Mathcad V1 B

7/30/2019 Mathcad V1 B

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JOINT NO: 19 IPE500-to-IPE500 SHEAR CONNECTION DESIGN


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References;

1. BS EN 1993-1-1:2005 / Eurocode 3: Design of steel structures - General rules and rules for buildings

2. BS-EN1993-1-8:2005 / Eurocode 3: Design of steel structures -Design of joints3. Joints-in-Steel-Construction-Simple-Joints-to-Eurocode-3-P358

4. Manual for the design of steelworkbuilding structures to Eurocode-3-British Institutution of Structural

Engineers

Loads and dimensions: Supported beam section properties: IPE500

VEd 725kN:=Supported beam depth: D 500mm:=

Shear force :

NEd 0kN:=Supported beam flange width: B 200mm:=

Axial force :

Supported beam web thickness: tws 10.2mm:=tf 20mm:=Fin plate thickness:

Supported beam flange thickness: tfb 16mm:=p1 60mm:=Vertical bolt distance:

Radius: rb 21mm:=e1 40mm:=Edge distance vertical:

Bolt diameter : db 20mm:=e2 40mm:=Edge distance horizontal. :

e3 40mm:=Hole diameter : Dh 22mm:=

eb 100mm:=Number of bolt rows: n1 6:=

et 100mm:=Number of bolts in a row : n2 2:=

p2 60mm:=Total number of bolts: n n1 n2 12=:=Horizontal bolt distance:

lf n1 1( ) p1 2e1+ 380 mm=:=Fin plate length:

Supporting beam section properties: IPE500

Supporting beam flange width: Bb 200mm:=

Supporting beam depth: Db 500mm:=

Supporting beam flange thickness: tfbs 16mm:=

Supporting beam web thickness: twb 10.2mm:=

Radius of supporting beam: r2 21mm:=

Distance between supporting beam and supported beam: gh 20mm:=


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ap2

2

e2+

2Bb

2

twb

2

gh+

+ 299.8 mm=:=

The angle between supporting and supported beam differs at almost every connection because of the radial

axis lines.

For not to list every angle between beams, all the angles were taken into calculations as "30 degrees"

conservatively and the changed part of eccentricity was multiplied by 2.

When the angle is smaller than this value, connection type will change.

Weld properties:

Design strength of fillet weld: pw 241MPa:=BS EN 1993-1-8:2005, clause 4.5.3.3 (1) & National Annex

Design strength of partial butt weld: pbw 355MPa:=BS EN 1993-1-8:2005, clause 4.7.2 & National Annex

Bolt properties:fyb 900MPa:=

BS EN 1993-1-8:2005, Table 3.1.Design yield strength:

Design ultimate strength: fub 1000MPa:=BS EN 1993-1-8:2005, Table 3.1.

Main Steel Material : S355

Design strength : fy 355.MPa:=BS EN 1993-1-1:2005, Table 3.1.

Ultimate tensile strength : fu 470MPa:=BS EN 1993-1-1:2005, Table 3.1.

Plate Material : S355

Design strength : fyp 345MPa:=BS EN 1993-1-1:2005, Table 3.1.

Ultimate tensile strength : fup 470MPa:=BS EN 1993-1-1:2005, Table 3.1.


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Check-1:Recommended detailing practice:

(Joints-in-Steel-Construction-Simple-Joints-to-Eurocode-3-P358 - Page 103)

* Requirement for the height of the fin plate to give adequate nominal torsional restraint:

Check lf 0.6D>( )

lf 380 mm= 0.6 D 300 mm=

380mm 300mm> OK

* Minimum and maximum bolt spacing, end and edge distance requirements:

Check 1.2D

h

e

2

< 40mm 4t

f

+

Bolt Shear Resistance:

v 0.5:=

m2 1.25:=(BS EN 1993-1-1:2005, Section 6.1.)

Ab 245mm2

:= Bolt Area

FVRd v fubA

bm2

98 kN=:=

Ratio1VEd

n FVRd0.62=:=

Check 2 (continued): Fin plate - Bolt group bearing check :

(Joints-in-Steel-Construction-Simple-Joints-to-Eurocode-3-P358 - Page 105

Bolt bearing in the fin plate:

k1 min 2.8e2

Dh

1.7 2.5, 1.4p2

Dh

1.7,

2.12=:=

b min 1e1

3 Dh,

p1

3 Dh0.25,

fub

fup

,

0.61=:=

FbRdv k1 b db tffup

m2

193.1 kN=:=

z e2

p2

2+ 70 mm=:=

ln1

2p2

2

n1

6n1

21 p1

2+ 1368 cm

2=:=

z p2

2l0.015=:=

Vrd1

n

1 n+

FbRdv

2 1956.5 kN=:=

Ratio2VEd

Vrd1

0.37=:=


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Check 2 (continued) : Supported beam - Bolt group bearing check in Supported Beam Web:


Bolt Bearing in Supported Beam Web:

k1b min 2.8e2

Dh

1.7 2.5, 1.4p2

Dh

1.7,

2.12=:=

bb min 1eb

3 Dh,

p1

3 Dh0.25,

fub

fu

,

0.66=:=

FbRdv2 k1b bb db twsfu

m2

107.1 kN=:=

Vrd2n

1 n+

FbRdv2

2

1085.1 kN=:=

Ratio3VEd

Vrd2

0.67=:=


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Check 3 - Fin Plate : Shear Resistance of the fin plate


1) Shear

Basic Requrement : VEd VRdminOK

Leg length of horizontal weld: swh 10mm:=

Effective thickness of horizontal partial butt weld:

awh swh:=

Bad 120mm:=Stiffener width:

Length of vertical weld: Lw Db 2 tfbs 2 r2 3mm+( ) 420 mm=:=

Weld area: Aw 2 Lw aw 4 Bad 2aw 2 3 mm( ) awh+:=

Ratio5VEd

Aw pw0.32=:=


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2) Weld bending check;

Static moment of vertical weld: Swv 2 awLw

2

6 374.2 cm

3=:=

Moment on the weld: Mv1 VEd a 217.4 kN m=:=

x tfbs r2+ 25mm+ tf+:= Ls

Db

2x:=

Moment of inertia

of horizontal weld:Ihw 4

Bad awh3

12Bad 2s 2 3 mm( ) awh Ls

2+

:=

Static moment of horizontal weld: Swh

Ihw

Ls

:=

Sw Swh Swv+:=

pp1

Mv1

Sw

213.2 MPa=:=

Ratio6

pp1

pw 0.88=:=

3)Fin plate bending check for Mv1

Static moment vertical plate section: Spv tf

Lw2

6 588 cm

3=:=

Moment of inertia of horizontal plate:I2 4

Bad tf3

12Bad tf Ls

2+

:=

Static moment horizontal plate section: Sph

I2

Ls

:=

Sp Spv Sph+( ):=

pp2

Mv1

Sp

99 MPa=:= Ratio7pp2

fyp

0.29=:=

4)Fin plate bending check for Mv2

Static moment of the fin plate section: Sp2 tf

lf2

6 481.3 cm

3=:=

Moment of the section: Mv2 VEd e2

p2

2+

50.8 kN m=:=

pp3

Mv2

Sp2

105.4 MPa=:= Ratio8pp3

fyp

0.31=:=


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Check 4-Supported Beam Web in Shear: Shear Resistance of HE 600B


1 ) Shear

Basic Requirement VEd

VRdmin2

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