Date post: | 03-Jun-2018 |
Category: |
Documents |
Upload: | cesar-alexis |
View: | 222 times |
Download: | 0 times |
of 28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
1/28
1
Composite bridge design (EN1994-2)
Bridge modelling and structural analysis
Laurence DAVAINE
French Railwa s SNCF
Bridge Engineering Department (IGOA)
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
2/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
3/28
Dissemination of information for training Vienna, 4-6 October 2010 3
Twin-girder bridge modelling
C3
G P2
P1xy
simply supported bar model (dz=0 for every support)
half-bridge cross-section represented by its centre of gravity G
(neutral fibre)
C0
structural steel alone, or composite, mechanical properties
according to the construct ion phases of the bridge slab
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
4/28
Dissemination of information for training Vienna, 4-6 October 2010 4
Concrete slab thickness
Actual slab Computed slab
Sactual = Scomputed (same area)
actual = computed (same location of the slab gravity centre Gc)
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
5/28
Dissemination of information for training Vienna, 4-6 October 2010 5
Shear lag in the concrete slab according to EN 1994-2
effb
,maxxx
xx Non-uniform transversedistribution of the
longitudinal stresses
750 mmb
1 1eb
2 2eb
13.125 mb
22.125 mb 0b
0eff i ei
i
b b b
min ;8
e
ei i
Lb b
0.55 0.025 1.0e
i
ei
L
b
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
6/28
Dissemination of information for training Vienna, 4-6 October 2010 6
Shear lag in the concrete slab according to EN 1994-2
Equivalent span length Le
Global analysis (calculation of internal forces and moments) : constant
along each span (equal to the value at mid-span)
Section analysis (calculation of stresses) : linearly variable along Li/4
surrounding the internal supports
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
7/28
Dissemination of information for training Vienna, 4-6 October 2010 7
Application to the twin-girder bridge example
C0 P1 C3P2
60 m 80 m 60 m
L m 0.85x60 = 51 0.7x80 = 56 0.85x60 = 510.25 x (60+80) = 35 0.25 x (60+80) = 35
e e e 1 2 e
In-span 1 and 3 48 3.125 2.125 1 1 6.0
In-span 2 56 3.125 2.125 1 1 6.0
. . .
End supports C0 and C3 48 3.125 2.125 0.958 1.15 but < 1.0 5.869 < 6.0
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
8/28
Dissemination of information for training Vienna, 4-6 October 2010 8
Application to the twin-girder bridge example
P1 P2 C3C0
2
0
11 12
L2/4L2/4L1/4L1/4 L1/4 L1/4
-2
-1
-3
-4
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
9/28
Dissemination of information for training Vienna, 4-6 October 2010 9
Composite cross-sections mechanical properties
effb
Un-cracked behaviour (mid-span regions, Mc,Ed > 0)
caA A
n
A elastic
neutral axis
c
GGy
Gcy
e n orcemen neg ec e n compress on
cG a Ga Gc
AAy A y
ny
22 1( )a a G Ga c c G GcI I A y y I A y
n
y
aG
Gay
Cracked behaviour (support regions, Mc,Ed < 0)
effb
Ea = Es = 210 000 N/mm (n = 1)
elasticneutral axis
s
GGsy a sA A A G a Ga s GsAy A y A y
a
GayGy ( )a a G Ga s s G GsI I A y y I A y y
0sI
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
10/28
Dissemination of information for training Vienna, 4-6 October 2010 10
Modular ratios (creep effect)
a
0
cm
En
EShort-term modular ratio:
0.3
cm
cm
fE 22000
10
L 0 L tn n . 1
t 0t t
ong- erm mo u ar ra o:
Creep coefficient according to EN 1992-1-1 with :
t = age of concrete at the considered time during the bridge life
t0 = age of concrete when the considered loading is applied to the bridge
t0 = 1 day for shrinkage
t0 = mean value of age of concrete segments, in case of composites structurescast in several sta es ermanent load
L depends on theload case :
Permanent loads 1.1
Imposed deformations 1.5
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
11/28
Dissemination of information for training Vienna, 4-6 October 2010 11
Creep coefficient according to Annex B in EN 1992-1-1
000
0.3
t 0 c 0 0
H
t
t. t .
t
tt
t
(end of bridge life)
18H 0 3 31.5. 1 0.012 RH .h 250. 1500.
00
0 RH cm 1 2 0.2
3 0 cm
RH1
16.8 1100. f . 1 . . . .
0.11 tf
t
0 . 0 h
with : RH = 80 % (relative humidity in the bridge area)
c0h
u notional size (u is the concrete slab
perimeter exposed to drying)
0.7
1
cm
350.8658
f
0.2
2cm
350.9597
f
0.5
3
cm
350.9022
f
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
12/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
13/28
Dissemination of information for training Vienna, 4-6 October 2010 13
Application to the twin-girder bridge example
Short-term modular ratio
aE
Long-term modular ratio
0cm
.E
Load case L t0 (days) t = 0 nL
Concrete slab segment (selfweight)
Settlement
Shrinka e
1.10
1.50
0.55
35.25
49.25
1
1.394
1.291
2.677
15.61
18.09
15.24
Bridge equipments 1.10 79.25 1.179 14.15
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
14/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
15/28
Dissemination of information for training Vienna, 4-6 October 2010 15
Application to the traffic load model LM1
1. Conventional traffic lanes positioning
0.5 m1 m
3 m3 m 3 m 2 m
. . .
Bridge axle
girder no. 2Girder no.1
(modeled)3.5 m 3.5 m
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
16/28
Dissemination of information for training Vienna, 4-6 October 2010 16
Application to the traffic load model LM1
2. Tandem TS
Bridge axle
TS 1 per axle :
=
TS 2 per axle :
1.0 x 200 = 200 kNTS 3 per axle :
1
.1.0 x 100 = 100 kN
0
Influence line of the
support reaction on
girder no. 1
0.5 m 1 m 2 m
Support reaction on each main girder : R1 = 471.4 kN
R2 = 128.6 kN
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
17/28
Dissemination of information for training Vienna, 4-6 October 2010 17
Application to the traffic load model LM1
3. Uniform Design Load UDL
Bridge axle
Load on lane no.1 :1.0 x 9 x 3 = 27 kN/ml
Load on lane no.2 :1.0 x 2.5 x 3 = 7.5 kN/ml
1
Load on lane no.3 :
1.0 x 2.5 x 3 = 7.5 kN/ml
LANE 1
LANE 2 LANE 3
R1
0Influence Line
R2
0.5 m 1 m 2 m
Support reaction for each main girder : R1 = 35.36 kN/ml
R2 = 6.64 kN/ml
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
18/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
19/28
Dissemination of information for training Vienna, 4-6 October 2010 19
Contents
1. Bridge modelling
Geometry
Effective width (shear lag effect) Cross-sectional
Transversal distribution
mechanical properties
2. The global cracked analysis according to EN 1994-2
Results from the global analysis
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
20/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
21/28
Dissemination of information for training Vienna, 4-6 October 2010 21
1Global cracked analysis
Stress distribution c in the concrete slab for the characteristic SLScombination of actions assuming the concrete resists in every cross
1
In the zones where c < - 2 fctm , the concrete is assumed to be cracked(and then neglected) for the bending stiffness distribution (EI2)
EI1
EI2
EI1= un-cracked composite second moment of area
+
EI2= cracked composite second moment of area
(structural steel + reinforcement in tension)
This approach is not iterative (the cracked zones are
determined only once).!
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
22/28
Dissemination of information for training Vienna, 4-6 October 2010 22
Global cracked analysis 1
Simplified method is possible if :
- no re-stress
EI2
0.15 (L1+ L2)
- Lmin/Lmax > 0.6
s
EI1
L1 L2
Ac = 0
concrete in tension is neglected
reinforcement are included
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
23/28
Dissemination of information for training Vienna, 4-6 October 2010 23
In-span steel yielding 2
Mid-span eventual yielding is taken into account if : Class 1 or 2 at mid span (and MEd > Mel,Rd )
Lmin/Lmax < 0.6
max min
Class 1 or 2 Class 3 or 4
As Lmin/Lmax > 0.6 in the example, the redistribution due toyielding near mid-span is not taken into account.
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
24/28
Dissemination of information for training Vienna, 4-6 October 2010 24
Application to the twin-girder bridge example
1 2 3 16 15 14 4 5 6 7 13 12 11 10 9 8
Concreting phases, Slab segments order:
5
N/mm)
ination
0
0 20 40 60 80 100 120 140 160 180 200
ncreteslab
icS
LScomb
-10
-5
2
ctm2f 6.4 N/mm
tressesinc
Characterist
-15
x = 35.0 m x = 76.0 m x = 124.0 m x = 152.0 m
Cracked zone for P1
41.0 % 19.5 %
Cracked zone for P2
19.5 % 20.0 %
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
25/28
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
26/28
Dissemination of information for training Vienna, 4-6 October 2010 26
Application to the twin-girder bridge example
SLS and ULS shear force distribution VEd
10
6.02 5.98
.
4.83
.
6
8 Characteristic SLS
Fundamental ULS
2.78
2
4
es(MN)
-1.90-2
0
0 20 40 60 80 100 120 140 160 180 200
Shearforc
-6.04
-5.74
-6
-4
-8.14-8.01
-10
-
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
27/28
Dissemination of information for training Vienna, 4-6 October 2010 27
Application to the twin-girder bridge example
400
ULS stresses (N/mm) along the steel flanges, calculated without concrete resistance
272.6277.5
200
300
100
-100
0
0 20 40 60 80 100 120 140 160 180 200
-287.1-300
-200
- .
-400
8/12/2019 2010 Bridges AnalysisandModelling LDavaine
28/28
Dissemination of information for training Vienna, 4-6 October 2010 28
Thank you for your kind attention !