STEEL RAILWAY BRIDGE DESIGN

1.2 Influence lines and internal forces

q

1.689

kN

m

:=

Pl

275kN

:=

L

15.3m

:=

Pw

88

kN

m

:=

g

41.75

kN

m

:=

CROSS SECTION A - A

V1

1

2

Pl 1 0.869

+

0.741

+

0.616

+

(

)

⋅

Pw

9.7

0.555

×

2

⋅

L

⋅

+

q

g

+

(

)

15.3 1

⋅

2

⋅

L

⋅

+













⋅

:=

V1

4797.82 kN

⋅

=

M1

0kN m

⋅

:=

STEEL RAILWAY BRIDGE DESIGN

CROSS SECTION B - B

V2

1

2

Pl

−

0.276

0.381

+

0.485

+

0.594

+

(

)

⋅

Pw

6.85

0.348

×

2

2.05 0.162

⋅

2

−

0.001

−













⋅

L

⋅

+

q

g

+

(

)

0.594

−

0.406

+

(

) 15.3

⋅

4

0.001

−













⋅

L

⋅

+













⋅

:=

V2

211.93 kN

⋅

=

M2

1

2

Pl 2.389 3.108

+

2.295

+

1.557

+

(

)

⋅

L

⋅

Pw

5.25 2.029

⋅

2

3.65 1.224

⋅

2

+













⋅

L

2

⋅

+

q

g

+

(

)

15.3 3.108

⋅

2

⋅

L

2

⋅

+













⋅

:=

M2

48.42 MN m

⋅

⋅

=

M2uż

1

2

Pl 2.389 3.108

+

2.295

+

1.557

+

(

)

⋅

L

⋅

Pw

5.25 2.029

⋅

2

3.65 1.224

⋅

2

+













⋅

L

2

⋅

+













⋅

:=

M2uż 22.53 MN m

⋅

=

STEEL RAILWAY BRIDGE DESIGN

CROSS SECTION C - C

V3

1

2

Pl

−

0.616

0.741

+

0.869

+

1

+

(

)

⋅

Pw

10.2

0.759

×

2

0.001

+













⋅

L

⋅

−

q

g

+

(

)

15.3 1

⋅

2

0.001

+













⋅

L

⋅

−













⋅

:=

V3

5592.629

−

kN

⋅

=

M3

1

2

Pl

−

1.147

1.363

+

1.466

+

1.42

+

(

)

⋅

L

⋅

Pw 0.003 0.015

+

(

)

⋅

L

2

⋅

−

q

g

+

(

) 0.03

(

)

⋅

L

2

⋅

−









⋅

:=

M3

11.69

−

MN m

⋅

⋅

=

STEEL RAILWAY BRIDGE DESIGN

2. Calculations

2.1. Steel parameters:

- Type: 18G2A

- Bending strength (in chords)

R

280MPa

:=

- Shear strength (in web)

Rt

170MPa

:=

fd

285MPa

:=

h

1.91m

:=

E

205GPa

:=

hw

1.860m

:=

bf

0.5m

:=

bftop

2.830m

:=

tw

0.02m

:=

hf

0.03 m

⋅

:=

hftop

0.02 m

⋅

:=

2.2. Geometrical parameters of the profile

Moment of inertia:

Ix

0.2m

4

:=

First moment of inertia:

S

0.022m

3

:=

Bending indicator:

Wx

Ix

h

2

0.209 m

3

⋅

=

:=

2.3. Stresses

2.3.1. Cross section A-A

τA

V1 S

⋅

Ix tw

⋅

26.39 MPa

⋅

=

:=

<

Rt

170 MPa

⋅

=

2.3.2. Cross section B-B

- shear stresses

τB

V2 S

⋅

Ix tw

⋅

1.17 MPa

⋅

=

:=

<

Rt

170 MPa

⋅

=

- bending stresses

σB

M2
Wx

231.21 MPa

⋅

=

:=

<

R

280 MPa

⋅

=

- total stresses

τB

2

σB

2

+

231.21 MPa

⋅

=

<

1.1 R

⋅

308 MPa

⋅

=

2.3.3. Cross section C-C

- shear stresses

τC

V3 S

⋅

Ix tw

⋅

39.54 MPa

⋅

=

:=

Rt

170 MPa

⋅

=

<

- bending stresses

σC

M3

Wx

55.82 MPa

⋅

=

:=

<

R

280 MPa

⋅

=

- total stresses

τC

2

σC

2

+

68.4 MPa

⋅

=

<

1.1 R

⋅

308 MPa

⋅

=

2.4 Checking of deflection

f

5

348

M2uż L

2

⋅

E Ix

⋅

⋅

0.002 m

=

:=

<

fdop

L

600

0.026 m

=

:=

STEEL RAILWAY BRIDGE DESIGN

V3

7188.43

−

:=

M2

48.42MN m

⋅

:=

M2uż

22.53MN m

⋅

:=

M3

1151726.47

−

:=

STEEL RAILWAY BRIDGE DESIGN

V3

7188.43

−

:=

STEEL RAILWAY BRIDGE DESIGN

2 10

11

⋅

mm

4

0.2 m

4

=

Ix

bftop hftop

3

⋅

12

bf hf

3

⋅

12

+

2hf bf

⋅

0.885m

(

)

2

⋅

+

tw hw

3

⋅

12

+

:=

S

bf hf

⋅

bftop hftop

⋅

+

hw tw

⋅

+

(

)

400

⋅

mm

4.352

10

7

×

mm

3

⋅

=

:=

S

67053.0442mm

2

322.3528

⋅

mm

0.022 m

3

⋅

=

:=

STEEL RAILWAY BRIDGE DESIGN

7188.43kN

1151726.47kN m

⋅

STEEL RAILWAY BRIDGE DESIGN

7188.43kN