T8

CALCULATION NOTE FOR T8-INTERDIKE STAIRCASE Loads Cases Case 1 2 3

Label

Case name

DL1 LL1 COMB1

Dead load Live load Combination 1

Result

Member 1 Simple bar_1 2 Simple bar_2 3 Simple bar_3 4 Simple bar_4 5 Simple bar_5 6 Simple bar_6 9 Simple bar_9 10 Simple bar_10 12 Simple bar_12 13 Simple bar_13

Section

Material

Lay

Laz

Ratio

Case

IPE 200

S275

11.73

43.34

0.19

3 COMB1

IPE 200

S275

11.73

43.34

0.19

3 COMB1

IPE 200

S275

43.10

159.24

0.27

3 COMB1

IPE 200

S275

43.10

159.24

0.08

3 COMB1

HEA 140

S275

43.42

70.73

0.27

3 COMB1

HEA 140

S275

43.42

70.73

0.27

3 COMB1

UPN 200

S275

49.25

177.08

0.10

3 COMB1

UPN 200

S275

49.25

177.08

0.18

3 COMB1

UPN 200

S275

49.25

177.08

0.18

3 COMB1

UPN 200

S275

49.25

177.08

0.10

3 COMB1

Autodesk Robot Structural Analysis Professional 2012

Design of fixed beam-to-column connection EN 1993-1-8:2005/AC:2009

GENERAL Connection no.: Connection name: Structure node: Structure bars:

1 Column-Beam 12 5, 4

GEOMETRY COLUMN Section: HEA 140 Bar no.: 5 -90.0 [Deg] Inclination angle = 133.000 [mm] Height of column section hc = 140.000 [mm] Width of column section bfc = 5.500 [mm] Thickness of the web of column section twc = 8.500 [mm] Thickness of the flange of column section tfc = 12.000 [mm] Radius of column section fillet rc = 3141.610 [mm2] Cross-sectional area of a column Ac = 4 Ixc = 10331300.000 [mm ] Moment of inertia of the column section Material: S275 0.28 [kN/mm2] Resistance fyc =

BEAM Section: IPE 200

Ratio 0.14

Section: IPE 200 Bar no.: 4 -0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bf = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Ixb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Resistance fyb =

BOLTS 16.000 [mm] d= 8.8 Class = 90.43 [kN] FtRd = 2 nh = 3 nv = 60.000 [mm] h1 = Horizontal spacing ei = Vertical spacing pi =

Bolt diameter Bolt class Tensile resistance of a bolt Number of bolt columns Number of bolt rows Distance between first bolt and upper edge of front plate 50.000 [mm] 50.000;50.000 [mm]

PLATE 220.000 [mm] hp = 100.000 [mm] bp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp =

Plate height Plate width Plate thickness Resistance

FILLET WELDS aw = af =

4.000 6.000

[mm] [mm]

Web weld Flange weld

MATERIAL FACTORS M0 = M1 = M2 = M3 =

1.00 1.00 1.25 1.25

Partial safety factor Partial safety factor Partial safety factor Partial safety factor

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 -4.61 Vb1,Ed = [kN] Shear force in the right beam 0.05 Nb1,Ed = [kN] Axial force in the right beam Mc1,Ed = -1682.26 [kN*mm] Bending moment in the lower column 1.06 Vc1,Ed = [kN] Shear force in the lower column -15.09 Nc1,Ed = [kN] Axial force in the lower column -0.03 Nc2,Ed = [kN] Axial force in the upper column

RESULTS

[2.2] [2.2] [2.2] [2.2]

BEAM RESISTANCES TENSION 2848.410 Ab = Ntb,Rd = Ab fyb / M0 Ntb,Rd = 783.31

2

[mm ]

Area

[kN] Design tensile resistance of the section SHEAR 1400.010 [mm2] Shear area Avb = Vcb,Rd = Avb (fyb / 3) / M0 Vcb,Rd = 222.28 [kN] Design sectional resistance for shear 0.02 < 1.00 verified Vb1,Ed / Vcb,Rd  1,0 BENDING - PLASTIC MOMENT (WITHOUT BRACKETS) 3 Wplb = 220657.000 [mm ] Plastic section modulus Mb,pl,Rd = W plb fyb / M0 60680.6 [kN*mm Plastic resistance of the section for bending (without Mb,pl,Rd 8 = ] stiffeners) BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT 3 Wpl = 220657.000 [mm ] Plastic section modulus Mcb,Rd = W pl fyb / M0 Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending FLANGE AND WEB - COMPRESSION Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending 191.500 [mm] Distance between the centroids of flanges hf = Fc,fb,Rd = Mcb,Rd / hf Fc,fb,Rd = 316.87 [kN] Resistance of the compressed flange and web

EN1993-1-1:[6.2.3] EN1993-1-1:[6.2.3] EN1993-1-1:[6.2.6.(3)] EN1993-1-1:[6.2.6.(2)] (0.02) EN1993-1-1:[6.2.5.(2)] EN1993-11:[6.2.5.(2)] EN1993-1-1:[6.2.5] EN1993-1-1:[6.2.5] EN1993-1-1:[6.2.5] [6.2.6.7.(1)] [6.2.6.7.(1)]

COLUMN RESISTANCES WEB PANEL - SHEAR Mb1,Ed = 1672.26 [kN*mm] Bending moment (right beam) 0.00 [kN*mm] Bending moment (left beam) Mb2,Ed = 1.06 Vc1,Ed = [kN] Shear force (lower column) 0.00 Vc2,Ed = [kN] Shear force (upper column) 120.750 [mm] Lever arm z= Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2 13.32 Vwp,Ed = [kN] Shear force acting on the web panel 2 1012.360 Avs = [mm ] Shear area of the column web 1012.360 [mm2] Shear area Avc = 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 0.09 < 1.00 verified Vwp,Ed / Vwp,Rd  1,0

[5.3.(3)] [5.3.(3)] [5.3.(3)] [5.3.(3)] [6.2.5] [5.3.(3)] EN1993-1-1:[6.2.6.(3)] EN1993-1-1:[6.2.6.(3)] [6.2.6.1] (0.09)

WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE Bearing: 5.500 [mm] Effective thickness of the column web twc = beff,c,wc = 139.971 [mm] Effective width of the web for compression 1012.360 [mm2] Shear area Avc = 0.76 Reduction factor for interaction with shear = 0.01 [kN/mm2] Maximum compressive stress in web com,Ed = 1.00 kwc = Reduction factor conditioned by compressive stresses Fc,wc,Rd1 =  kwc beff,c,wbc twc fyc / M0 Fc,wc,Rd1 = 159.95 [kN] Column web resistance Buckling: 92.000 [mm] Height of compressed web dwc = 0.70 Plate slenderness of an element p = 1.00 Reduction factor for element buckling = Fc,wb,Rd2 =  kwc  beff,c,wc twc fyc / M1

[6.2.6.2.(6)] [6.2.6.2.(1)] EN1993-1-1:[6.2.6.(3)] [6.2.6.2.(1)] [6.2.6.2.(2)] [6.2.6.2.(2)] [6.2.6.2.(1)] [6.2.6.2.(1)] [6.2.6.2.(1)] [6.2.6.2.(1)]

Fc,wc,Rd2 = 159.95 [kN] Column web resistance 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)]

[6.2.6.2.(1)]

GEOMETRICAL PARAMETERS OF A CONNECTION EFFECTIVE LENGTHS AND PARAMETERS - COLUMN FLANGE Nr

m mx 12.65 1 0 12.65 2 0 12.65 3 0

e ex 45.00 0 45.00 0 45.00 0

p 50.00 0 50.00 0 50.00 0

leff,cp 79.48 2 79.48 2 79.48 2

leff,nc 106.85 0 106.85 0 106.85 0

leff,1 79.48 2 79.48 2 79.48 2

leff,2 106.85 0 106.85 0 106.85 0

leff,cp,g

leff,nc,g 78.42 89.741 5 100.00 50.00 0 0 78.42 89.741 5

leff,1,g 78.42 5 50.00 0 78.42 5

leff,2,g 78.42 5 50.00 0 78.42 5

leff,1,g 78.50 8 50.00 0 75.97 4

leff,2,g 78.50 8 50.00 0 75.97 4

EFFECTIVE LENGTHS AND PARAMETERS - FRONT PLATE Nr

m mx 17.67 1 5 17.67 2 5 17.67 3 5

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

e ex 25.00 0 25.00 0 25.00 0

p 50.00 0 50.00 0 50.00 0

leff,cp 111.05 2 111.05 2 111.05 2

leff,nc 104.48 2 101.94 8 101.94 8

leff,1 104.48 2 101.94 8 101.94 8

leff,2 104.48 2 101.94 8 101.94 8

leff,cp,g 105.52 6 100.00 0 105.52 6

leff,nc,g 78.50 8 50.00 0 75.97 4

– Bolt distance from the web – Bolt distance from the beam flange – Bolt distance from the outer edge – Bolt distance from the horizontal outer edge – Distance between bolts – Effective length for a single bolt in the circular failure mode – Effective length for a single bolt in the non-circular failure mode – Effective length for a single bolt for mode 1 – Effective length for a single bolt for mode 2 – Effective length for a group of bolts in the circular failure mode – Effective length for a group of bolts in the non-circular failure mode – Effective length for a group of bolts for mode 1 – Effective length for a group of bolts for mode 2

CONNECTION RESISTANCE FOR TENSION 90.43 Ft,Rd = [kN] Bolt resistance for tension 93.37 Bp,Rd = [kN] Punching shear resistance of a bolt Nj,Rd = Min (Ntb,Rd , nv nh Ft,Rd , nv nh Bp,Rd) 542.59 Nj,Rd = [kN] Connection resistance for tension 0.00 < 1.00 Nb1,Ed / Nj,Rd  1,0

[Table 3.4] [Table 3.4]

verified

[6.2] (0.00)

CONNECTION RESISTANCE FOR BENDING 90.43 Ft,Rd = [kN] Bolt resistance for tension 93.37 Bp,Rd = [kN] Punching shear resistance of a bolt 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) Ft,wc,Rd =  beff,t,wc twc fyc / M0 Ft,ep,Rd = Min (FT,1,ep,Rd , FT,2,ep,Rd , FT,3,ep,Rd) Ft,wb,Rd = beff,t,wb twb fyb / M0 RESISTANCE OF THE BOLT ROW NO. 1

[Table 3.4] [Table 3.4]

[6.2.6.4] , [Tab.6.2] [6.2.6.3.(1)] [6.2.6.5] , [Tab.6.2] [6.2.6.8.(1)]

Ft1,Rd,comp - Formula Ft1,Rd = Min (Ft1,Rd,comp) Ft,fc,Rd(1) = 124.84 Ft,wc,Rd(1) = 107.85 Ft,ep,Rd(1) = 58.52 Ft,wb,Rd(1) = 160.90 Bp,Rd = 186.75 Vwp,Rd/ = 144.66 Fc,wc,Rd = 159.95 Fc,fb,Rd = 316.87

Ft1,Rd,comp 58.52 124.84 107.85 58.52 160.90 186.75 144.66 159.95 316.87

Component

Ft2,Rd,comp 13.46 124.84 107.85 57.10 157.00 186.75 86.14 101.43 258.35 143.19 93.49 13.46 139.38

Component

Ft3,Rd,comp 42.56 124.84 107.85 57.10 157.00 186.75 72.68 87.97 244.89 188.25 138.55 252.91 120.51 57.10 180.54 42.56 242.92

Component

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression

RESISTANCE OF THE BOLT ROW NO. 2 Ft2,Rd,comp - Formula Ft2,Rd = Min (Ft2,Rd,comp) Ft,fc,Rd(2) = 124.84 Ft,wc,Rd(2) = 107.85 Ft,ep,Rd(2) = 57.10 Ft,wb,Rd(2) = 157.00 Bp,Rd = 186.75 1 Vwp,Rd/ - 1 Fti,Rd = 144.66 - 58.52 1 Fc,wc,Rd - 1 Ftj,Rd = 159.95 - 58.52 1 Fc,fb,Rd - 1 Ftj,Rd = 316.87 - 58.52 1 Ft,fc,Rd(2 + 1) - 1 Ftj,Rd = 201.71 - 58.52 1 Ft,wc,Rd(2 + 1) - 1 Ftj,Rd = 152.01 - 58.52 1 Ft,ep,Rd(2 + 1) - 1 Ftj,Rd = 71.98 - 58.52 1 Ft,wb,Rd(2 + 1) - 1 Ftj,Rd = 197.90 - 58.52

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression Column flange - tension - group Column web - tension - group Front plate - tension - group Beam web - tension - group

RESISTANCE OF THE BOLT ROW NO. 3 Ft3,Rd,comp - Formula Ft3,Rd = Min (Ft3,Rd,comp) Ft,fc,Rd(3) = 124.84 Ft,wc,Rd(3) = 107.85 Ft,ep,Rd(3) = 57.10 Ft,wb,Rd(3) = 157.00 Bp,Rd = 186.75 2 Vwp,Rd/ - 1 Fti,Rd = 144.66 - 71.98 2 Fc,wc,Rd - 1 Ftj,Rd = 159.95 - 71.98 2 Fc,fb,Rd - 1 Ftj,Rd = 316.87 - 71.98 2 Ft,fc,Rd(3 + 2) - 2 Ftj,Rd = 201.71 - 13.46 2 Ft,wc,Rd(3 + 2) - 2 Ftj,Rd = 152.01 - 13.46 1 Ft,fc,Rd(3 + 2 + 1) - 2 Ftj,Rd = 324.89 - 71.98 1 Ft,wc,Rd(3 + 2 + 1) - 2 Ftj,Rd = 192.49 - 71.98 2 Ft,ep,Rd(3 + 2) - 2 Ftj,Rd = 70.56 - 13.46 2 Ft,wb,Rd(3 + 2) - 2 Ftj,Rd = 194.00 - 13.46 1 Ft,ep,Rd(3 + 2 + 1) - 2 Ftj,Rd = 114.54 - 71.98 1 Ft,wb,Rd(3 + 2 + 1) - 2 Ftj,Rd = 314.90 - 71.98

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression Column flange - tension - group Column web - tension - group Column flange - tension - group Column web - tension - group Front plate - tension - group Beam web - tension - group Front plate - tension - group Beam web - tension - group

SUMMARY TABLE OF FORCES Nr hj 1 145.750 2 95.750 3 45.750

Ftj,Rd 58.52 13.46 42.56

Ft,fc,Rd 124.84 124.84 124.84

Ft,wc,Rd 107.85 107.85 107.85

Ft,ep,Rd 58.52 57.10 57.10

CONNECTION RESISTANCE FOR BENDING Mj,Rd Mj,Rd =  hj Ftj,Rd Mj,Rd = 11765.23 [kN*mm] Connection resistance for bending 0.14 < 1.00 Mb1,Ed / Mj,Rd  1,0

Ft,wb,Rd 160.90 157.00 157.00

verified

Ft,Rd 180.86 180.86 180.86

Bp,Rd 186.75 186.75 186.75

[6.2] (0.14)

CONNECTION RESISTANCE FOR SHEAR v = Fv,Rd = Ft,Rd,max = Fb,Rd,int = Fb,Rd,ext =

0.60 77.21 90.43 48.86 72.29

Nr Ftj,Rd,N 1 180.86 2 180.86 3 180.86

[kN] [kN] [kN] [kN]

Coefficient for calculation of Fv,Rd Shear resistance of a single bolt Tensile resistance of a single bolt Bearing resistance of an intermediate bolt Bearing resistance of an outermost bolt Ftj,Ed,N

0.02 0.02 0.02

Ftj,Rd,M 58.52 13.46 42.56

[Table 3.4] [Table 3.4] [Table 3.4] [Table 3.4] [Table 3.4]

Ftj,Ed,M 8.32 1.91 6.05

Ftj,Ed 8.34 1.93 6.07

Fvj,Rd 97.72 97.72 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 Fvj,Rd 293.16 Vj,Rd = n

[kN]

Vb1,Ed / Vj,Rd  1,0

Connection resistance for shear 0.02 < 1.00

[Table 3.4] [Table 3.4] (0.02)

verified

WELD RESISTANCE Aw =

3196.800 [mm2] Area of all welds

Awy =

1924.800 [mm2] Area of horizontal welds

Awz =

1272.000 [mm2] Area of vertical welds

Iwy = max=max = = = II =

20726644.20 Moment of inertia of the weld arrangement with respect to the 4 0 [mm ] hor. axis 2 0.01 [kN/mm Normal stress in a weld ] 2 [kN/mm 0.00 Stress in a vertical weld ] 2 -0.00 [kN/mm Tangent stress ]

w =

0.85

Correlation coefficient

[max + 3*(max )]  fu/(w*M2) 2 2 2 [ + 3*( +II )]  fu/(w*M2)   0.9*fu/M2 2

2

0.01 < 0.40 0.01 < 0.40 0.01 < 0.31

verified verified verified

[4.5.3.2(2 )] [4.5.3.2(2 )] [4.5.3.2(2 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(7 )] (0.03) (0.03) (0.02)

CONNECTION STIFFNESS 4.000 [mm] Washer thickness twash = hhead = 12.000 [mm] Bolt head height 16.000 [mm] Bolt nut height hnut = 36.500 [mm] Bolt length Lb = 6.882 [mm] Stiffness coefficient of bolts k10 = STIFFNESSES OF BOLT ROWS Nr

hj

k3

k4

k5

[6.2.6.3.(2)] [6.2.6.3.(2)] [6.2.6.3.(2)] [6.2.6.3.(2)] [6.3.2.(1)] keff,j Sum

keff,j hj 272.472

keff,j hj 31450.892

2

Nr hj 1 145.750 2 95.750 3 45.750

k3 2.603 1.659 2.603

k4 21.413 13.652 21.413

k5 2.764 1.760 2.675

keff,j 1.066 0.720 1.053

5

keff,j hj 22648.134 6599.595 2203.164

2

[6.3.3.1.(2)]

keff,j = 1 / (3 (1 / ki,j)) zeq = j keff,j hj / j keff,j hj 115.428 [mm] zeq =

keff,j hj 155.390 68.925 48.157

2

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)] 2 Avc = 1012.360 [mm ] Shear area EN1993-1-1:[6.2.6.(3)] 1.00 Transformation parameter [5.3.(7)] = 115.428 [mm] Lever arm z= [6.2.5] 3.333 [mm] Stiffness coefficient of the column web panel subjected to shear k1 = [6.3.2.(1)] beff,c,wc = 135.485 [mm] Effective width of the web for compression [6.2.6.2.(1)] 5.500 [mm] Effective thickness of the column web twc = [6.2.6.2.(6)] 116.000 [mm] Height of compressed web dc = [6.2.6.2.(1)] 4.497 [mm] Stiffness coefficient of the compressed column web k2 = [6.3.2.(1)] Sj,ini = E zeq / i (1 / k1 + 1 / k2 + 1 / keq) Sj,ini = 2887049.32 [kN*mm] Initial rotational stiffness 1.00 Stiffness coefficient of a connection = 2

Sj = Sj,ini /  2887049.32 [kN*mm] Final rotational stiffness Sj = Connection classification due to stiffness. Sj,rig = 8951682.02 [kN*mm] Stiffness of a rigid connection Sj,pin = 559480.13 [kN*mm] Stiffness of a pinned connection

[6.3.1.(4)] [6.3.1.(4)] [6.3.1.(6)] [6.3.1.(4)] [6.3.1.(4)] [5.2.2.5] [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

GENERAL Connection no.: Connection name: Structure node: Structure bars:

7 Beam-column (web) 12 5, 1

GEOMETRY COLUMN Section: HEA 140 Bar no.: 5 -90.0 [Deg] Inclination angle = 133.000 [mm] Height of column section hc = 140.000 [mm] Width of column section bfc = 5.500 [mm] Thickness of the web of column section twc = 8.500 [mm] Thickness of the flange of column section tfc = 12.000 [mm] Radius of column section fillet rc = 3141.610 [mm2] Cross-sectional area of a column Ac = 4 Iyc = 10331300.000 [mm ] Moment of inertia of the column section Material: S275 0.28 [kN/mm2] Design resistance fyc = 0.43 [kN/mm2] Tensile resistance fuc =

BEAM Section: IPE 200 Bar no.: 1

Ratio 0.40

0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bb = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Iyb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Design resistance fyb = 0.43 [kN/mm2] Tensile resistance fub =

PLATE Type: unilateral 85.000 [mm] lp = 130.000 [mm] hp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp = 0.43 [kN/mm2] fup =

Plate length Plate height Plate thickness Design resistance Tensile resistance

UPPER BRACKET OF A BEAM 85.000 [mm] lbu = 130.000 [mm] hbu = 6.000 [mm] tbu = Material: S275 0.28 [kN/mm2] fybu = 0.43 [kN/mm2] fubu =

Bracket length Bracket height Bracket thickness Design resistance Tensile resistance

LOWER BRACKET OF A BEAM 85.000 [mm] lbd = 130.000 [mm] hbd = 6.000 [mm] tbd = Material: S275 0.28 [kN/mm2] fybd = 0.43 [kN/mm2] fubd =

Bracket length Bracket height Bracket thickness Design resistance Tensile resistance

BOLTS BOLTS CONNECTING BEAM WITH PLATE 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

BOLTS CONNECTING UPPER BRACKET WITH BEAM Class = d=

8.8 16.000

[mm]

Bolt class Bolt diameter

8.8 Class = 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

BOLTS CONNECTING LOWER BRACKET WITH BEAM 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 e1 = [mm] 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

WELDS acp = aswu = aswd =

5.000 5.000 5.000

[mm] [mm] [mm]

Fillet welds connecting plate with column Fillet welds connecting upper bracket with column Fillet welds connecting lower bracket with column

MATERIAL FACTORS M0 = M2 =

1.00 1.25

Partial safety factor Partial safety factor

[2.2] [2.2]

LOADS Case: 3: COMB1 1*1.20+2*1.60 -3.18 Nb,Ed = [kN] Axial force -10.46 Vb,Ed = [kN] Shear force Mb,Ed = 4547.38 [kN*mm] Bending moment

RESULTS BOLTS CONNECTING BEAM WITH PLATE BOLT CAPACITIES 77.21 Fv,Rd = [kN] Bolt bearing on the beam Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd1x =

49.94

Direction z 2.50 k1z = k1z > 0.0

Shear resistance of the shank of a single bolt

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt Coefficient for calculation of Fb,Rd 2.50 > 0.00

Fv,Rd= 0.6*fub*Av*m/M2

k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd1x=k1x*bx*fu*d*ti/M2 k1z=min[2.8*(e2/d0)-1.7, 2.5] verified

0.86 bz = bz > 0.0 Fb,Rd1z = 66.35 [kN] Bolt bearing on the plate

Coefficient for calculation of Fb,Rd 0.86 > 0.00 Bearing resistance of a single bolt

bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd1z=k1z*bz*fu*d*ti/M2

Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd2x = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd2x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.65 bz = bz > 0.0 Fb,Rd2z = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd2z=k1z*bz*fu*d*ti/M2

[kN]

FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION Bolt shear e= M0 = FNx = FVz = FMx = FMz =

52.750 [mm] Distance between centroid of a bolt group and center of column web - [kN*m 551.57 m] Real bending moment 1.59 [kN] Component force in a bolt due to influence of the longitudinal force 5.23 [kN] Component force in a bolt due to influence of the shear force -9.19 [kN] Component force in a bolt due to influence of the moment on the x direction 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction

Fx,Ed -7.60 = Fz,Ed 5.23 = FRdx 49.94 = FRdz 53.51 = |Fx,Ed|  FRdx |Fz,Ed|  FRdz

M0=Vb,Ed*e FNx=Nb,Ed/n FVz=Vb,Ed/n 2

2

2

2

FMx=M0*zi/(xi +zi ) FMz=M0*xi/(xi +zi )

[kN] Design total force in a bolt on the direction x

Fx,Ed = FNx + FMx

[kN] Design total force in a bolt on the direction z

Fz,Ed = FVz + FMz

[kN] Effective design capacity of a bolt on the direction x [kN] Effective design capacity of a bolt on the direction z |-7.60| < 49.94 |5.23| < 53.51

verified verified

FRdx=min(FvRd, FbRd1x, FbRd2x) FRdz=min(FvRd, FbRd1z, FbRd2z) (0.15) (0.10)

BOLTS CONNECTING UPPER BRACKET WITH BEAM BOLT CAPACITIES 77.21 Fv,Rd = [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2 Bolt bearing on the beam flange 1.41 k1 = Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 42.79 Fb,Rd1 = [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2 Bolt bearing on the bracket 1.41 k1 = Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0

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 10.57 FEd = 30.20 FRd = |FEd|  FRd

[kN] [kN]

Shear force in a bolt Effective design capacity of a bolt |10.57| < 30.20

verified

FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n FRd=min(FvRd, FbRd1, FbRd2) (0.35)

BOLTS CONNECTING LOWER BRACKET WITH BEAM BOLT CAPACITIES 77.21 Fv,Rd = [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2 Bolt bearing on the beam flange 1.41 k1 = Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 42.79 Fb,Rd1 = [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2 Bolt bearing on the bracket 1.41 k1 = Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 30.20 Fb,Rd2 = [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 -12.16 FEd = 30.20 FRd = |FEd|  FRd

[kN] [kN]

Shear force in a bolt Effective design capacity of a bolt |-12.16| < 30.20

verified

FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n FRd=min(FvRd, FbRd1, FbRd2) (0.40)

VERIFICATION OF THE SECTION DUE TO BLOCK TEARING PLATE 2 Ant = 246.000 [mm ] Net area of the section in tension 2 Anv = 408.000 [mm ] 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 |-10.46| < 107.09 (0.10) verified |Vb,Ed|  VeffRd

BEAM 2

Ant = 145.600 [mm ] Net area of the section in tension 2 Anv = 576.800 [mm ] 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 |-10.46| < 116.62 (0.09) verified |Vb,Ed|  VeffRd

WELD RESISTANCE FILLET WELDS CONNECTING PLATE WITH COLUMN 650.000 [mm2] Weld area As = -0.01 [kN/mm2] Parallel tangent stress II = 0.85 Correlation coefficient w = 2 2 2 0.03 < 0.40 [ +3*(II + )]  fu/(w*M2)

verified

As = hp*agp II=0.5*Vb,Ed/As [Table 4.1] (0.07)

FILLET WELDS CONNECTING UPPER BRACKET WITH COLUMN 650.000 [mm2] Weld area As = 0.02 [kN/mm2] Normal stress in a weld = 0.01 [kN/mm2] Normal perpendicular stress in the weld  = |0.01| < 0.31 ||  0.9*fu/M2 0.01 [kN/mm2] Perpendicular tangent stress  = 0.85 Correlation coefficient w = 2 2 0.03 < 0.40 [ +3* ]  fu/(w*M2)

verified

 =0.5*[Nb,Ed/2 + Mb,Ed/hb]/As =/2 (0.04) =  [Table 4.1] (0.07)

verified

 =0.5*[Nb,Ed/2 - Mb,Ed/hb]/As =/2 (0.04)

verified

=  [Table 4.1] (0.07)

verified

FILLET WELDS CONNECTING LOWER BRACKET WITH COLUMN 650.000 [mm2] Weld area As = -0.02 [kN/mm2] Normal stress in a weld = -0.01 [kN/mm2] Normal perpendicular stress in the weld  = |-0.01| < 0.31 ||  0.9*fu/M2 2 -0.01 [kN/mm ] Perpendicular tangent stress  = 0.85 Correlation coefficient w = 2 2 0.03 < 0.40 [ +3* ]  fu/(w*M2)

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

GENERAL Connection no.: Connection name: Structure node: Structure bars:

6 Beam-beam (web) 4 2, 3

GEOMETRY PRINCIPAL BEAM Section: IPE 200 Bar no.: 2 -90.0 [Deg] Inclination angle = 200.000 hg = [mm] Height of the principal beam section 100.000 [mm] Width of the flange of the principal beam section bfg = 5.600 [mm] Thickness of the web of the principal beam section twg = 8.500 [mm] Thickness of the flange of the principal beam section tfg = 12.000 [mm] Fillet radius of the web of the principal beam section rg = 2848.410 [mm2] Cross-sectional area of a principal beam Ap = 4 Iyp = 19431700.000 [mm ] Moment of inertia of the principal beam section Material: S275 0.28 [kN/mm2] Design resistance fyg = 0.43 [kN/mm2] Tensile resistance fug =

BEAM

Ratio 0.11

Section: IPE 200 Bar no.: 3 0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bb = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Iyb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Design resistance fyb = 0.43 [kN/mm2] Tensile resistance fub =

PLATE Type: unilateral 85.000 [mm] lp = 130.000 [mm] hp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp = 0.43 [kN/mm2] fup =

Plate length Plate height Plate thickness Design resistance Tensile resistance

BOLTS BOLTS CONNECTING BEAM WITH PLATE 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

WELDS agp =

5.000

[mm]

Fillet welds connecting plate with principal beam

MATERIAL FACTORS M0 = M2 =

1.00 1.25

Partial safety factor Partial safety factor

LOADS Case: 3: COMB1 1*1.20+2*1.60 -1.15 Nb,Ed = [kN] Axial force -8.91 Vb,Ed = [kN] Shear force Mb,Ed = 109.81 [kN*mm] Bending moment

RESULTS

[2.2] [2.2]

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 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd1x = 49.94

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd1x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.86 bz = bz > 0.0 Fb,Rd1z = 66.35

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.86 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd1z=k1z*bz*fu*d*ti/M2

53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd2x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.65 bz = bz > 0.0 Fb,Rd2z = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd2z=k1z*bz*fu*d*ti/M2

[kN]

Bolt bearing on the plate Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd2x =

[kN]

FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION Bolt shear 52.80 e= 0 M0 = 360.7 5 FNx = 0.57 FVz = 4.46

[mm]

Distance between centroid of a bolt group and center of the principal beam web

[kN*m Real bending moment m]

[kN] Component force in a bolt due to influence of the longitudinal force [kN] Component force in a bolt due to influence of the shear force Component force in a bolt due to influence of the moment on the x FMx = -6.01 [kN] direction Component force in a bolt due to influence of the moment on the z FMz = 0.00 [kN] direction Fx,Ed -5.44 [kN] Design total force in a bolt on the direction x = Fz,Ed 4.46 [kN] Design total force in a bolt on the direction z = FRdx 49.94 [kN] Effective design capacity of a bolt on the direction x = FRdz 53.51 [kN] Effective design capacity of a bolt on the direction z = |-5.44| < 49.94 verified |Fx,Ed|  FRdx |4.46| < 53.51 verified |Fz,Ed|  FRdz

M0=Mb,Ed+Vb,Ed*e FNx=Nb,Ed/n FVz=Vb,Ed/n 2

2

2

2

FMx=M0*zi/(xi +zi ) FMz=M0*xi/(xi +zi ) Fx,Ed = FNx + FMx Fz,Ed = FVz + FMz FRdx=min(FvRd, FbRd1x, FbRd2x) FRdz=min(FvRd, FbRd1z, FbRd2z) (0.11) (0.08)

VERIFICATION OF THE SECTION DUE TO BLOCK TEARING PLATE 2

Ant = 246.000 [mm ] Net area of the section in tension 2 Anv = 408.000 [mm ] 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 |-8.91| < 107.09 (0.08) verified |Vb,Ed|  VeffRd

BEAM 2

Ant = 145.600 [mm ] Net area of the section in tension 2 Anv = 464.800 [mm ] 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 |-8.91| < 98.84 (0.09) verified |Vb,Ed|  VeffRd

WELD RESISTANCE FILLET WELDS CONNECTING PLATE WITH PRINCIPAL BEAM 650.000 As = 0.00 = 0.00  = ||  0.9*fu/M2 0.00  = -0.01 II = 0.85 w =

2

[mm ] Weld area 2 [kN/mm ] Normal stress in a weld 2 [kN/mm ] Normal perpendicular stress in the weld |0.00| < 0.31 2 [kN/mm ] Perpendicular tangent stress 2 [kN/mm ] Parallel tangent stress Correlation coefficient 2 2 2 0.03 < 0.40 [ +3*(II + )]  fu/(w*M2)

Connection conforms to the code

verified

As = hp*agp  =Nb,Ed/As + Mb,Ed/W ys =/2 (0.01)

verified

= II=0.5*Vb,Ed/As [Table 4.1] (0.07)

Ratio 0.11

Autodesk Robot Structural Analysis Professional 2012

Calculation of the beam-to-beam (web) connection EN 1993-1-8:2005/AC:2009

GENERAL Connection no.: Connection name: Structure node: Structure bars:

5 Beam-beam (web) 1 1, 3

GEOMETRY PRINCIPAL BEAM Section: IPE 200 Bar no.: 1 -90.0 [Deg] Inclination angle = 200.000 hg = [mm] Height of the principal beam section 100.000 [mm] Width of the flange of the principal beam section bfg = 5.600 [mm] Thickness of the web of the principal beam section twg = 8.500 [mm] Thickness of the flange of the principal beam section tfg = 12.000 [mm] Fillet radius of the web of the principal beam section rg = 2848.410 [mm2] Cross-sectional area of a principal beam Ap = 4 Iyp = 19431700.000 [mm ] Moment of inertia of the principal beam section Material: S275 0.28 [kN/mm2] Design resistance fyg = 0.43 [kN/mm2] Tensile resistance fug =

BEAM

Ratio 0.11

Section: IPE 200 Bar no.: 3 0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bb = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Iyb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Design resistance fyb = 0.43 [kN/mm2] Tensile resistance fub =

PLATE Type: unilateral 85.000 [mm] lp = 130.000 [mm] hp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp = 0.43 [kN/mm2] fup =

Plate length Plate height Plate thickness Design resistance Tensile resistance

BOLTS BOLTS CONNECTING BEAM WITH PLATE 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

WELDS agp =

5.000

[mm]

Fillet welds connecting plate with principal beam

MATERIAL FACTORS M0 = M2 =

1.00 1.25

Partial safety factor Partial safety factor

LOADS Case: 3: COMB1 1*1.20+2*1.60 -1.15 Nb,Ed = [kN] Axial force -8.91 Vb,Ed = [kN] Shear force Mb,Ed = 109.81 [kN*mm] Bending moment

RESULTS

[2.2] [2.2]

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 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd1x = 49.94

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd1x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.86 bz = bz > 0.0 Fb,Rd1z = 66.35

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.86 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd1z=k1z*bz*fu*d*ti/M2

53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd2x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.65 bz = bz > 0.0 Fb,Rd2z = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd2z=k1z*bz*fu*d*ti/M2

[kN]

Bolt bearing on the plate Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd2x =

[kN]

FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION Bolt shear 52.80 e= 0 M0 = 360.7 5 FNx = 0.57 FVz = 4.46

[mm]

Distance between centroid of a bolt group and center of the principal beam web

[kN*m Real bending moment m]

[kN] Component force in a bolt due to influence of the longitudinal force [kN] Component force in a bolt due to influence of the shear force Component force in a bolt due to influence of the moment on the x FMx = -6.01 [kN] direction Component force in a bolt due to influence of the moment on the z FMz = 0.00 [kN] direction Fx,Ed -5.44 [kN] Design total force in a bolt on the direction x = Fz,Ed 4.46 [kN] Design total force in a bolt on the direction z = FRdx 49.94 [kN] Effective design capacity of a bolt on the direction x = FRdz 53.51 [kN] Effective design capacity of a bolt on the direction z = |-5.44| < 49.94 verified |Fx,Ed|  FRdx |4.46| < 53.51 verified |Fz,Ed|  FRdz

M0=Mb,Ed+Vb,Ed*e FNx=Nb,Ed/n FVz=Vb,Ed/n 2

2

2

2

FMx=M0*zi/(xi +zi ) FMz=M0*xi/(xi +zi ) Fx,Ed = FNx + FMx Fz,Ed = FVz + FMz FRdx=min(FvRd, FbRd1x, FbRd2x) FRdz=min(FvRd, FbRd1z, FbRd2z) (0.11) (0.08)

VERIFICATION OF THE SECTION DUE TO BLOCK TEARING PLATE 2

Ant = 246.000 [mm ] Net area of the section in tension 2 Anv = 408.000 [mm ] 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 |-8.91| < 107.09 (0.08) verified |Vb,Ed|  VeffRd

BEAM 2

Ant = 145.600 [mm ] Net area of the section in tension 2 Anv = 464.800 [mm ] 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 |-8.91| < 98.84 (0.09) verified |Vb,Ed|  VeffRd

WELD RESISTANCE FILLET WELDS CONNECTING PLATE WITH PRINCIPAL BEAM 650.000 As = 0.00 = 0.00  = ||  0.9*fu/M2 0.00  = -0.01 II = 0.85 w =

2

[mm ] Weld area 2 [kN/mm ] Normal stress in a weld 2 [kN/mm ] Normal perpendicular stress in the weld |0.00| < 0.31 2 [kN/mm ] Perpendicular tangent stress 2 [kN/mm ] Parallel tangent stress Correlation coefficient 2 2 2 0.03 < 0.40 [ +3*(II + )]  fu/(w*M2)

Connection conforms to the code

verified

As = hp*agp  =Nb,Ed/As + Mb,Ed/W ys =/2 (0.01)

verified

= II=0.5*Vb,Ed/As [Table 4.1] (0.07)

Ratio 0.11

Autodesk Robot Structural Analysis Professional 2012

Calculation of the beam-column (web) connection EN 1993-1-8:2005/AC:2009

GENERAL Connection no.: Connection name: Structure node: Structure bars:

4 Beam-column (web) 13 6, 2

GEOMETRY COLUMN Section: HEA 140 Bar no.: 6 -90.0 [Deg] Inclination angle = 133.000 [mm] Height of column section hc = 140.000 [mm] Width of column section bfc = 5.500 [mm] Thickness of the web of column section twc = 8.500 [mm] Thickness of the flange of column section tfc = 12.000 [mm] Radius of column section fillet rc = 3141.610 [mm2] Cross-sectional area of a column Ac = 4 Iyc = 10331300.000 [mm ] Moment of inertia of the column section Material: S275 0.28 [kN/mm2] Design resistance fyc = 0.43 [kN/mm2] Tensile resistance fuc =

BEAM Section: IPE 200 Bar no.: 2

Ratio 0.40

0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bb = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Iyb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Design resistance fyb = 0.43 [kN/mm2] Tensile resistance fub =

PLATE Type: unilateral 85.000 [mm] lp = 130.000 [mm] hp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp = 0.43 [kN/mm2] fup =

Plate length Plate height Plate thickness Design resistance Tensile resistance

UPPER BRACKET OF A BEAM 85.000 [mm] lbu = 130.000 [mm] hbu = 6.000 [mm] tbu = Material: S275 0.28 [kN/mm2] fybu = 0.43 [kN/mm2] fubu =

Bracket length Bracket height Bracket thickness Design resistance Tensile resistance

LOWER BRACKET OF A BEAM 85.000 [mm] lbd = 130.000 [mm] hbd = 6.000 [mm] tbd = Material: S275 0.28 [kN/mm2] fybd = 0.43 [kN/mm2] fubd =

Bracket length Bracket height Bracket thickness Design resistance Tensile resistance

BOLTS BOLTS CONNECTING BEAM WITH PLATE 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

BOLTS CONNECTING UPPER BRACKET WITH BEAM Class = d=

8.8 16.000

[mm]

Bolt class Bolt diameter

8.8 Class = 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 [mm] e1 = 60.000 [mm] p1 =

Bolt class Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

BOLTS CONNECTING LOWER BRACKET WITH BEAM 8.8 Class = 16.000 [mm] d= 18.000 [mm] d0 = 157.000 [mm2] As = 201.062 [mm2] Av = 0.80 [kN/mm2] fub = 1 k= 2 w= 35.000 e1 = [mm] 60.000 [mm] p1 =

Bolt class Bolt diameter Bolt opening diameter Effective section area of a bolt Area of bolt section Tensile resistance Number of bolt columns Number of bolt rows Level of first bolt Vertical spacing

WELDS acp = aswu = aswd =

5.000 5.000 5.000

[mm] [mm] [mm]

Fillet welds connecting plate with column Fillet welds connecting upper bracket with column Fillet welds connecting lower bracket with column

MATERIAL FACTORS M0 = M2 =

1.00 1.25

Partial safety factor Partial safety factor

[2.2] [2.2]

LOADS Case: 3: COMB1 1*1.20+2*1.60 -3.18 Nb,Ed = [kN] Axial force -10.46 Vb,Ed = [kN] Shear force Mb,Ed = 4547.38 [kN*mm] Bending moment

RESULTS BOLTS CONNECTING BEAM WITH PLATE BOLT CAPACITIES 77.21 Fv,Rd = [kN] Bolt bearing on the beam Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd1x =

49.94

Direction z 2.50 k1z = k1z > 0.0

Shear resistance of the shank of a single bolt

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt Coefficient for calculation of Fb,Rd 2.50 > 0.00

Fv,Rd= 0.6*fub*Av*m/M2

k1x = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd1x=k1x*bx*fu*d*ti/M2 k1z=min[2.8*(e2/d0)-1.7, 2.5] verified

0.86 bz = bz > 0.0 Fb,Rd1z = 66.35 [kN] Bolt bearing on the plate

Coefficient for calculation of Fb,Rd 0.86 > 0.00 Bearing resistance of a single bolt

bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd1z=k1z*bz*fu*d*ti/M2

Direction x 2.50 k1x = k1x > 0.0 0.65 bx = bx > 0.0 Fb,Rd2x = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 [kN] Bearing resistance of a single bolt

k1x=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] verified bx=min[e2/(3*d0), fub/fu, 1] verified Fb,Rd2x=k1x*bx*fu*d*ti/M2

Direction z 2.50 k1z = k1z > 0.0 0.65 bz = bz > 0.0 Fb,Rd2z = 53.51

Coefficient for calculation of Fb,Rd 2.50 > 0.00 Coefficient for calculation of Fb,Rd 0.65 > 0.00 Bearing resistance of a single bolt

k1z=min[2.8*(e2/d0)-1.7, 2.5] verified bz=min[e1/(3*d0), p1/(3*d0)-0.25, fub/fu, 1] verified Fb,Rd2z=k1z*bz*fu*d*ti/M2

[kN]

FORCES ACTING ON BOLTS IN THE PLATE - BEAM CONNECTION Bolt shear e= M0 = FNx = FVz = FMx = FMz =

52.750 [mm] Distance between centroid of a bolt group and center of column web - [kN*m 551.57 m] Real bending moment 1.59 [kN] Component force in a bolt due to influence of the longitudinal force 5.23 [kN] Component force in a bolt due to influence of the shear force -9.19 [kN] Component force in a bolt due to influence of the moment on the x direction 0.00 [kN] Component force in a bolt due to influence of the moment on the z direction

Fx,Ed -7.60 = Fz,Ed 5.23 = FRdx 49.94 = FRdz 53.51 = |Fx,Ed|  FRdx |Fz,Ed|  FRdz

M0=Vb,Ed*e FNx=Nb,Ed/n FVz=Vb,Ed/n 2

2

2

2

FMx=M0*zi/(xi +zi ) FMz=M0*xi/(xi +zi )

[kN] Design total force in a bolt on the direction x

Fx,Ed = FNx + FMx

[kN] Design total force in a bolt on the direction z

Fz,Ed = FVz + FMz

[kN] Effective design capacity of a bolt on the direction x [kN] Effective design capacity of a bolt on the direction z |-7.60| < 49.94 |5.23| < 53.51

verified verified

FRdx=min(FvRd, FbRd1x, FbRd2x) FRdz=min(FvRd, FbRd1z, FbRd2z) (0.15) (0.10)

BOLTS CONNECTING UPPER BRACKET WITH BEAM BOLT CAPACITIES 77.21 Fv,Rd = [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2 Bolt bearing on the beam flange 1.41 k1 = Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 42.79 Fb,Rd1 = [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2 Bolt bearing on the bracket 1.41 k1 = Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0

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 10.57 FEd = 30.20 FRd = |FEd|  FRd

[kN] [kN]

Shear force in a bolt Effective design capacity of a bolt |10.57| < 30.20

verified

FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n FRd=min(FvRd, FbRd1, FbRd2) (0.35)

BOLTS CONNECTING LOWER BRACKET WITH BEAM BOLT CAPACITIES 77.21 Fv,Rd = [kN] Shear resistance of the shank of a single bolt Fv,Rd= 0.6*fub*Av*m/M2 Bolt bearing on the beam flange 1.41 k1 = Coefficient for calculation of Fb,Rd k1 = min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 42.79 Fb,Rd1 = [kN] Bearing resistance of a single bolt Fb,Rd1=k1*b*fu*d*ti/M2 Bolt bearing on the bracket 1.41 k1 = Coefficient for calculation of Fb,Rd k1=min[2.8*(e1/d0)-1.7, 1.4*(p1/d0)-1.7, 2.5] 1.41 > 0.00 k1 > 0.0 verified 0.65 Coefficient for calculation of Fb,Rd b = b=min[e2/(3*d0), fub/fu, 1] 0.65 > 0.00 verified b > 0.0 30.20 Fb,Rd2 = [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 -12.16 FEd = 30.20 FRd = |FEd|  FRd

[kN] [kN]

Shear force in a bolt Effective design capacity of a bolt |-12.16| < 30.20

verified

FEd = [0.5*Nb,Ed - Mb,Ed/hbr]/n FRd=min(FvRd, FbRd1, FbRd2) (0.40)

VERIFICATION OF THE SECTION DUE TO BLOCK TEARING PLATE 2 Ant = 246.000 [mm ] Net area of the section in tension 2 Anv = 408.000 [mm ] 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 |-10.46| < 107.09 (0.10) verified |Vb,Ed|  VeffRd

BEAM 2

Ant = 145.600 [mm ] Net area of the section in tension 2 Anv = 576.800 [mm ] 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 |-10.46| < 116.62 (0.09) verified |Vb,Ed|  VeffRd

WELD RESISTANCE FILLET WELDS CONNECTING PLATE WITH COLUMN 650.000 [mm2] Weld area As = -0.01 [kN/mm2] Parallel tangent stress II = 0.85 Correlation coefficient w = 2 2 2 0.03 < 0.40 [ +3*(II + )]  fu/(w*M2)

verified

As = hp*agp II=0.5*Vb,Ed/As [Table 4.1] (0.07)

FILLET WELDS CONNECTING UPPER BRACKET WITH COLUMN 650.000 [mm2] Weld area As = 0.02 [kN/mm2] Normal stress in a weld = 0.01 [kN/mm2] Normal perpendicular stress in the weld  = |0.01| < 0.31 ||  0.9*fu/M2 0.01 [kN/mm2] Perpendicular tangent stress  = 0.85 Correlation coefficient w = 2 2 0.03 < 0.40 [ +3* ]  fu/(w*M2)

verified

 =0.5*[Nb,Ed/2 + Mb,Ed/hb]/As =/2 (0.04) =  [Table 4.1] (0.07)

verified

 =0.5*[Nb,Ed/2 - Mb,Ed/hb]/As =/2 (0.04)

verified

=  [Table 4.1] (0.07)

verified

FILLET WELDS CONNECTING LOWER BRACKET WITH COLUMN 650.000 [mm2] Weld area As = -0.02 [kN/mm2] Normal stress in a weld = -0.01 [kN/mm2] Normal perpendicular stress in the weld  = |-0.01| < 0.31 ||  0.9*fu/M2 2 -0.01 [kN/mm ] Perpendicular tangent stress  = 0.85 Correlation coefficient w = 2 2 0.03 < 0.40 [ +3* ]  fu/(w*M2)

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

GENERAL Connection no.: Connection name: Structure node: Structure bars:

2 Column-Beam 13 6, 4

GEOMETRY COLUMN Section: HEA 140 Bar no.: 6 -90.0 [Deg] Inclination angle = 133.000 [mm] Height of column section hc = 140.000 [mm] Width of column section bfc = 5.500 [mm] Thickness of the web of column section twc = 8.500 [mm] Thickness of the flange of column section tfc = 12.000 [mm] Radius of column section fillet rc = 3141.610 [mm2] Cross-sectional area of a column Ac = 4 Ixc = 10331300.000 [mm ] Moment of inertia of the column section Material: S275 0.28 [kN/mm2] Resistance fyc =

BEAM Section: IPE 200

Ratio 0.14

Section: IPE 200 Bar no.: 4 0.0 [Deg] Inclination angle = 200.000 hb = [mm] Height of beam section 100.000 [mm] Width of beam section bf = 5.600 [mm] Thickness of the web of beam section twb = 8.500 [mm] Thickness of the flange of beam section tfb = 12.000 [mm] Radius of beam section fillet rb = 12.000 [mm] Radius of beam section fillet rb = 2848.410 [mm2] Cross-sectional area of a beam Ab = 4 Ixb = 19431700.000 [mm ] Moment of inertia of the beam section Material: S275 0.28 [kN/mm2] Resistance fyb =

BOLTS 16.000 [mm] d= 8.8 Class = 90.43 [kN] FtRd = 2 nh = 3 nv = 60.000 [mm] h1 = Horizontal spacing ei = Vertical spacing pi =

Bolt diameter Bolt class Tensile resistance of a bolt Number of bolt columns Number of bolt rows Distance between first bolt and upper edge of front plate 50.000 [mm] 50.000;50.000 [mm]

PLATE 220.000 [mm] hp = 100.000 [mm] bp = 6.000 [mm] tp = Material: S275 0.28 [kN/mm2] fyp =

Plate height Plate width Plate thickness Resistance

FILLET WELDS aw = af =

4.000 6.000

[mm] [mm]

Web weld Flange weld

MATERIAL FACTORS M0 = M1 = M2 = M3 =

1.00 1.00 1.25 1.25

Partial safety factor Partial safety factor Partial safety factor Partial safety factor

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 -4.61 Vb1,Ed = [kN] Shear force in the right beam 0.05 Nb1,Ed = [kN] Axial force in the right beam Mc1,Ed = 1682.26 [kN*mm] Bending moment in the lower column -1.06 Vc1,Ed = [kN] Shear force in the lower column Nc1,Ed = -15.09 [kN] Axial force in the lower column -0.03 Nc2,Ed = [kN] Axial force in the upper column

RESULTS

[2.2] [2.2] [2.2] [2.2]

BEAM RESISTANCES TENSION 2848.410 Ab = Ntb,Rd = Ab fyb / M0 Ntb,Rd = 783.31

2

[mm ]

Area

[kN] Design tensile resistance of the section SHEAR 1400.010 [mm2] Shear area Avb = Vcb,Rd = Avb (fyb / 3) / M0 Vcb,Rd = 222.28 [kN] Design sectional resistance for shear 0.02 < 1.00 verified Vb1,Ed / Vcb,Rd  1,0 BENDING - PLASTIC MOMENT (WITHOUT BRACKETS) 3 Wplb = 220657.000 [mm ] Plastic section modulus Mb,pl,Rd = W plb fyb / M0 60680.6 [kN*mm Plastic resistance of the section for bending (without Mb,pl,Rd 8 = ] stiffeners) BENDING ON THE CONTACT SURFACE WITH PLATE OR CONNECTED ELEMENT 3 Wpl = 220657.000 [mm ] Plastic section modulus Mcb,Rd = W pl fyb / M0 Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending FLANGE AND WEB - COMPRESSION Mcb,Rd = 60680.68 [kN*mm] Design resistance of the section for bending 191.500 [mm] Distance between the centroids of flanges hf = Fc,fb,Rd = Mcb,Rd / hf Fc,fb,Rd = 316.87 [kN] Resistance of the compressed flange and web

EN1993-1-1:[6.2.3] EN1993-1-1:[6.2.3] EN1993-1-1:[6.2.6.(3)] EN1993-1-1:[6.2.6.(2)] (0.02) EN1993-1-1:[6.2.5.(2)] EN1993-11:[6.2.5.(2)] EN1993-1-1:[6.2.5] EN1993-1-1:[6.2.5] EN1993-1-1:[6.2.5] [6.2.6.7.(1)] [6.2.6.7.(1)]

COLUMN RESISTANCES WEB PANEL - SHEAR Mb1,Ed = 1672.26 [kN*mm] Bending moment (right beam) 0.00 [kN*mm] Bending moment (left beam) Mb2,Ed = -1.06 Vc1,Ed = [kN] Shear force (lower column) 0.00 Vc2,Ed = [kN] Shear force (upper column) 120.750 [mm] Lever arm z= Vwp,Ed = (Mb1,Ed - Mb2,Ed) / z - (Vc1,Ed - Vc2,Ed) / 2 14.38 Vwp,Ed = [kN] Shear force acting on the web panel 2 1012.360 Avs = [mm ] Shear area of the column web 1012.360 [mm2] Shear area Avc = 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 0.10 < 1.00 verified Vwp,Ed / Vwp,Rd  1,0

[5.3.(3)] [5.3.(3)] [5.3.(3)] [5.3.(3)] [6.2.5] [5.3.(3)] EN1993-1-1:[6.2.6.(3)] EN1993-1-1:[6.2.6.(3)] [6.2.6.1] (0.10)

WEB - TRANSVERSE COMPRESSION - LEVEL OF THE BEAM BOTTOM FLANGE Bearing: 5.500 [mm] Effective thickness of the column web twc = beff,c,wc = 139.971 [mm] Effective width of the web for compression 1012.360 [mm2] Shear area Avc = 0.76 Reduction factor for interaction with shear = 0.01 [kN/mm2] Maximum compressive stress in web com,Ed = 1.00 kwc = Reduction factor conditioned by compressive stresses Fc,wc,Rd1 =  kwc beff,c,wbc twc fyc / M0 Fc,wc,Rd1 = 159.95 [kN] Column web resistance Buckling: 92.000 [mm] Height of compressed web dwc = 0.70 Plate slenderness of an element p = 1.00 Reduction factor for element buckling = Fc,wb,Rd2 =  kwc  beff,c,wc twc fyc / M1

[6.2.6.2.(6)] [6.2.6.2.(1)] EN1993-1-1:[6.2.6.(3)] [6.2.6.2.(1)] [6.2.6.2.(2)] [6.2.6.2.(2)] [6.2.6.2.(1)] [6.2.6.2.(1)] [6.2.6.2.(1)] [6.2.6.2.(1)]

Fc,wc,Rd2 = 159.95 [kN] Column web resistance 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)]

[6.2.6.2.(1)]

GEOMETRICAL PARAMETERS OF A CONNECTION EFFECTIVE LENGTHS AND PARAMETERS - COLUMN FLANGE Nr

m mx 12.65 1 0 12.65 2 0 12.65 3 0

e ex 45.00 0 45.00 0 45.00 0

p 50.00 0 50.00 0 50.00 0

leff,cp 79.48 2 79.48 2 79.48 2

leff,nc 106.85 0 106.85 0 106.85 0

leff,1 79.48 2 79.48 2 79.48 2

leff,2 106.85 0 106.85 0 106.85 0

leff,cp,g

leff,nc,g 78.42 89.741 5 100.00 50.00 0 0 78.42 89.741 5

leff,1,g 78.42 5 50.00 0 78.42 5

leff,2,g 78.42 5 50.00 0 78.42 5

leff,1,g 78.50 8 50.00 0 75.97 4

leff,2,g 78.50 8 50.00 0 75.97 4

EFFECTIVE LENGTHS AND PARAMETERS - FRONT PLATE Nr

m mx 17.67 1 5 17.67 2 5 17.67 3 5

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

e ex 25.00 0 25.00 0 25.00 0

p 50.00 0 50.00 0 50.00 0

leff,cp 111.05 2 111.05 2 111.05 2

leff,nc 104.48 2 101.94 8 101.94 8

leff,1 104.48 2 101.94 8 101.94 8

leff,2 104.48 2 101.94 8 101.94 8

leff,cp,g 105.52 6 100.00 0 105.52 6

leff,nc,g 78.50 8 50.00 0 75.97 4

– Bolt distance from the web – Bolt distance from the beam flange – Bolt distance from the outer edge – Bolt distance from the horizontal outer edge – Distance between bolts – Effective length for a single bolt in the circular failure mode – Effective length for a single bolt in the non-circular failure mode – Effective length for a single bolt for mode 1 – Effective length for a single bolt for mode 2 – Effective length for a group of bolts in the circular failure mode – Effective length for a group of bolts in the non-circular failure mode – Effective length for a group of bolts for mode 1 – Effective length for a group of bolts for mode 2

CONNECTION RESISTANCE FOR TENSION 90.43 Ft,Rd = [kN] Bolt resistance for tension 93.37 Bp,Rd = [kN] Punching shear resistance of a bolt Nj,Rd = Min (Ntb,Rd , nv nh Ft,Rd , nv nh Bp,Rd) 542.59 Nj,Rd = [kN] Connection resistance for tension 0.00 < 1.00 Nb1,Ed / Nj,Rd  1,0

[Table 3.4] [Table 3.4]

verified

[6.2] (0.00)

CONNECTION RESISTANCE FOR BENDING 90.43 Ft,Rd = [kN] Bolt resistance for tension 93.37 Bp,Rd = [kN] Punching shear resistance of a bolt 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) Ft,wc,Rd =  beff,t,wc twc fyc / M0 Ft,ep,Rd = Min (FT,1,ep,Rd , FT,2,ep,Rd , FT,3,ep,Rd) Ft,wb,Rd = beff,t,wb twb fyb / M0 RESISTANCE OF THE BOLT ROW NO. 1

[Table 3.4] [Table 3.4]

[6.2.6.4] , [Tab.6.2] [6.2.6.3.(1)] [6.2.6.5] , [Tab.6.2] [6.2.6.8.(1)]

Ft1,Rd,comp - Formula Ft1,Rd = Min (Ft1,Rd,comp) Ft,fc,Rd(1) = 124.84 Ft,wc,Rd(1) = 107.85 Ft,ep,Rd(1) = 58.52 Ft,wb,Rd(1) = 160.90 Bp,Rd = 186.75 Vwp,Rd/ = 144.66 Fc,wc,Rd = 159.95 Fc,fb,Rd = 316.87

Ft1,Rd,comp 58.52 124.84 107.85 58.52 160.90 186.75 144.66 159.95 316.87

Component

Ft2,Rd,comp 13.46 124.84 107.85 57.10 157.00 186.75 86.14 101.43 258.35 143.19 93.49 13.46 139.38

Component

Ft3,Rd,comp 42.56 124.84 107.85 57.10 157.00 186.75 72.68 87.97 244.89 188.25 138.55 252.91 120.51 57.10 180.54 42.56 242.92

Component

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression

RESISTANCE OF THE BOLT ROW NO. 2 Ft2,Rd,comp - Formula Ft2,Rd = Min (Ft2,Rd,comp) Ft,fc,Rd(2) = 124.84 Ft,wc,Rd(2) = 107.85 Ft,ep,Rd(2) = 57.10 Ft,wb,Rd(2) = 157.00 Bp,Rd = 186.75 1 Vwp,Rd/ - 1 Fti,Rd = 144.66 - 58.52 1 Fc,wc,Rd - 1 Ftj,Rd = 159.95 - 58.52 1 Fc,fb,Rd - 1 Ftj,Rd = 316.87 - 58.52 1 Ft,fc,Rd(2 + 1) - 1 Ftj,Rd = 201.71 - 58.52 1 Ft,wc,Rd(2 + 1) - 1 Ftj,Rd = 152.01 - 58.52 1 Ft,ep,Rd(2 + 1) - 1 Ftj,Rd = 71.98 - 58.52 1 Ft,wb,Rd(2 + 1) - 1 Ftj,Rd = 197.90 - 58.52

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression Column flange - tension - group Column web - tension - group Front plate - tension - group Beam web - tension - group

RESISTANCE OF THE BOLT ROW NO. 3 Ft3,Rd,comp - Formula Ft3,Rd = Min (Ft3,Rd,comp) Ft,fc,Rd(3) = 124.84 Ft,wc,Rd(3) = 107.85 Ft,ep,Rd(3) = 57.10 Ft,wb,Rd(3) = 157.00 Bp,Rd = 186.75 2 Vwp,Rd/ - 1 Fti,Rd = 144.66 - 71.98 2 Fc,wc,Rd - 1 Ftj,Rd = 159.95 - 71.98 2 Fc,fb,Rd - 1 Ftj,Rd = 316.87 - 71.98 2 Ft,fc,Rd(3 + 2) - 2 Ftj,Rd = 201.71 - 13.46 2 Ft,wc,Rd(3 + 2) - 2 Ftj,Rd = 152.01 - 13.46 1 Ft,fc,Rd(3 + 2 + 1) - 2 Ftj,Rd = 324.89 - 71.98 1 Ft,wc,Rd(3 + 2 + 1) - 2 Ftj,Rd = 192.49 - 71.98 2 Ft,ep,Rd(3 + 2) - 2 Ftj,Rd = 70.56 - 13.46 2 Ft,wb,Rd(3 + 2) - 2 Ftj,Rd = 194.00 - 13.46 1 Ft,ep,Rd(3 + 2 + 1) - 2 Ftj,Rd = 114.54 - 71.98 1 Ft,wb,Rd(3 + 2 + 1) - 2 Ftj,Rd = 314.90 - 71.98

Bolt row resistance Column flange - tension Column web - tension Front plate - tension Beam web - tension Bolts due to shear punching Web panel - shear Column web - compression Beam flange - compression Column flange - tension - group Column web - tension - group Column flange - tension - group Column web - tension - group Front plate - tension - group Beam web - tension - group Front plate - tension - group Beam web - tension - group

SUMMARY TABLE OF FORCES Nr hj 1 145.750 2 95.750 3 45.750

Ftj,Rd 58.52 13.46 42.56

Ft,fc,Rd 124.84 124.84 124.84

Ft,wc,Rd 107.85 107.85 107.85

Ft,ep,Rd 58.52 57.10 57.10

CONNECTION RESISTANCE FOR BENDING Mj,Rd Mj,Rd =  hj Ftj,Rd Mj,Rd = 11765.23 [kN*mm] Connection resistance for bending 0.14 < 1.00 Mb1,Ed / Mj,Rd  1,0

Ft,wb,Rd 160.90 157.00 157.00

verified

Ft,Rd 180.86 180.86 180.86

Bp,Rd 186.75 186.75 186.75

[6.2] (0.14)

CONNECTION RESISTANCE FOR SHEAR v = Fv,Rd = Ft,Rd,max = Fb,Rd,int = Fb,Rd,ext =

0.60 77.21 90.43 48.86 72.29

Nr Ftj,Rd,N 1 180.86 2 180.86 3 180.86

[kN] [kN] [kN] [kN]

Coefficient for calculation of Fv,Rd Shear resistance of a single bolt Tensile resistance of a single bolt Bearing resistance of an intermediate bolt Bearing resistance of an outermost bolt Ftj,Ed,N

0.02 0.02 0.02

Ftj,Rd,M 58.52 13.46 42.56

[Table 3.4] [Table 3.4] [Table 3.4] [Table 3.4] [Table 3.4]

Ftj,Ed,M 8.32 1.91 6.05

Ftj,Ed 8.34 1.93 6.07

Fvj,Rd 97.72 97.72 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 Fvj,Rd 293.16 Vj,Rd = n

[kN]

Vb1,Ed / Vj,Rd  1,0

Connection resistance for shear 0.02 < 1.00

[Table 3.4] [Table 3.4] (0.02)

verified

WELD RESISTANCE Aw =

3196.800 [mm2] Area of all welds

Awy =

1924.800 [mm2] Area of horizontal welds

Awz =

1272.000 [mm2] Area of vertical welds

Iwy = max=max = = = II =

20726644.20 Moment of inertia of the weld arrangement with respect to the 4 0 [mm ] hor. axis 2 0.01 [kN/mm Normal stress in a weld ] 2 [kN/mm 0.00 Stress in a vertical weld ] 2 -0.00 [kN/mm Tangent stress ]

w =

0.85

Correlation coefficient

[max + 3*(max )]  fu/(w*M2) 2 2 2 [ + 3*( +II )]  fu/(w*M2)   0.9*fu/M2 2

2

0.01 < 0.40 0.01 < 0.40 0.01 < 0.31

verified verified verified

[4.5.3.2(2 )] [4.5.3.2(2 )] [4.5.3.2(2 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(5 )] [4.5.3.2(7 )] (0.03) (0.03) (0.02)

CONNECTION STIFFNESS 4.000 [mm] Washer thickness twash = hhead = 12.000 [mm] Bolt head height 16.000 [mm] Bolt nut height hnut = 36.500 [mm] Bolt length Lb = 6.882 [mm] Stiffness coefficient of bolts k10 = STIFFNESSES OF BOLT ROWS Nr

hj

k3

k4

k5

[6.2.6.3.(2)] [6.2.6.3.(2)] [6.2.6.3.(2)] [6.2.6.3.(2)] [6.3.2.(1)] keff,j Sum

keff,j hj 272.472

keff,j hj 31450.892

2

Nr hj 1 145.750 2 95.750 3 45.750

k3 2.603 1.659 2.603

k4 21.413 13.652 21.413

k5 2.764 1.760 2.675

keff,j 1.066 0.720 1.053

5

keff,j hj 22648.134 6599.595 2203.164

2

[6.3.3.1.(2)]

keff,j = 1 / (3 (1 / ki,j)) zeq = j keff,j hj / j keff,j hj 115.428 [mm] zeq =

keff,j hj 155.390 68.925 48.157

2

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)] 2 Avc = 1012.360 [mm ] Shear area EN1993-1-1:[6.2.6.(3)] 1.00 Transformation parameter [5.3.(7)] = 115.428 [mm] Lever arm z= [6.2.5] 3.333 [mm] Stiffness coefficient of the column web panel subjected to shear k1 = [6.3.2.(1)] beff,c,wc = 135.485 [mm] Effective width of the web for compression [6.2.6.2.(1)] 5.500 [mm] Effective thickness of the column web twc = [6.2.6.2.(6)] 116.000 [mm] Height of compressed web dc = [6.2.6.2.(1)] 4.497 [mm] Stiffness coefficient of the compressed column web k2 = [6.3.2.(1)] Sj,ini = E zeq / i (1 / k1 + 1 / k2 + 1 / keq) Sj,ini = 2887049.32 [kN*mm] Initial rotational stiffness 1.00 Stiffness coefficient of a connection = 2

Sj = Sj,ini /  2887049.32 [kN*mm] Final rotational stiffness Sj = Connection classification due to stiffness. Sj,rig = 8951682.02 [kN*mm] Stiffness of a rigid connection Sj,pin = 559480.13 [kN*mm] Stiffness of a pinned connection

[6.3.1.(4)] [6.3.1.(4)] [6.3.1.(6)] [6.3.1.(4)] [6.3.1.(4)] [5.2.2.5] [5.2.2.5]

Sj,pin  Sj,ini < Sj,rig SEMI-RIGID

Connection conforms to the code

Ratio 0.14