7/30/2019 Ec9 Ex61 Shear No Stiffeners

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Ec9_ex61_Shear_No stiffeners.mcd Plate girder - shear force Page 1 of 3

a lw:= a 4000mm=a

hw2=

Ref. to Eurocode 9

(6.127) or(6.128)

k ifa

hw1.00> 5.34 4.00

hw

a

2

+, 4.00 5.34hw

a

2

+,

:=

k 6.34=

(6.126) w0.81

k

hw

tw

fow

E

:=

w3.055=

Table 6.13 v if w 0.937>2.3

1.66 w+,

0.83

w

,

:=

v 0.488=

Table 6.13 0.7 0.35fuw

fow+:= 1.163=

Table 6.13 v min v,( ):= v 0.488=

Table 6.13 v if endpost 0= if v0.83

w

>0.83

w

, v,

, v,

:=

v 0.488=

(6.122)Vw.Rd v tw

hw

fow

M1

:=Vw.Rd 4.723 10

3

kN=

Example 6.1 Shear resistance of a plate girder with rigid end post

lw

hw

bf

tf

tw

Dimensions and strength of material Data input in highlighted regions

Web depth hw 2000 mm:= MPa 1000000 Pa

Web thickness tw 15 mm:= kN 1000 newton

Total length of web panel lw 4000 mm:= spv 2.4kg

0.1m( )3

(Mass)0,2 proof strength of web plate material fow 355 MPa:=

Ultimate strength of web plate material fuw 470 MPa:=

Elastic modulus E 70000 MPa:=

Partial coefficient M1 1.1:=

a) Shear resistance of the webIf "rigid end post" then endpost =1 else endpost =0 endpost 1:=

Length of web panel

T Hglund aluMATTER 2007-07-27

7/30/2019 Ec9 Ex61 Shear No Stiffeners

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Ec9_ex61_Shear_No stiffeners.mcd Plate girder - shear force Page 2 of 3

Singlesided stiffener tst 18 mm:= bst 220 mm:=

Figure 6.29 Ast tst bst 30 tw2

+:= Ast 1.071 104

mm2

=

C. G. esttst bst

2

2 Ast:= est 40.672mm=

Secondmomentof area

Isttst bst

3

3Ast est

2:= Ist 4.617 10

7 mm

4=

(6.153) or(6.154) Ilimit if ahw2< 1.5

hw

3tw

3

a2

, 0.75 hw tw3,

:= Ilimit 5.062 106 mm4=

Stiffness if Ist Ilimit> "OK!", "Non-rigid",( ):= Stiffness "OK!"=

Axial forcein stiffener6.7.8.3 (3)

a lw:= a 4000mm=

(6.127) k 5.34:= Intermediate stiffener removed k 5.34=

(6.126) w0.81

k

hw

tw

fow

E:= w 3.328=

Table 6.13 v if w 0.937>2.3

1.66 w+,

0.83

w

,

:=

v 0.461=

b) Shear resistance contribution of the flanges

The largest shear force of a simply supported girder is at the end of the plate girder. The bending moment isusually small.

Flange thickness and width tf 50 mm:= bf 750 mm:=

Yield strength of flange plate fof 355 MPa:=

Design shear force VEd 4800 kN:=

Design bending moment MEd VEd lw:= MEd 1.92 104

kN m=

6.7.4.2 (10) MfRd bf tf hw tf+( )fof

M1

:=MEd

MfRd0.774= MfRd 2.481 10

4 kN m=

(6.131a) c 0.084.4bf tf

2 fof

tw hw

2

fow

+

a:=c 870mm=

(6.131) Vf.Rd if MEd MfRd if 2> if 3> 4, 3,( ), 2,( ), 1,( ):=3 15.1=3 18 :=2 10.9=2 13 :=1 7.6=1 9 :=Table 6.2

BC "A, with weld":= 0.839=

250 MPa

fow:=

OKVEd 4800kN=>Nb.Rd 5026kN=Nb.Rd

fow

M1 Ast:=(6.49)

0.93= 0.618=

1

2

2

+

:= 0.5 1 o( )+ 2

+:=(6.50)

0.417=l

r

1

fow

E:=

1:=o 0.1:= 0.2:=Table 6.6

l k hf:=

Stiffeners above support

te 20mm=teAe

be:=be 450 mm:=

Ae 9000mm2

=Ae4 hf tw

2

e:=

e 205mm=e 0.1hf:=hf hw tf+:=6.7.8.1 (5)

Stiffener at girder end

d) Check of rigid end post

eAe

a

hf

be,

te

bst

tst

st < fow OK!fow

M1

323MPa=st 208MPa=stNst

Ast:=

Nst VEd v hw twfow

3 M1:=

Element classification6.1.4.4

12.5=bst

tst:=

Local buckling6.1.4.3

r 111.5mm=rIst

Ast:=

Ist 2.083 108

mm4

=Isttst 2 bst( )

3

12:=

Secondmomentof area

Ast 1.675 104

mm2

=Ast 2 tst bst 30 tw2

+:=Figure 6.27

bst 250 mm:=tst 20 mm:=Double stiffener

6.7.8.1 (2)

T Hglund aluMATTER 2007-07-27