T13

CALCULATION NOTE FOR T13-FIRESTATION STAIRCASE

Loads Cases

Result

Member

Section

Material

Lay

Laz

Ratio

Case

1 Simple

bar_1

IPE 200 S275 11.50 42.49 0.01 3 COMB1

2 Simple

bar_2

IPE 200 S275 14.41 53.23 0.01 3 COMB1

3 Simple

bar_3

IPE 200 S275 11.50 42.49 0.01 3 COMB1

4 Simple

bar_4

IPE 200 S275 14.41 53.23 0.01 3 COMB1

5 Simple bar

_5

UPN 200 S275 17.58 63.20 0.01 3 COMB1

6 Simple bar

_6

UPN 200 S275 17.58 63.20 0.01 3 COMB1

7 Simple bar

_7

UPN 200 S275 17.58 63.20 0.01 3 COMB1

8 Simple bar

_8

UPN 200 S275 17.58 63.20 0.01 3 COMB1

Case

Label

Case name

1 DL1 Dead load

2 LL1 Live load

3 COMB1 Combination 1

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.: 4

Connection name: Beam-beam (web)

Structure node: 1

Structure bars: 1, 4

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.: 4

= 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


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


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


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


LOADS

Case: 3: COMB1 1*1.20+2*1.60

Nb,Ed = -4.40 [kN] Axial force

Vb,Ed = -0.97 [kN] Shear force

Mb,Ed = 249.60 [kN*mm] Bending moment

RESULTS


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


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.65


bz > 0.0 0.65 > 0.00 verified


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 = 198.2

9

[kN*mm]

Real bending moment M0=Mb,Ed+Vb,Ed*e

FNx = 2.20 [kN] Component force in a bolt due to influence of the longitudinal force FNx=Nb,Ed/n

FVz = 0.49 [kN] Component force in a bolt due to influence of the shear force FVz=Vb,Ed/n

FMx = 3.30 [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 =

5.50 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx

Fz,Ed =

0.49 [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 |5.50| < 49.94 verified (0.11)

|Fz,Ed| FRdz |0.49| < 53.51 verified (0.01)

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 |-0.97| < 107.09 verified (0.01)

BEAM


Anv = 464.800 [mm




WELD RESISTANCE

FILLET WELDS CONNECTING PLATE WITH PRINCIPAL BEAM

As = 650.000 [mm2] Weld area As = hp*agp

= 0.01 [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 = -0.00 [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) 0.02 < 0.40 verified (0.06)

Connection conforms to the code Ratio 0.11



EN 1993-1-8:2005/AC:2009

Ratio 0.11

GENERAL

Connection no.: 3


Structure node: 2


GEOMETRY

PRINCIPAL BEAM

Section: IPE 200

Bar no.: 1








Iyp = 19431700.000 [mm


Material: S275


fug = 0.43 [kN/mm


BEAM

Section: IPE 200

Bar no.: 2









Iyb = 19431700.000 [mm


Material: S275


fub = 0.43 [kN/mm


PLATE

Type: unilateral




Material: S275


fup = 0.43 [kN/mm


BOLTS


Class = 8.8

Bolt class




Av = 201.062 [mm


fub = 0.80 [kN/mm


k = 1


w = 2

Number of bolt rows



WELDS


MATERIAL FACTORS

M0 = 1.00


M2 = 1.25


LOADS

Case: 3: COMB1 1*1.20+2*1.60




RESULTS


BOLT CAPACITIES



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.86


bz > 0.0 0.86 > 0.00 verified



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.65


bz > 0.0 0.65 > 0.00 verified



Bolt shear

e = 52.80

0 [mm]


M0 = 198.2

9

[kN*mm]





FMx=M0*zi/(xi2+zi

2)


FMz=M0*xi/(xi2+zi

2)

Fx,Ed =


Fz,Ed =


FRdx =


FbRd2x)

FRdz =


FbRd2z)




PLATE


Anv = 408.000 [mm





BEAM


Anv = 464.800 [mm




WELD RESISTANCE





|| 0.9*fu/M2 |0.00| < 0.31 verified (0.01)



w = 0.85


[2+3*(II

2+

2)] fu/(w*M2) 0.02 < 0.40 verified (0.06)




EN 1993-1-8:2005/AC:2009

Ratio 0.11

GENERAL

Connection no.: 2


Structure node: 4


GEOMETRY

PRINCIPAL BEAM

Section: IPE 200

Bar no.: 3








Iyp = 19431700.000 [mm


Material: S275


fug = 0.43 [kN/mm


BEAM

Section: IPE 200

Bar no.: 4









Iyb = 19431700.000 [mm


Material: S275


fub = 0.43 [kN/mm


PLATE

Type: unilateral




Material: S275


fup = 0.43 [kN/mm


BOLTS


Class = 8.8

Bolt class




Av = 201.062 [mm


fub = 0.80 [kN/mm


k = 1


w = 2

Number of bolt rows



WELDS


MATERIAL FACTORS

M0 = 1.00


M2 = 1.25


LOADS

Case: 3: COMB1 1*1.20+2*1.60




RESULTS


BOLT CAPACITIES



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.86


bz > 0.0 0.86 > 0.00 verified



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.65


bz > 0.0 0.65 > 0.00 verified



Bolt shear

e = 52.80

0 [mm]


M0 = 198.2

9

[kN*mm]





FMx=M0*zi/(xi2+zi

2)


FMz=M0*xi/(xi2+zi

2)

Fx,Ed =


Fz,Ed =


FRdx =


FbRd2x)

FRdz =


FbRd2z)




PLATE


Anv = 408.000 [mm





BEAM


Anv = 464.800 [mm




WELD RESISTANCE





|| 0.9*fu/M2 |0.00| < 0.31 verified (0.01)



w = 0.85


[2+3*(II

2+

2)] fu/(w*M2) 0.02 < 0.40 verified (0.06)




EN 1993-1-8:2005/AC:2009

Ratio 0.06

GENERAL

Connection no.: 1


Structure node: 3


GEOMETRY

PRINCIPAL BEAM

Section: IPE 200

Bar no.: 2








Iyp = 19431700.000 [mm


Material: S275


fug = 0.43 [kN/mm


BEAM

Section: IPE 200

Bar no.: 3









Iyb = 19431700.000 [mm


Material: S275


fub = 0.43 [kN/mm


PLATE

Type: unilateral




Material: S275


fup = 0.43 [kN/mm


BOLTS


Class = 8.8

Bolt class




Av = 201.062 [mm


fub = 0.80 [kN/mm


k = 1


w = 2

Number of bolt rows



WELDS


MATERIAL FACTORS

M0 = 1.00


M2 = 1.25


LOADS

Case: 3: COMB1 1*1.20+2*1.60




RESULTS


BOLT CAPACITIES



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.86


bz > 0.0 0.86 > 0.00 verified



Direction x

k1x = 2.50


k1x > 0.0 2.50 > 0.00 verified

bx = 0.65


bx > 0.0 0.65 > 0.00 verified


Direction z

k1z = 2.50


k1z > 0.0 2.50 > 0.00 verified

bz = 0.65


bz > 0.0 0.65 > 0.00 verified



Bolt shear

e = 52.80

0 [mm]


M0 = -

58.22

[kN*mm]




FMx = -0.97 [kN] Component force in a bolt due to influence of the moment on the x direction

FMx=M0*zi/(xi2+zi

2)


FMz=M0*xi/(xi2+zi

2)

Fx,Ed =

-0.97 [kN] Design total force in a bolt on the direction x Fx,Ed = FNx + FMx

Fz,Ed =


FRdx =


FbRd2x)

FRdz =


FbRd2z)

|Fx,Ed| FRdx |-0.97| < 49.94 verified (0.02)



PLATE


Anv = 408.000 [mm





BEAM


Anv = 464.800 [mm




WELD RESISTANCE





|| 0.9*fu/M2 |0.00| < 0.31 verified (0.00)



w = 0.85


[2+3*(II

2+

2)] fu/(w*M2) 0.02 < 0.40 verified (0.06)


T13

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