 [kN] Component force in a bolt due to influence of the longitudinal force
FNx=Nb,Ed/n
FVz = 5.23 [kN] Component force in a bolt due to influence of the shear force FVz=Vb,Ed/n
FMx = -9.19 [kN] Component force in a bolt due to influence of the moment on the x direction
FMx=M0*zi/(xi2+zi
2)
FMz = 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction
FMz=M0*xi/(xi2+zi
2)
Fx,Ed =
-7.60 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx
Fz,Ed =
5.23 [kN] Design total force in a bolt on the direction z Fz,Ed = FVz + FMz
FRdx =
49.94 [kN] Effective design capacity of a bolt on the direction x FRdx=min(FvRd, FbRd1x,
FbRd2x)
FRdz =
53.51 [kN] Effective design capacity of a bolt on the direction z FRdz=min(FvRd, FbRd1z,
FbRd2z)
|Fx,Ed| FRdx |-7.60| < 49.94 verified (0.15)
|Fz,Ed| FRdz |5.23| < 53.51 verified (0.10)
BOLTS CONNECTING UPPER BRACKET WITH BEAM
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam flange
k1 = 1.41
Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd1 = 42.79 [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2
Bolt bearing on the bracket
k1 = 1.41
Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd2 = 30.20 [kN] Bearing resistance of a single bolt Fb,Rd2=k1*b*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE UPPER BRACKET - BEAM CONNECTION
Bolt shear
FEd = 10.57 [kN] Shear force in a bolt FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n
FRd = 30.20 [kN] Effective design capacity of a bolt FRd=min(FvRd, FbRd1, FbRd2)
|FEd| FRd |10.57| < 30.20 verified (0.35)
BOLTS CONNECTING LOWER BRACKET WITH BEAM
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam flange
k1 = 1.41
Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd1 = 42.79 [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2
Bolt bearing on the bracket
k1 = 1.41
Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd2 = 30.20 [kN] Bearing resistance of a single bolt Fb,Rd2=k1*b*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE LOWER BRACKET - BEAM CONNECTION
Bolt shear
FEd = -12.16 [kN] Shear force in a bolt FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n
FRd = 30.20 [kN] Effective design capacity of a bolt FRd=min(FvRd, FbRd1, FbRd2)
|FEd| FRd |-12.16| < 30.20 verified (0.40)
VERIFICATION OF THE SECTION DUE TO BLOCK TEARING
PLATE
Ant = 246.000 [mm2] Net area of the section in tension
Anv = 408.000 [mm
2] Area of the section in shear
VeffRd = 107.09 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-10.46| < 107.09 verified (0.10)
BEAM
Ant = 145.600 [mm2] Net area of the section in tension
Anv = 576.800 [mm
2] Area of the section in shear
VeffRd = 116.62 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-10.46| < 116.62 verified (0.09)
WELD RESISTANCE
FILLET WELDS CONNECTING PLATE WITH COLUMN
As = 650.000 [mm2] Weld area As = hp*agp
II = -0.01 [kN/mm2] Parallel tangent stress II=0.5*Vb,Ed/As
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*(II
2+
2)] fu/(w*M2) 0.03 < 0.40 verified (0.07)
FILLET WELDS CONNECTING UPPER BRACKET WITH COLUMN
As = 650.000 [mm2] Weld area
= 0.02 [kN/mm
2] Normal stress in a weld =0.5*[Nb,Ed/2 + Mb,Ed/hb]/As
= 0.01 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |0.01| < 0.31 verified (0.04)
= 0.01 [kN/mm2] Perpendicular tangent stress =
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*
2] fu/(w*M2) 0.03 < 0.40 verified (0.07)
FILLET WELDS CONNECTING LOWER BRACKET WITH COLUMN
As = 650.000 [mm2] Weld area
= -0.02 [kN/mm
2] Normal stress in a weld =0.5*[Nb,Ed/2 - Mb,Ed/hb]/As
= -0.01 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |-0.01| < 0.31 verified (0.04)
= -0.01 [kN/mm2] Perpendicular tangent stress =
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*
2] fu/(w*M2) 0.03 < 0.40 verified (0.07)
Connection conforms to the code Ratio 0.40
Autodesk Robot Structural Analysis Professional 2012
Calculation of the beam-to-beam (web) connection
EN 1993-1-8:2005/AC:2009
Ratio 0.11
GENERAL
Connection no.: 6
Connection name: Beam-beam (web)
Structure node: 4
Structure bars: 2, 3
GEOMETRY
PRINCIPAL BEAM
Section: IPE 200
Bar no.: 2
= -90.0 [Deg] Inclination angle
hg = 200.000 [mm] Height of the principal beam section
bfg = 100.000 [mm] Width of the flange of the principal beam section
twg = 5.600 [mm] Thickness of the web of the principal beam section
tfg = 8.500 [mm] Thickness of the flange of the principal beam section
rg = 12.000 [mm] Fillet radius of the web of the principal beam section
Ap = 2848.410 [mm2] Cross-sectional area of a principal beam
Iyp = 19431700.000 [mm
4] Moment of inertia of the principal beam section
Material: S275
fyg = 0.28 [kN/mm2] Design resistance
fug = 0.43 [kN/mm
2] Tensile resistance
BEAM
Section: IPE 200
Bar no.: 3
= 0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bb = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Iyb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Design resistance
fub = 0.43 [kN/mm
2] Tensile resistance
PLATE
Type: unilateral
lp = 85.000 [mm] Plate length
hp = 130.000 [mm] Plate height
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Design resistance
fup = 0.43 [kN/mm
2] Tensile resistance
BOLTS
BOLTS CONNECTING BEAM WITH PLATE
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
WELDS
agp = 5.000 [mm] Fillet welds connecting plate with principal beam
MATERIAL FACTORS
M0 = 1.00
Partial safety factor [2.2]
M2 = 1.25
Partial safety factor [2.2]
LOADS
Case: 3: COMB1 1*1.20+2*1.60
Nb,Ed = -1.15 [kN] Axial force
Vb,Ed = -8.91 [kN] Shear force
Mb,Ed = 109.81 [kN*mm] Bending moment
RESULTS
BOLTS CONNECTING BEAM WITH PLATE
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd1x = 49.94 [kN] Bearing resistance of a single bolt Fb,Rd1x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.86
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.86 > 0.00 verified
Fb,Rd1z = 66.35 [kN] Bearing resistance of a single bolt Fb,Rd1z=k1z*bz*fu*d*ti/M2
Bolt bearing on the plate
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd2x = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.65
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.65 > 0.00 verified
Fb,Rd2z = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2z=k1z*bz*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION
Bolt shear
e = 52.80
0 [mm]
Distance between centroid of a bolt group and center of the principal beam web
M0 =
-
360.7
5
[kN*mm]
Real bending moment M0=Mb,Ed+Vb,Ed*e
FNx = 0.57 [kN] Component force in a bolt due to influence of the longitudinal force FNx=Nb,Ed/n
FVz = 4.46 [kN] Component force in a bolt due to influence of the shear force FVz=Vb,Ed/n
FMx = -6.01 [kN] Component force in a bolt due to influence of the moment on the x direction
FMx=M0*zi/(xi2+zi
2)
FMz = 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction
FMz=M0*xi/(xi2+zi
2)
Fx,Ed =
-5.44 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx
Fz,Ed =
4.46 [kN] Design total force in a bolt on the direction z Fz,Ed = FVz + FMz
FRdx =
49.94 [kN] Effective design capacity of a bolt on the direction x FRdx=min(FvRd, FbRd1x,
FbRd2x)
FRdz =
53.51 [kN] Effective design capacity of a bolt on the direction z FRdz=min(FvRd, FbRd1z,
FbRd2z)
|Fx,Ed| FRdx |-5.44| < 49.94 verified (0.11)
|Fz,Ed| FRdz |4.46| < 53.51 verified (0.08)
VERIFICATION OF THE SECTION DUE TO BLOCK TEARING
PLATE
Ant = 246.000 [mm2] Net area of the section in tension
Anv = 408.000 [mm
2] Area of the section in shear
VeffRd = 107.09 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-8.91| < 107.09 verified (0.08)
BEAM
Ant = 145.600 [mm2] Net area of the section in tension
Anv = 464.800 [mm
2] Area of the section in shear
VeffRd = 98.84 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-8.91| < 98.84 verified (0.09)
WELD RESISTANCE
FILLET WELDS CONNECTING PLATE WITH PRINCIPAL BEAM
As = 650.000 [mm2] Weld area As = hp*agp
= 0.00 [kN/mm2] Normal stress in a weld =Nb,Ed/As + Mb,Ed/Wys
= 0.00 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |0.00| < 0.31 verified (0.01)
= 0.00 [kN/mm2] Perpendicular tangent stress =
II = -0.01 [kN/mm2] Parallel tangent stress II=0.5*Vb,Ed/As
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*(II
2+
2)] fu/(w*M2) 0.03 < 0.40 verified (0.07)
Connection conforms to the code Ratio 0.11
Autodesk Robot Structural Analysis Professional 2012
Calculation of the beam-to-beam (web) connection
EN 1993-1-8:2005/AC:2009
Ratio 0.11
GENERAL
Connection no.: 5
Connection name: Beam-beam (web)
Structure node: 1
Structure bars: 1, 3
GEOMETRY
PRINCIPAL BEAM
Section: IPE 200
Bar no.: 1
= -90.0 [Deg] Inclination angle
hg = 200.000 [mm] Height of the principal beam section
bfg = 100.000 [mm] Width of the flange of the principal beam section
twg = 5.600 [mm] Thickness of the web of the principal beam section
tfg = 8.500 [mm] Thickness of the flange of the principal beam section
rg = 12.000 [mm] Fillet radius of the web of the principal beam section
Ap = 2848.410 [mm2] Cross-sectional area of a principal beam
Iyp = 19431700.000 [mm
4] Moment of inertia of the principal beam section
Material: S275
fyg = 0.28 [kN/mm2] Design resistance
fug = 0.43 [kN/mm
2] Tensile resistance
BEAM
Section: IPE 200
Bar no.: 3
= 0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bb = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Iyb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Design resistance
fub = 0.43 [kN/mm
2] Tensile resistance
PLATE
Type: unilateral
lp = 85.000 [mm] Plate length
hp = 130.000 [mm] Plate height
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Design resistance
fup = 0.43 [kN/mm
2] Tensile resistance
BOLTS
BOLTS CONNECTING BEAM WITH PLATE
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
WELDS
agp = 5.000 [mm] Fillet welds connecting plate with principal beam
MATERIAL FACTORS
M0 = 1.00
Partial safety factor [2.2]
M2 = 1.25
Partial safety factor [2.2]
LOADS
Case: 3: COMB1 1*1.20+2*1.60
Nb,Ed = -1.15 [kN] Axial force
Vb,Ed = -8.91 [kN] Shear force
Mb,Ed = 109.81 [kN*mm] Bending moment
RESULTS
BOLTS CONNECTING BEAM WITH PLATE
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd1x = 49.94 [kN] Bearing resistance of a single bolt Fb,Rd1x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.86
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.86 > 0.00 verified
Fb,Rd1z = 66.35 [kN] Bearing resistance of a single bolt Fb,Rd1z=k1z*bz*fu*d*ti/M2
Bolt bearing on the plate
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd2x = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.65
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.65 > 0.00 verified
Fb,Rd2z = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2z=k1z*bz*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION
Bolt shear
e = 52.80
0 [mm]
Distance between centroid of a bolt group and center of the principal beam web
M0 =
-
360.7
5
[kN*mm]
Real bending moment M0=Mb,Ed+Vb,Ed*e
FNx = 0.57 [kN] Component force in a bolt due to influence of the longitudinal force FNx=Nb,Ed/n
FVz = 4.46 [kN] Component force in a bolt due to influence of the shear force FVz=Vb,Ed/n
FMx = -6.01 [kN] Component force in a bolt due to influence of the moment on the x direction
FMx=M0*zi/(xi2+zi
2)
FMz = 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction
FMz=M0*xi/(xi2+zi
2)
Fx,Ed =
-5.44 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx
Fz,Ed =
4.46 [kN] Design total force in a bolt on the direction z Fz,Ed = FVz + FMz
FRdx =
49.94 [kN] Effective design capacity of a bolt on the direction x FRdx=min(FvRd, FbRd1x,
FbRd2x)
FRdz =
53.51 [kN] Effective design capacity of a bolt on the direction z FRdz=min(FvRd, FbRd1z,
FbRd2z)
|Fx,Ed| FRdx |-5.44| < 49.94 verified (0.11)
|Fz,Ed| FRdz |4.46| < 53.51 verified (0.08)
VERIFICATION OF THE SECTION DUE TO BLOCK TEARING
PLATE
Ant = 246.000 [mm2] Net area of the section in tension
Anv = 408.000 [mm
2] Area of the section in shear
VeffRd = 107.09 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-8.91| < 107.09 verified (0.08)
BEAM
Ant = 145.600 [mm2] Net area of the section in tension
Anv = 464.800 [mm
2] Area of the section in shear
VeffRd = 98.84 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-8.91| < 98.84 verified (0.09)
WELD RESISTANCE
FILLET WELDS CONNECTING PLATE WITH PRINCIPAL BEAM
As = 650.000 [mm2] Weld area As = hp*agp
= 0.00 [kN/mm2] Normal stress in a weld =Nb,Ed/As + Mb,Ed/Wys
= 0.00 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |0.00| < 0.31 verified (0.01)
= 0.00 [kN/mm2] Perpendicular tangent stress =
II = -0.01 [kN/mm2] Parallel tangent stress II=0.5*Vb,Ed/As
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*(II
2+
2)] fu/(w*M2) 0.03 < 0.40 verified (0.07)
Connection conforms to the code Ratio 0.11
Autodesk Robot Structural Analysis Professional 2012
Calculation of the beam-column (web) connection
EN 1993-1-8:2005/AC:2009
Ratio 0.40
GENERAL
Connection no.: 4
Connection name: Beam-column (web)
Structure node: 13
Structure bars: 6, 2
GEOMETRY
COLUMN
Section: HEA 140
Bar no.: 6
= -90.0 [Deg] Inclination angle
hc = 133.000 [mm] Height of column section
bfc = 140.000 [mm] Width of column section
twc = 5.500 [mm] Thickness of the web of column section
tfc = 8.500 [mm] Thickness of the flange of column section
rc = 12.000 [mm] Radius of column section fillet
Ac = 3141.610 [mm2] Cross-sectional area of a column
Iyc = 10331300.000 [mm
4] Moment of inertia of the column section
Material: S275
fyc = 0.28 [kN/mm2] Design resistance
fuc = 0.43 [kN/mm
2] Tensile resistance
BEAM
Section: IPE 200
Bar no.: 2
= 0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bb = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Iyb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Design resistance
fub = 0.43 [kN/mm
2] Tensile resistance
PLATE
Type: unilateral
lp = 85.000 [mm] Plate length
hp = 130.000 [mm] Plate height
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Design resistance
fup = 0.43 [kN/mm
2] Tensile resistance
UPPER BRACKET OF A BEAM
lbu = 85.000 [mm] Bracket length
hbu = 130.000 [mm] Bracket height
tbu = 6.000 [mm] Bracket thickness
Material: S275
fybu = 0.28 [kN/mm2] Design resistance
fubu = 0.43 [kN/mm
2] Tensile resistance
LOWER BRACKET OF A BEAM
lbd = 85.000 [mm] Bracket length
hbd = 130.000 [mm] Bracket height
tbd = 6.000 [mm] Bracket thickness
Material: S275
fybd = 0.28 [kN/mm2] Design resistance
fubd = 0.43 [kN/mm
2] Tensile resistance
BOLTS
BOLTS CONNECTING BEAM WITH PLATE
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
BOLTS CONNECTING UPPER BRACKET WITH BEAM
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
Class = 8.8
Bolt class
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
BOLTS CONNECTING LOWER BRACKET WITH BEAM
Class = 8.8
Bolt class
d = 16.000 [mm] Bolt diameter
d0 = 18.000 [mm] Bolt opening diameter
As = 157.000 [mm2] Effective section area of a bolt
Av = 201.062 [mm
2] Area of bolt section
fub = 0.80 [kN/mm
2] Tensile resistance
k = 1
Number of bolt columns
w = 2
Number of bolt rows
e1 = 35.000 [mm] Level of first bolt
p1 = 60.000 [mm] Vertical spacing
WELDS
acp = 5.000 [mm] Fillet welds connecting plate with column
aswu = 5.000 [mm] Fillet welds connecting upper bracket with column
aswd = 5.000 [mm] Fillet welds connecting lower bracket with column
MATERIAL FACTORS
M0 = 1.00
Partial safety factor [2.2]
M2 = 1.25
Partial safety factor [2.2]
LOADS
Case: 3: COMB1 1*1.20+2*1.60
Nb,Ed = -3.18 [kN] Axial force
Vb,Ed = -10.46 [kN] Shear force
Mb,Ed = 4547.38 [kN*mm] Bending moment
RESULTS
BOLTS CONNECTING BEAM WITH PLATE
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd1x = 49.94 [kN] Bearing resistance of a single bolt Fb,Rd1x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.86
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.86 > 0.00 verified
Fb,Rd1z = 66.35 [kN] Bearing resistance of a single bolt Fb,Rd1z=k1z*bz*fu*d*ti/M2
Bolt bearing on the plate
Direction x
k1x = 2.50
Coefficient for calculation of Fb,Rd k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1x > 0.0 2.50 > 0.00 verified
bx = 0.65
Coefficient for calculation of Fb,Rd bx=min[e2/(3*d0), fub/fu, 1]
bx > 0.0 0.65 > 0.00 verified
Fb,Rd2x = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2x=k1x*bx*fu*d*ti/M2
Direction z
k1z = 2.50
Coefficient for calculation of Fb,Rd k1z=min[2.8*(e2/d0)-1.7, 2.5]
k1z > 0.0 2.50 > 0.00 verified
bz = 0.65
Coefficient for calculation of Fb,Rd bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1]
bz > 0.0 0.65 > 0.00 verified
Fb,Rd2z = 53.51 [kN] Bearing resistance of a single bolt Fb,Rd2z=k1z*bz*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION
Bolt shear
e = 52.750 [mm] Distance between centroid of a bolt group and center of column web
M0 = -
551.57
[kN*mm]
Real bending moment M0=Vb,Ed*e
FNx = 1.59 [kN] Component force in a bolt due to influence of the longitudinal force
FNx=Nb,Ed/n
FVz = 5.23 [kN] Component force in a bolt due to influence of the shear force FVz=Vb,Ed/n
FMx = -9.19 [kN] Component force in a bolt due to influence of the moment on the x direction
FMx=M0*zi/(xi2+zi
2)
FMz = 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction
FMz=M0*xi/(xi2+zi
2)
Fx,Ed =
-7.60 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx
Fz,Ed =
5.23 [kN] Design total force in a bolt on the direction z Fz,Ed = FVz + FMz
FRdx =
49.94 [kN] Effective design capacity of a bolt on the direction x FRdx=min(FvRd, FbRd1x,
FbRd2x)
FRdz =
53.51 [kN] Effective design capacity of a bolt on the direction z FRdz=min(FvRd, FbRd1z,
FbRd2z)
|Fx,Ed| FRdx |-7.60| < 49.94 verified (0.15)
|Fz,Ed| FRdz |5.23| < 53.51 verified (0.10)
BOLTS CONNECTING UPPER BRACKET WITH BEAM
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam flange
k1 = 1.41
Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd1 = 42.79 [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2
Bolt bearing on the bracket
k1 = 1.41
Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd2 = 30.20 [kN] Bearing resistance of a single bolt Fb,Rd2=k1*b*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE UPPER BRACKET - BEAM CONNECTION
Bolt shear
FEd = 10.57 [kN] Shear force in a bolt FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n
FRd = 30.20 [kN] Effective design capacity of a bolt FRd=min(FvRd, FbRd1, FbRd2)
|FEd| FRd |10.57| < 30.20 verified (0.35)
BOLTS CONNECTING LOWER BRACKET WITH BEAM
BOLT CAPACITIES
Fv,Rd = 77.21 [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2
Bolt bearing on the beam flange
k1 = 1.41
Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd1 = 42.79 [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2
Bolt bearing on the bracket
k1 = 1.41
Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5]
k1 > 0.0 1.41 > 0.00 verified
b = 0.65
Coefficient for calculation of Fb,Rd b=min[e2/(3*d0), fub/fu, 1]
b > 0.0 0.65 > 0.00 verified
Fb,Rd2 = 30.20 [kN] Bearing resistance of a single bolt Fb,Rd2=k1*b*fu*d*ti/M2
FORCES ACTING ON BOLTS IN THE LOWER BRACKET - BEAM CONNECTION
Bolt shear
FEd = -12.16 [kN] Shear force in a bolt FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n
FRd = 30.20 [kN] Effective design capacity of a bolt FRd=min(FvRd, FbRd1, FbRd2)
|FEd| FRd |-12.16| < 30.20 verified (0.40)
VERIFICATION OF THE SECTION DUE TO BLOCK TEARING
PLATE
Ant = 246.000 [mm2] Net area of the section in tension
Anv = 408.000 [mm
2] Area of the section in shear
VeffRd = 107.09 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-10.46| < 107.09 verified (0.10)
BEAM
Ant = 145.600 [mm2] Net area of the section in tension
Anv = 576.800 [mm
2] Area of the section in shear
VeffRd = 116.62 [kN] Design capacity of a section weakened by openings VeffRd=0.5*fu*Ant/M2 + (1/3)*fy*Anv/M0
|Vb,Ed| VeffRd |-10.46| < 116.62 verified (0.09)
WELD RESISTANCE
FILLET WELDS CONNECTING PLATE WITH COLUMN
As = 650.000 [mm2] Weld area As = hp*agp
II = -0.01 [kN/mm2] Parallel tangent stress II=0.5*Vb,Ed/As
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*(II
2+
2)] fu/(w*M2) 0.03 < 0.40 verified (0.07)
FILLET WELDS CONNECTING UPPER BRACKET WITH COLUMN
As = 650.000 [mm2] Weld area
= 0.02 [kN/mm
2] Normal stress in a weld =0.5*[Nb,Ed/2 + Mb,Ed/hb]/As
= 0.01 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |0.01| < 0.31 verified (0.04)
= 0.01 [kN/mm2] Perpendicular tangent stress =
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*
2] fu/(w*M2) 0.03 < 0.40 verified (0.07)
FILLET WELDS CONNECTING LOWER BRACKET WITH COLUMN
As = 650.000 [mm2] Weld area
= -0.02 [kN/mm
2] Normal stress in a weld =0.5*[Nb,Ed/2 - Mb,Ed/hb]/As
= -0.01 [kN/mm2] Normal perpendicular stress in the weld =/2
|| 0.9*fu/M2 |-0.01| < 0.31 verified (0.04)
= -0.01 [kN/mm2] Perpendicular tangent stress =
w = 0.85
Correlation coefficient [Table 4.1]
[2+3*
2] fu/(w*M2) 0.03 < 0.40 verified (0.07)
Connection conforms to the code Ratio 0.40
Autodesk Robot Structural Analysis Professional 2012
Design of fixed beam-to-column connection
EN 1993-1-8:2005/AC:2009
Ratio 0.14
GENERAL
Connection no.: 2
Connection name: Column-Beam
Structure node: 13
Structure bars: 6, 4
GEOMETRY
COLUMN
Section: HEA 140
Bar no.: 6
= -90.0 [Deg] Inclination angle
hc = 133.000 [mm] Height of column section
bfc = 140.000 [mm] Width of column section
twc = 5.500 [mm] Thickness of the web of column section
tfc = 8.500 [mm] Thickness of the flange of column section
rc = 12.000 [mm] Radius of column section fillet
Ac = 3141.610 [mm2] Cross-sectional area of a column
Ixc = 10331300.000 [mm
4] Moment of inertia of the column section
Material: S275
fyc = 0.28 [kN/mm2] Resistance
BEAM
Section: IPE 200
Section: IPE 200
Bar no.: 4
= 0.0 [Deg] Inclination angle
hb = 200.000 [mm] Height of beam section
bf = 100.000 [mm] Width of beam section
twb = 5.600 [mm] Thickness of the web of beam section
tfb = 8.500 [mm] Thickness of the flange of beam section
rb = 12.000 [mm] Radius of beam section fillet
rb = 12.000 [mm] Radius of beam section fillet
Ab = 2848.410 [mm2] Cross-sectional area of a beam
Ixb = 19431700.000 [mm
4] Moment of inertia of the beam section
Material: S275
fyb = 0.28 [kN/mm2] Resistance
BOLTS
d = 16.000 [mm] Bolt diameter
Class = 8.8
Bolt class
FtRd = 90.43 [kN] Tensile resistance of a bolt
nh = 2
Number of bolt columns
nv = 3
Number of bolt rows
h1 = 60.000 [mm] Distance between first bolt and upper edge of front plate
Horizontal spacing ei = 50.000 [mm]
Vertical spacing pi = 50.000;50.000 [mm]
PLATE
hp = 220.000 [mm] Plate height
bp = 100.000 [mm] Plate width
tp = 6.000 [mm] Plate thickness
Material: S275
fyp = 0.28 [kN/mm2] Resistance
FILLET WELDS
aw = 4.000 [mm] Web weld
af = 6.000 [mm] Flange 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: 3: COMB1 1*1.20+2*1.60
Mb1,Ed = 1672.26 [kN*mm] Bending moment in the right beam
Vb1,Ed = -4.61 [kN] Shear force in the right beam
Nb1,Ed = 0.05 [kN] Axial force in the right beam
Mc1,Ed = 1682.26 [kN*mm] Bending moment in the lower column
Vc1,Ed = -1.06 [kN] Shear force in the lower column
Nc1,Ed = -15.09 [kN] Axial force in the lower column
Nc2,Ed = -0.03 [kN] Axial force in the upper column
RESULTS
BEAM RESISTANCES
TENSION
Ab = 2848.410 [mm2] Area EN1993-1-1:[6.2.3]
Ntb,Rd = Ab fyb / M0 Ntb,Rd = 783.31 [kN] Design tensile resistance of the section EN1993-1-1:[6.2.3]
SHEAR
Avb = 1400.010 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
Vcb,Rd = Avb (fyb / 3) / M0 Vcb,Rd = 222.28 [kN] Design sectional resistance for shear EN1993-1-1:[6.2.6.(2)]
Vb1,Ed / Vcb,Rd 1,0 0.02 < 1.00 verified (0.02)
BENDING - PLASTIC MOMENT (WITHOUT BRACKETS)
Wplb = 220657.000 [mm3] Plastic section modulus EN1993-1-1:[6.2.5.(2)]
Mb,pl,Rd = Wplb fyb / M0 Mb,pl,Rd =
60680.6
8
[kN*mm]
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 = 220657.000 [mm3] Plastic section modulus EN1993-1-1:[6.2.5]
Mcb,Rd = Wpl fyb / M0 Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending EN1993-1-1:[6.2.5]
FLANGE AND WEB - COMPRESSION
Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending EN1993-1-1:[6.2.5]
hf = 191.500 [mm] Distance between the centroids of flanges [6.2.6.7.(1)]
Fc,fb,Rd = Mcb,Rd / hf Fc,fb,Rd = 316.87 [kN] Resistance of the compressed flange and web [6.2.6.7.(1)]
COLUMN RESISTANCES
WEB PANEL - SHEAR
Mb1,Ed = 1672.26 [kN*mm] Bending moment (right beam) [5.3.(3)]
Mb2,Ed = 0.00 [kN*mm] Bending moment (left beam) [5.3.(3)]
Vc1,Ed = -1.06 [kN] Shear force (lower column) [5.3.(3)]
Vc2,Ed = 0.00 [kN] Shear force (upper column) [5.3.(3)]
z = 120.750 [mm] Lever arm [6.2.5]
Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2
Vwp,Ed = 14.38 [kN] Shear force acting on the web panel [5.3.(3)]
Avs = 1012.360 [mm2] Shear area of the column web EN1993-1-1:[6.2.6.(3)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
Vwp,Rd = 0.9*( fy,wc*Avc+fy,wp*Avp+fys*Avd ) / (3 M0) Vwp,Rd = 144.66 [kN] Resistance of the column web panel for shear [6.2.6.1]
Vwp,Ed / Vwp,Rd 1,0 0.10 < 1.00 verified (0.10)
WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE
Bearing:
twc = 5.500 [mm] Effective thickness of the column web [6.2.6.2.(6)]
beff,c,wc = 139.971 [mm] Effective width of the web for compression [6.2.6.2.(1)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 0.76
Reduction factor for interaction with shear [6.2.6.2.(1)]
com,Ed = 0.01 [kN/mm2] Maximum compressive stress in web [6.2.6.2.(2)]
kwc = 1.00
Reduction factor conditioned by compressive stresses [6.2.6.2.(2)]
Fc,wc,Rd1 = kwc beff,c,wbc twc fyc / M0 Fc,wc,Rd1 = 159.95 [kN] Column web resistance [6.2.6.2.(1)]
Buckling:
dwc = 92.000 [mm] Height of compressed web [6.2.6.2.(1)]
p = 0.70
Plate slenderness of an element [6.2.6.2.(1)]
= 1.00
Reduction factor for element buckling [6.2.6.2.(1)]
Fc,wb,Rd2 = kwc beff,c,wc twc fyc / M1
Fc,wc,Rd2 = 159.95 [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 = 159.95 [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 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 89.741
78.42
5 78.42
5 78.42
5
2 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 100.00
0 50.00
0 50.00
0 50.00
0
3 12.65
0 -
45.00
0 -
50.00
0 79.48
2 106.85
0 79.48
2 106.85
0 89.741
78.42
5 78.42
5 78.42
5
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 17.67
5 -
25.00
0 -
50.00
0 111.05
2 104.48
2 104.48
2 104.48
2 105.52
6 78.50
8 78.50
8 78.50
8
2 17.67
5 -
25.00
0 -
50.00
0 111.05
2 101.94
8 101.94
8 101.94
8 100.00
0 50.00
0 50.00
0 50.00
0
3 17.67
5 -
25.00
0 -
50.00
0 111.05
2 101.94
8 101.94
8 101.94
8 105.52
6 75.97
4 75.97
4 75.97
4
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
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 TENSION
Ft,Rd = 90.43 [kN] Bolt resistance for tension [Table 3.4]
Bp,Rd = 93.37 [kN] Punching shear resistance of a bolt [Table 3.4]
Nj,Rd = Min (Ntb,Rd , nv nh Ft,Rd , nv nh Bp,Rd) Nj,Rd = 542.59 [kN] Connection resistance for tension [6.2]
Nb1,Ed / Nj,Rd 1,0 0.00 < 1.00 verified (0.00)
CONNECTION RESISTANCE FOR BENDING
Ft,Rd = 90.43 [kN] Bolt resistance for tension [Table 3.4]
Bp,Rd = 93.37 [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
Ft1,Rd = Min (Ft1,Rd,comp) 58.52 Bolt row resistance
Ft,fc,Rd(1) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(1) = 107.85 107.85 Column web - tension
Ft,ep,Rd(1) = 58.52 58.52 Front plate - tension
Ft,wb,Rd(1) = 160.90 160.90 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ = 144.66 144.66 Web panel - shear
Fc,wc,Rd = 159.95 159.95 Column web - compression
Fc,fb,Rd = 316.87 316.87 Beam flange - compression
RESISTANCE OF THE BOLT ROW NO. 2
Ft2,Rd,comp - Formula Ft2,Rd,comp Component
Ft2,Rd = Min (Ft2,Rd,comp) 13.46 Bolt row resistance
Ft,fc,Rd(2) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(2) = 107.85 107.85 Column web - tension
Ft,ep,Rd(2) = 57.10 57.10 Front plate - tension
Ft,wb,Rd(2) = 157.00 157.00 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ - 11 Fti,Rd = 144.66 - 58.52 86.14 Web panel - shear
Fc,wc,Rd - 11 Ftj,Rd = 159.95 - 58.52 101.43 Column web - compression
Fc,fb,Rd - 11 Ftj,Rd = 316.87 - 58.52 258.35 Beam flange - compression
Ft,fc,Rd(2 + 1) - 11 Ftj,Rd = 201.71 - 58.52 143.19 Column flange - tension - group
Ft,wc,Rd(2 + 1) - 11 Ftj,Rd = 152.01 - 58.52 93.49 Column web - tension - group
Ft,ep,Rd(2 + 1) - 11 Ftj,Rd = 71.98 - 58.52 13.46 Front plate - tension - group
Ft,wb,Rd(2 + 1) - 11 Ftj,Rd = 197.90 - 58.52 139.38 Beam web - tension - group
RESISTANCE OF THE BOLT ROW NO. 3
Ft3,Rd,comp - Formula Ft3,Rd,comp Component
Ft3,Rd = Min (Ft3,Rd,comp) 42.56 Bolt row resistance
Ft,fc,Rd(3) = 124.84 124.84 Column flange - tension
Ft,wc,Rd(3) = 107.85 107.85 Column web - tension
Ft,ep,Rd(3) = 57.10 57.10 Front plate - tension
Ft,wb,Rd(3) = 157.00 157.00 Beam web - tension
Bp,Rd = 186.75 186.75 Bolts due to shear punching
Vwp,Rd/ - 12 Fti,Rd = 144.66 - 71.98 72.68 Web panel - shear
Fc,wc,Rd - 12 Ftj,Rd = 159.95 - 71.98 87.97 Column web - compression
Fc,fb,Rd - 12 Ftj,Rd = 316.87 - 71.98 244.89 Beam flange - compression
Ft,fc,Rd(3 + 2) - 22 Ftj,Rd = 201.71 - 13.46 188.25 Column flange - tension - group
Ft,wc,Rd(3 + 2) - 22 Ftj,Rd = 152.01 - 13.46 138.55 Column web - tension - group
Ft,fc,Rd(3 + 2 + 1) - 21 Ftj,Rd = 324.89 - 71.98 252.91 Column flange - tension - group
Ft,wc,Rd(3 + 2 + 1) - 21 Ftj,Rd = 192.49 - 71.98 120.51 Column web - tension - group
Ft,ep,Rd(3 + 2) - 22 Ftj,Rd = 70.56 - 13.46 57.10 Front plate - tension - group
Ft,wb,Rd(3 + 2) - 22 Ftj,Rd = 194.00 - 13.46 180.54 Beam web - tension - group
Ft,ep,Rd(3 + 2 + 1) - 21 Ftj,Rd = 114.54 - 71.98 42.56 Front plate - tension - group
Ft,wb,Rd(3 + 2 + 1) - 21 Ftj,Rd = 314.90 - 71.98 242.92 Beam web - tension - group
SUMMARY TABLE OF FORCES
Nr hj Ftj,Rd Ft,fc,Rd Ft,wc,Rd Ft,ep,Rd Ft,wb,Rd Ft,Rd Bp,Rd
1 145.750 58.52 124.84 107.85 58.52 160.90 180.86 186.75
2 95.750 13.46 124.84 107.85 57.10 157.00 180.86 186.75
3 45.750 42.56 124.84 107.85 57.10 157.00 180.86 186.75
CONNECTION RESISTANCE FOR BENDING Mj,Rd
Mj,Rd = hj Ftj,Rd Mj,Rd = 11765.23 [kN*mm] Connection resistance for bending [6.2]
Mb1,Ed / Mj,Rd 1,0 0.14 < 1.00 verified (0.14)
CONNECTION RESISTANCE FOR SHEAR
v = 0.60
Coefficient for calculation of Fv,Rd [Table 3.4]
Fv,Rd = 77.21 [kN] Shear resistance of a single bolt [Table 3.4]
Ft,Rd,max = 90.43 [kN] Tensile resistance of a single bolt [Table 3.4]
Fb,Rd,int = 48.86 [kN] Bearing resistance of an intermediate bolt [Table 3.4]
Fb,Rd,ext = 72.29 [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
1 180.86 0.02 58.52 8.32 8.34 97.72
2 180.86 0.02 13.46 1.91 1.93 97.72
3 180.86 0.02 42.56 6.05 6.07 97.72
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,Rd (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 = 293.16 [kN] Connection resistance for shear [Table 3.4]
Vb1,Ed / Vj,Rd 1,0 0.02 < 1.00 verified (0.02)
WELD RESISTANCE
Aw = 3196.800 [mm2] Area of all welds
[4.5.3.2(2)]
Awy = 1924.800 [mm2] Area of horizontal welds
[4.5.3.2(2)]
Awz = 1272.000 [mm2] Area of vertical welds
[4.5.3.2(2)]
Iwy = 20726644.20
0 [mm
4]
Moment of inertia of the weld arrangement with respect to the hor. axis
[4.5.3.2(5)]
max=max =
0.01 [kN/mm
2
] Normal stress in a weld
[4.5.3.2(5)]
= = 0.00 [kN/mm
2
] Stress in a vertical weld
[4.5.3.2(5)]
II = -0.00 [kN/mm
2
] Tangent stress
[4.5.3.2(5)]
w = 0.85
Correlation coefficient [4.5.3.2(7
)]
[max2 + 3*(max
2)] fu/(w*M2) 0.01 < 0.40 verified (0.03)
[2 + 3*(
2+II
2)] fu/(w*M2) 0.01 < 0.40 verified (0.03)
0.9*fu/M2 0.01 < 0.31 verified (0.02)
CONNECTION STIFFNESS
twash = 4.000 [mm] Washer thickness [6.2.6.3.(2)]
hhead = 12.000 [mm] Bolt head height [6.2.6.3.(2)]
hnut = 16.000 [mm] Bolt nut height [6.2.6.3.(2)]
Lb = 36.500 [mm] Bolt length [6.2.6.3.(2)]
k10 = 6.882 [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 hj2
Sum 272.472 31450.892
Nr hj k3 k4 k5 keff,j keff,j hj keff,j hj2
1 145.750 2.603 21.413 2.764 1.066 155.390 22648.134
2 95.750 1.659 13.652 1.760 0.720 68.925 6599.595
3 45.750 2.603 21.413 2.675 1.053 48.157 2203.164
keff,j = 1 / (35 (1 / ki,j)) [6.3.3.1.(2)]
zeq = j keff,j hj2 / j keff,j hj
zeq = 115.428 [mm] Equivalent force arm [6.3.3.1.(3)]
keq = j keff,j hj / zeq keq = 2.361 [mm] Equivalent stiffness coefficient of a bolt arrangement [6.3.3.1.(1)]
Avc = 1012.360 [mm2] Shear area EN1993-1-1:[6.2.6.(3)]
= 1.00
Transformation parameter [5.3.(7)]
z = 115.428 [mm] Lever arm [6.2.5]
k1 = 3.333 [mm] Stiffness coefficient of the column web panel subjected to shear [6.3.2.(1)]
beff,c,wc = 135.485 [mm] Effective width of the web for compression [6.2.6.2.(1)]
twc = 5.500 [mm] Effective thickness of the column web [6.2.6.2.(6)]
dc = 116.000 [mm] Height of compressed web [6.2.6.2.(1)]
k2 = 4.497 [mm] Stiffness coefficient of the compressed column web [6.3.2.(1)]
Sj,ini = E zeq2 / i (1 / k1 + 1 / k2 + 1 / keq) [6.3.1.(4)]
Sj,ini = 2887049.32 [kN*mm] Initial rotational stiffness [6.3.1.(4)]
= 1.00
Stiffness coefficient of a connection [6.3.1.(6)]
Sj = Sj,ini / [6.3.1.(4)]
Sj = 2887049.32 [kN*mm] Final rotational stiffness [6.3.1.(4)]
Connection classification due to stiffness.
Sj,rig = 8951682.02 [kN*mm] Stiffness of a rigid connection [5.2.2.5]
Sj,pin = 559480.13 [kN*mm] Stiffness of a pinned connection [5.2.2.5]
Sj,pin Sj,ini < Sj,rig SEMI-RIGID
Connection conforms to the code Ratio 0.14