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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
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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
member representing concrete slab
steelflange
e = 143
member representing steel chordexcentrical to nodes
305
concreteslab
member representing concrete slab
steelflange
concreteslab
member representing concrete slab
steelflange
member representing steel chordin compression chord axis
DD
e = 0
D
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(only steel part shown)
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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
Stud dia D106.06 - length 305 mm
Stud dia D109.64 - length 305 mm
Stud dia D113.14 - length 305 mm
14
Elastic 2D approximation of shear connection
Simplified linear approach (frame software) shear
forc
e [
N]
slip d [mm]
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-10000
10000
30000
50000
70000
90000
110000
0 5000 10000 15000 20000 25000 30000
Distance from support [mm]
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
Distance from support [mm]
Shear
forc
e p
er
connecto
r
[N]
D097.58
D106.06
D109.64
D113.14
distance from support [mm]
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
]
Distance from support [mm]
EN 1994 (trapezoidal: non-ductile connectors)
EN 1994 (rectangular: stud connectors)
Auxiliary technical calculation
FEM-ANSYS
FEM-SCIA (D109.64)
distance from support [mm]
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
D2 4 studs per e = 100 mm, d = D/6
D3 4 studs per e = 100 mm, d = D/8
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Example: concentration D1
-20000
0
20000
40000
60000
80000
100000
120000
140000
0 5000 10000 15000 20000 25000 30000
Distance from support [mm]
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
]
distance from support [mm]
basic arrangement: 4/400
concentration D1
as basic (4/400) due to increased local rigidity:
Increased shear: D1 71 %
D2 79 %
D3 87 %
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3.2 Road bridges without gusset plates
20 METNET Aarhus 2011
all steel members are only flats
21 METNET Aarhus 2011
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
22 METNET Aarhus 2011
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]
Distance from support [mm]
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
distance from support [mm]
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]
Distance from support [mm]
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
distance from support [mm]
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.
23 METNET Aarhus 2011
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
]
Distance from support [mm]
EN 1994 (trapezoidal: non-ductile connectors)
EN 1994 (rectangular: stud connectors)
Auxiliary technical calculation
FEM
less stiff shear connection:
T2
sh
ear
flo
w [
N/m
m]
distance from support [mm]
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
]
Distance from support [mm]
EN 1994 (trapezoidal: non-ductile connectors)
EN 1994 (rectangular: stud connectors)
Auxiliary technical calculation
FEM
stiffer shear connection
T1
sh
ea
r fl
ow
[N
/mm
]
distance from support [mm]
Eurocode
FEM analysis
non-ductile
ductile (studs)
24 METNET Aarhus 2011
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
]
distance from support [mm]
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
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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.
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Prague - River Vltava
Czech Republic
Thanks for
attention
METNET Aarhus 2011