STEEL RAILWAY BRIDGE DESIGN

1.2 Influence lines and internal forces kN

q := 1.689

P :=

L := 15.3m

m

l

275kN

kN

kN

P

:=

w

88

g := 41.75

m

m

CROSS SECTION A - A 1 

9.7 × 0.555

15.3⋅ 1 

V :=

⋅ ⋅( +

+

+

+

⋅

⋅ + ( + ⋅

⋅ 

1

P

0.741

0.616)

P

L

q

g)

L

2

l 1

0.869

w



2

2



V =

⋅

1

4797.82 kN

M :=

⋅

1

0kN m

STEEL RAILWAY BRIDGE DESIGN

CROSS SECTION B - B

1 

 6.85 × 0.348

2.05⋅ 0.162



(−0.594 + 0.406)⋅15.3

 

V :=

⋅ −



⋅(

+

+

+

+

⋅

−

−

⋅ + ( + ⋅

−

⋅ 

2

P

0.276

0.381

0.485

0.594)

P

0.001 L

q

g)

0.001 L

2

l

w





2

2





4

 

V =

⋅

2

211.93 kN

1 

 5.25⋅2.029

3.65⋅ 1.224 

2

15.3⋅ 3.108

2

M :=

⋅ ⋅(

+

+

+

⋅ +

⋅

+

⋅

+ ( + ⋅

⋅ 

2

P

2.295

1.557) L

P

L

q

g)

L

2

l 2.389

3.108

w





2

2



2



M =

⋅

⋅

2

48.42 MN m

1 

 5.25⋅2.029

3.65⋅ 1.224 

2

M

:= ⋅ ⋅(

+

+

+

⋅ +

⋅

+

⋅ 

2uż

P

2.295

1.557) L

P

L

2

l 2.389

3.108

w





2

2





M

=

⋅

2uż

22.53 MN m

STEEL RAILWAY BRIDGE DESIGN

CROSS SECTION C - C

1 

 10.2 × 0.759



 15.3⋅1

 

V :=

⋅ −



⋅(

+

+

+

−

⋅

+

⋅ − ( + ⋅

+

⋅ 

3

P

0.616

0.741

0.869

1)

P

0.001 L

q

g)

0.001 L

2

l

w





2





2

 

V = −

⋅

3

5592.629 kN

1 

2

2

M :=

⋅ − ⋅(

+

+

+

⋅ −

⋅(

+

⋅

− ( + ⋅

⋅

3

P

1.147

1.363

1.466

1.42) L

P

) L

q

g) ( 0.03) L





2

l

w 0.003

0.015

M = −

⋅

⋅

3

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) R :=

t

170MPa

f :=

d

285MPa

h := 1.91m

E := 205GPa

h

:=

:=

:=

w

1.860m

bf

0.5m

bftop

2.830m

t

:=

:=

⋅

:=

⋅

w

0.02m

hf

0.03 m

hftop

0.02 m

2.2. Geometrical parameters of the profile Moment of inertia: 4

I :=

x

0.2m

First moment of inertia: 3

S := 0.022m

Ix

Bending indicator: 3

W :=

=

⋅

x

0.209 m

h

2.3. Stresses

2

2.3.1. Cross section A-A V ⋅

1 S

τ

:=

=

⋅

<

=

⋅

A

26.39 MPa

R

I ⋅

t

170 MPa

x tw

2.3.2. Cross section B-B

- shear stresses V ⋅

2 S

τ

:=

=

⋅

<

=

⋅

B

1.17 MPa

R

I ⋅

t

170 MPa

x tw

- bending stresses M2

σ

:=

=

⋅

<

=

⋅

B

231.21 MPa

R

280 MPa

Wx

- total stresses 2

2

τ

+

=

⋅

<

⋅ =

⋅

B

σB

231.21 MPa

1.1 R

308 MPa

2.3.3. Cross section C-C

- shear stresses V

⋅

3 S

τ

:=

=

⋅

=

⋅

C

39.54 MPa

R

I ⋅

<

t

170 MPa

x tw

- bending stresses M3

σ

:=

=

⋅

<

=

⋅

C

55.82 MPa

R

280 MPa

Wx

- total stresses 2

2

τ

+

=

⋅

<

⋅ =

⋅

C

σC

68.4 MPa

1.1 R

308 MPa

2.4 Checking of deflection 2

⋅

5

M2uż L

L

f :=

⋅

= 0.002 m

<

f

:=

= 0.026 m

348

E⋅ I

dop

x

600

STEEL RAILWAY BRIDGE DESIGN

V := −

3

7188.43

M :=

⋅

2

48.42MN m

M

:=

⋅

2uż

22.53MN m

M := −

3

1151726.47

STEEL RAILWAY BRIDGE DESIGN

V := −

3

7188.43

STEEL RAILWAY BRIDGE DESIGN

11

4

4

2⋅ 10 mm = 0.2 m 3

3

3

b

⋅

⋅

⋅

ftop hftop

bf hf

t

2

w hw

I :=

+

+

⋅ ⋅

+

x

2h

( 0.885m)

12

12

f bf

12

7

3

S := b

( ⋅ +

⋅

+

⋅ )⋅

=

×

⋅

f hf

bftop hftop hw tw 400mm 4.352

10 mm

2

3

S := 67053.0442mm ⋅ 322.3528mm = 0.022⋅ m

STEEL RAILWAY BRIDGE DESIGN

7188.43kN

1151726.47kN⋅ m

STEEL RAILWAY BRIDGE DESIGN

7188.43kN