steel and concrete composite bridge trusses 2011/presentations/day1/machacek... · steel and...

METNET Aarhus 2011 1

STEEL AND CONCRETE COMPOSITE

BRIDGE TRUSSES

Prof. Josef Machacek

Martin Charvat, PhD student

Czech Technical University in Prague

Czech Republic

2

Contents 1. Introduction

- elastic and plastic analysis of longitudinal shear

in composite trusses

- previous studies

2. Theoretical model

- 3D FE modelling

- simplified 2D elastic model

3. Numerical studies - railway composite truss bridge with large span

- road composite truss bridge with short span

4. Conclusions and recommendations

METNET Aarhus 2011

3

CL CL

Elastic and plastic analysis of longitudinal shear:

beam truss

Plastic analysis: common.

Elastic analysis: - class 3 & 4 cross sections,

- "non ductile" shear connectors,

- fatigue.

1. Introduction

longitudinal

shear flow

plastic elastic

plastic

elastic

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Previous studies:

'70th Galambos & Tide, Azmi, Iyengar & Zils

(research and practical applications)

'90th Brattland & Kennedy, Woldegiorgis, Viest

(experimental and theoretical studies)

Steel Construction Institute

after 2000 Johnson & Ivanov:

- numerical studies on concentrated longitudinal shear,

- Eurocod 4 (part 2 - Bridges)

Authors of this paper: - experimental investigation of floor trusses, 2005-6

- numerical analysis, Engineering Structures, 31(6), 2009

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1. 3D ANSYS software analysis GMNA (geometrically and materially non-linear analysis)

2. Theoretical model

3D modelling:

concrete slab: SOLID65

upper steel chord: SHELL43

web steel bars: BEAM24

bottom steel chord: BEAM24

shear connection: COMBIN39

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Stress-strain relationships (used in numerical studies):

steel

(S355)

concrete

(e.g. C 30/37)

[mm/mm]

c [MPa]

a [MPa]

[mm/mm]

- 3.8

Ecm = 32 000 MPa

30

25

12

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Load-slip diagrams of shear connection:

- perforated shear connectors (own published results)

- headed studs (published by Oehlers and Coughlan)

example: studs Ø 19 mm

1,39; 54840

2,11; 73120

2,57; 82260

3,55; 86830 5,87; 91400

7,60; 86830

10,00; 73120

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 1 2 3 4 5 6 7 8 9 10 11 12

Sh

ea

r fo

rce

P[N

]

Slip d [mm] slip d [mm]

shear force P [N]

per 1 stud

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Two identical composite truss girders of span L = 6 m

(total depth of girder 510 mm)

Experiments

testing rig hydraulic jack PZ20

distributing beams HE 200 B

plaster bed

roller bearing

axis of symmetry perforated connector

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Details of experimental work

Loading

controlled by hydraulic jacks

Plastic collapse

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Comparison of experimental results, FE model and Eurocode

ANSYS FE model verification

Material properties:

• measured values

• relationships as given above

Theory-EN 1994

EX1

EX2

FE model

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 160

Deflection at midspan δ [mm]

Lo

ad

ing

pe

r ja

ck F

[kN

]

δ el

F el

F pl

0

20

40

60

80

100

120

140

0,00 0,02 0,04 0,06 0,08 0,10 0,12

End slip δ s [mm]

Lo

ad

ing

pe

r ja

ck F

[kN

]EX1

EX2

FE model

deflection at midspan d [mm] end slip ds [mm]

load

ing

/ jack F

[kN

]

loa

din

g / ja

ck

F [

kN

]

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2. Simplified 2D frame elastic model (SCIA Engineer software)

• all members modelled as bars,

• shear connectors (headed studs) as cantilevers

and pin connected at mid-plane of concrete slab.

D 161.5

concreteslab

member representing concrete slab

D

steelflange

e = 149D

concreteslab


steelflange

e = 143

member representing steel chordexcentrical to nodes

305

concreteslab


steelflange

concreteslab


steelflange

member representing steel chordin compression chord axis

DD

e = 0

D

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(only steel part shown)

12

3. Numerical studies

3.1 Large span railway bridge truss

L = 63 m

L/2 = 31 500

7229

7545

323

16003100

1600

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3D (ANSYS) resulting longitudinal shear

(half span shown)

1,39; 54840

2,11; 73120

2,57; 82260

3,55; 86830 5,87; 91400

7,60; 86830

10,00; 73120

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 1 2 3 4 5 6 7 8 9 10 11 12

Sh

ea

r fo

rce

P[N

]

Slip d [mm]slip [mm]

sh

ea

r fo

rce

[N

]

Headed studs Ø 19 mm: (by Oehlers and Coughlan)

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-20000

0

20000

40000

60000

80000

100000

0 5000 10000 15000 20000 25000 30000

Distance from support [mm]

Shear

forc

e p

er

connecto

r [N

]

q= 50 kN/m

q= 100 kN/m

q= 150 kN/m

q= 200 kN/m

q= 250 kN/m

q= 270 kN/m

q= 300 kN/m

q= 325 kN/m

sh

ea

r fo

rce

pe

r c

on

ne

cto

r [

N]

distance from support [mm]

design loading

approx. 200 kN/m)

4 studs per 400 mm

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Slip d [mm]

Sh

ea

r fo

rce

P [

N]

4x Stud D19/200 - push-out tests

Stud dia D097.58 - length 305 mm




14

Elastic 2D approximation of shear connection

Simplified linear approach (frame software) shear

forc

e [

N]

slip d [mm]

METNET Aarhus 2011

-10000

10000

30000

50000

70000

90000

110000

0 5000 10000 15000 20000 25000 30000


Shear

forc

e p

er

connecto

r [N

]

SCIA - D109.64

ANSYS

15

Comparison of 3D (ANSYS) and 2D (SCIA)

analyses for design level of loading 200 kN/m

2D analysis is in peaks slightly conservative due to elastic substitution.

distance from support

sh

ea

r fo

rce

pe

r

co

nn

ec

tor

[N]

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Influence of the shear connection rigidity (expressed by stud diameter D)

under design loading 200 kN/m (2D analysis)

Rigidity of shear connection dictates the behaviour.

-10000

10000

30000

50000

70000

90000

110000

0 5000 10000 15000 20000 25000 30000


Shear

forc

e p

er

connecto

r

[N]

D097.58

D106.06

D109.64

D113.14


shear force

per one connector [mm]

D 97.58

D 106.06

D 109.64

D 113.14

20 %

(due to 80 %

increase of rigidity)

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Approximation in EN 1994-2

(half span shown, at design loading 200 kN/m)

Standard is very conservative.

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-100

100

300

500

700

900

1100

1300

1500

1700

1900

0 5000 10000 15000 20000 25000 30000

Sh

ea

r flo

w

[N

/mm

]


EN 1994 (trapezoidal: non-ductile connectors)

EN 1994 (rectangular: stud connectors)

Auxiliary technical calculation

FEM-ANSYS

FEM-SCIA (D109.64)


shear flow [N/mm] Eurocode

ANSYS 3D FEM analysis

SCIA 2D analysis

non-ductile

ductile (studs)

18

Influence of shear connectors concentration

Parametrical study of amount of concentration and its length above

floor truss nodes has been published by Authors.

Large span bridge truss:

D

d d e ed

L/2 = 63 000/2 = 31 500

Basic arrangement: 4 studs per e = 400 mm

Concentrations:

D1 4 studs per e = 100 mm, d = D/4



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Example: concentration D1

-20000

0

20000

40000

60000

80000

100000

120000

140000

0 5000 10000 15000 20000 25000 30000


Shear

forc

e p

er

connecto

r [N

]

basic arrangement 4/400

densified connectors

as basic (4/400) due to increased local rigidity

pe

r c

on

ne

cto

r [N

]


basic arrangement: 4/400

concentration D1

as basic (4/400) due to increased local rigidity:

Increased shear: D1 71 %

D2 79 %

D3 87 %

METNET Aarhus 2011

3.2 Road bridges without gusset plates

20 METNET Aarhus 2011

all steel members are only flats


Analysed composite truss

steel: S355

concrete: C 30/37

3 headed studs Ø 19 mm per 200 mm:

Two variants, both full shear connection.

0,10; 39450

4,00; 77100

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 1 2 3 4 5 6 7 8 9 10 11

Sh

ea

r fo

rce

P[N

]

Slip d [mm]

0,10; 27615

4,00; 53970

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 1 2 3 4 5 6 7 8 9 10 11

Sh

ea

r fo

rce

P[N

]

Slip d [mm]

slip [mm] slip [mm]

sh

ear

forc

e [

N]

sh

ear

forc

e [

N]

T1 T2

less stiff


Resulting longitudinal shear

(half span shown, design loading approx. 75 kN/m)

-5000

5000

15000

25000

35000

45000

55000

65000

75000

85000

0 1500 3000 4500 6000 7500 9000 10500Shear

forc

e p

er

connecto

r [

N]


q= 15 kN/m

q= 30 kN/m

q= 45 kN/m

q= 60 kN/m

q= 75 kN/m

q= 90 kN/m

q= 105 kN/m

q= 115 kN/m


pe

r c

on

ne

cto

r [N

]

-5000

5000

15000

25000

35000

45000

55000

65000

75000

85000

0 1500 3000 4500 6000 7500 9000 10500Shear

forc

e p

er

connecto

r [

N]


q= 15 kN/m

q= 30 kN/m

q= 45 kN/m

q= 60 kN/m

q= 75 kN/m

q= 90 kN/m

q= 105 kN/m

q= 122 kN/m


pe

r c

on

ne

cto

r [N

]

T1 T2

stiffer shear connection less stiff shear connection: - still full shear connection;

- shear redistribution near collapse;

- 6% collapse load decrease.


Approximation in EN 1994-2

(half span shown, at design loading)

-100

100

300

500

700

900

1100

1300

1500

1700

1900

0 1500 3000 4500 6000 7500 9000 10500

Sh

ea

r flo

w

[N

/mm

]





FEM

less stiff shear connection:

T2

sh

ear

flo

w [

N/m

m]


FEM analysis

Eurocode

Standard is conservative

and the more the less rigid the shear connectors are.

-100

100

300

500

700

900

1100

1300

1500

1700

1900

0 1500 3000 4500 6000 7500 9000 10500

Sh

ea

r flo

w

[N

/mm

]





FEM

stiffer shear connection

T1

sh

ea

r fl

ow

[N

/mm

]


Eurocode

FEM analysis

non-ductile

ductile (studs)


Importance of upper steel chord stiffness

(half span shown, at design loading)

The thinner chord flange

the higher node shear peaks must be expected

-5000

45000

95000

145000

195000

245000

0 1500 3000 4500 6000 7500 9000 10500

Vzdálenost od podpory [mm]

Sm

yko

vá

síla

[N

]

t= 10 mm

t= 15 mm

t= 20 mm

t= 40 mm

t= 60 mm

t= 80 mm

sh

ea

r fo

rce

pe

r 3

stu

ds

[N

]


25

Within the elastic behaviour of shear connection the distinctive

peaks of shear flow occur above truss nodes.

Both proposed FEM models (3D ANSYS and 2D SCIA) provides

appropriate solution.

The shear flow peaks above nodes are considerably influenced

by:

- load-slip diagram of shear connectors,

- rigidity of the steel flange with the shear connectors,

- level of loading.

Eurocode 4 gives good estimate of the peaks in very low elastic

loading of a shear connection and rather conservative one,

when shear flow reaches the elastic (or design) strength

of the connection.

Conclusions

METNET Aarhus 2011

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The Eurocode 4 approach is conservative due to:

- use of a linear load-slip shear connector diagram,

- dependency on expected effective width of concrete slab

which usually is not available in bridges.

Concentration of shear connectors above nodes requires

appropriate length to cover proportionally the peaks.

The concentration invokes an increase of shear flow due to

greater stiffness (within the parametric study up to 87 %).

The full parametric study is aimed to refine the Eurocode formulas.

METNET Aarhus 2011

27

Prague - River Vltava

Czech Republic

Thanks for

attention

METNET Aarhus 2011

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