1

Plate girders

Section class 4 elements

COMPLEX STEEL STRUCTURES

LECTURE PLAN

PLATE GIRDERS

STIFFENERS

PLATE GIRDERS FABRICATION

SPECIAL PLATE GIRDERS

BIBLIOGRAPHY

2

PLATE GIRDERS

3

WHAT IS A PLATE GIRDER ?

PLATE GIRDERS

WHERE ARE THE PLATE GIRDERS USED ?

- main beams in frames

- bridge girders

- roof girders

- gantry girders

Source [8]

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PLATE GIRDERS

WHY THE PLATE GIRDERS ARE USED ?

- limited dimensions of hot-rolled sections

- efficient use of steel

- possible change of cross-section

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PLATE GIRDERS

PLATE GIRDERS TYPES:

- by connections

- welded

- riveted

- by cross-section

- I-section

- box

- by material

- homogeneous (one steel grade)

- hybrid (more steel grades)

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7

PLATE GIRDERS CROSS-SECTION

Source [2]

PLATE GIRDERS

8

Source [4]

PLATE GIRDERS CROSS-SECTION (RIVET JOINTS)

PLATE GIRDERS

9

Source [2]

PLATE GIRDERS CROSS-SECTION (WELDED JOINTS)

PLATE GIRDERS

10

OPTIMAL HEIGHT OF A PLATE GIRDER

1

1

16

10

h

l

⎛

⎞

=

÷

⋅

⎜

⎟

⎝

⎠

1

1

20

12

h

l

⎛

⎞

=

÷

⋅

⎜

⎟

⎝

⎠

- Single span:

- Continuous:

where:
l – girder span

PLATE GIRDERS

11

x

w

W

h

t

α

= ⋅

3

6

x

h

W

= ⋅

where:

α=1,1 ; 1,2 – for beams with uniform and changing cross-section

respectively

W

x

– required section modulus obtained from:

t

w

– web thickness

/

x

d

W

M

f

=

OPTIMAL HEIGHT OF A PLATE GIRDER

Source [2]

PLATE GIRDERS

12

PLATE GIRDER WEIGHT

700 100

ch

bl

q

l

=

+

⋅

- riveted girders:

- welded girders

(

)

700 100

0,85

ch

bl

q

l

=

+

⋅ ⋅

gdzie:
l – girder span [m]

PLATE GIRDERS

13

PLATE GIRDERS PRODUCED BY IRONWORKS

Source [7]

PLATE GIRDERS

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Source [9]

np.: IKS 1200-8

h = 1200 [mm]
b = 400 [mm]
g = 9 [mm]
t = 16 [mm]
m = 186,4 [kg/m]

PLATE GIRDERS PRODUCED BY IRONWORKS

PLATE GIRDERS

15

15

PLATE GIRDERS

16

SHEAR LAG EFFECT – nonlinear distribution of normal stresses in
wide flanges

b

0

When b

0

≥ L

e

/ 50, the shear lag effect must be taken into account.

Effective width for shear lag under elastic conditions:

PLATE GIRDERS

0

eff

b

b

β

= ⋅

b

0

PLATE GIRDERS

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PLATE GIRDERS

18

PLATE GIRDERS

19

SHEAR LAG - EXAMPLE

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LOCAL BUCKLING OF A CROSS-SECTION

Source [8]

PLATE GIRDERS

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21

Source [5]

PLATE GIRDERS

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EQUILIBRIUM PATH FOR SECTION CLASS 1, 2, 3 AND 4

Source [2]

PLATE GIRDERS

23

PLATE GIRDERS

24

Source [5]

The effective area of the compression zone of a plate with the gross
cross-section area A

c

should be obtained from:

,

c eff

c

A

A

ρ

= ⋅

where:

ρ - the reduction factor for plate buckling

(4.1)

PLATE GIRDERS

PLATE GIRDERS

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26

Source [5]

PLATE GIRDERS

27

Source [5]

PLATE GIRDERS

28

The reduction factor

ρ

may be taken as follows:

- internal compression elements

1, 0

ρ

=

2

0, 055 (3

)

1

p

p

λ

ψ

ρ

λ

−

⋅ +

=

≤

for

0, 673

p

λ

≤

for

0, 673

p

λ

>

where

(3

)

0

ψ

+

≥

(4.2)

PLATE GIRDERS

29

The reduction factor

ρ

may be taken as follows:

- outstand compression elements

1, 0

ρ

=

2

0,188

1

p

p

λ

ρ

λ

−

=

≤

for

0, 748

p

λ

≤

for

0, 748

p

λ

>

(4.3)

where:

1

28, 4

y

p

cr

b

f

t

k

σ

λ

σ

ε

=

=

≤

⋅ ⋅

PLATE GIRDERS

30

PLATE GIRDERS

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Buckling resistance of member in compression (section class 4):

where:
Χ – buckling coefficient for relevant buckling mode,
A – cross-section area,
A

c,eff

– effective cross-section area, W

eff,y

– effective section modulus,

f

y

– yield strength,

γ

M1

– partial factor for stability

,

,

1

c eff

y

b Rd

M

A

f

N

χ

γ

⋅

⋅

=

,

,

1

LT

eff y

y

b Rd

M

W

f

M

χ

γ

⋅

⋅

=

LTB resistance of a member in bending (section class 4):

PLATE GIRDERS

32

where:
N

Ed

, M

y,Ed

, M

z,Ed

– design forces

∆M

y,Rd

, ∆ M

z,Rd

– moments due to the shift of the centroidal axis for class 4

section
N

Rd

, M

y,Rd

, M

z,Rd

– characteristic resistance

C

my

, C

mz

– bending moment factor (according to Table B.3)

χ

y

,

χ

z

– buckling coefficients

χ

LT

– LTB coefficient

∆

0

– reduction factor

0

,

,

,

,

,

,

1

)

(

)

(

∆

∆

χ

∆

χ

−

≤

+

⋅

+

⋅

+

⋅

+

⋅

Rd

z

Ed

z

Ed

z

mz

Rd

y

LT

Ed

y

Ed

y

my

Rd

y

Ed

M

M

M

C

M

M

M

C

N

N

COMPRESSION AND BIAXIAL BENDING

0

,

,

,

,

,

,

1

)

(

)

(

∆

∆

χ

∆

χ

−

≤

+

⋅

+

⋅

+

⋅

+

⋅

Rd

z

Ed

z

Ed

z

mz

Rd

y

LT

Ed

y

Ed

y

my

Rd

z

Ed

M

M

M

C

M

M

M

C

N

N

32

PLATE GIRDERS

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SHEAR BUCKLING OF WEB

Source [8]

PLATE GIRDERS

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RESISTANCE TO SHEAR

When the following formulae for unstiffened web is not satisfied

ε

η

⋅

≤

72

w

w

t

h

the resistance to shear buckling of the web must be checked.

where:
h

w

– web heigth,

t

w

- web thickness

η = 1,2 for steel grades up to S460 and η =1,0 for higher steel grades.

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PLATE GIRDERS

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DESIGN RESISTANCE TO SHEAR

For unstiffened or stiffened webs the design resistance for shear is

1

,

,

,

3

M

w

w

yw

Rd

bf

Rd

bw

Rd

b

t

h

f

V

V

V

γ

η

⋅

⋅

⋅

⋅

≤

+

=

(5.1)

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PLATE GIRDERS

Source [2]

36

Contribution of web

(5.2)

- from Annex A

where:
Χw – shear buckling factor (depending on )

w

λ

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PLATE GIRDERS

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37

Source [5]

PLATE GIRDERS

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Source [5]

PLATE GIRDERS

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Contribution of flanges

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PLATE GIRDERS

PLATE GIRDERS

RESISTANCE TO TRANSVERSE FORCES

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Source [8]

PLATE GIRDERS

RESISTANCE TO TRANSVERSE FORCES

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PLATE GIRDERS

RESISTANCE TO TRANSVERSE FORCES

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PLATE GIRDERS

RESISTANCE TO TRANSVERSE FORCES

43

44

STIFFENERS TYPES:

- Longitudinal

- Transverse

PLATE GIRDERS

Source [8]

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STIFFENERS TYPES:

- single side

- double side

PLATE GIRDERS

Stiffeners can be made from flat bars or profiles.

TRANSVERSE STIFFENERS TYPES:

- end post

- rigid
- non-rigid

- intermediate

PLATE GIRDERS

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TRANSVERSE STIFFENERS ARE USED:
- where the point load is applied,
- at the supports,
- at rigid joints,
- where the slender panel need strengthening (section class 4).

PLATE GIRDERS

PLATE GIRDERS

48

End posts (support stiffeners) and intermediate stiffeners subjected to
point load are designed as a column with:

L

cr

= 0,75 h

w

– when both flanges are braced

L

cr

= h

w

- otherwise

PLATE GIRDERS

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Intermediate stiffeners are analysed as a member subjected to load
equivalent to initial imperfection w

0.

0

300

s

w

=

1

2

min( ,

, )

s

a a b

=

where

PLATE GIRDERS

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CHANGE OF CROSS SECTION

Źródło [2]

PLATE GIRDERS

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Źródło [7]

CHANGE OF CROSS SECTION – FLANGE CONNECTION

PLATE GIRDERS

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53

PLATE GIRDERS

Źródło [1]

CONNECTION OF WEB AND FLANGE

PLATE GIRDERS

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Fillet weld capacity:

2

/ 3

y

u

II

y

w

M

V S

f

J

a

τ

β γ

⋅

=

≤

⋅

⋅

∑

CONNECTION OF WEB AND FLANGE

where:
V – shear force,
S

y

- moment of area,

J

y

– moment of inertia.

Źródło [1]

PLATE GIRDERS

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Welding defect (undercut) may lead to stress concentration. Hence in
plate girders subjected to dynamic loads (gantry grirders) stiffeners
are not welded to tension chord (flange).

Źródło [1]

undercut

Detail A

PLATE GIRDERS

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STIFFENER CONNECTION TO WEB AND FLANGE

Źródło [5]

PLATE GIRDERS

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PLATE GIRDER FABRICATION

PLATE CUTTING

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PLATE GIRDER FABRICATION

ASSEMBLY AND WELDING

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PLATE GIRDER FABRICATION

FINAL CROSS SECTION

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SPECIAL PLATE GIRDERS

SPECIAL PLATE GIRDERS

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SPECIAL PLATE GIRDERS

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BIBLIOGRAPHY

1. Rykaluk K. „Konstrukcje stalowe. Podstawy i elementy” DWE, Wrocław 2001
2. Łubiński M., Filipowicz A., Żółtowski W. „Konstrukcje metalowe. Część I”

Wydawnictwo Arkady, Warszawa 2006

3. Żmuda J. „Podstawy projektowania konstrukcji metalowych” Wydawnictwo Arkady,

Warszawa 1997

4. Biegus A. „Stalowe budynki halowe” Wydawnictwa Arkady Warszawa 2007.
5. PN-EN 1993-1-5:2006 „Eurokod 3. Projektowanie konstrukcji stalowych. Część 1-5:

Blachownice”

6. Bogucki W., Żyburtowicz M. „Tablice do projektowania konstrukcji metalowych”

Wydawnictwo Arkady, Warszawa 2007

7. Bródka J., Broniewicz M. „Projektowanie konstrukcji stalowych zgodnie z

Eurokodem 3-1-1 wraz z przykładami obliczeń” Wydawnictwa Politechniki
Białostockiej, Białystok 2001.

8. Materiały dydaktyczne ESDEP