Load-Consistent Effective Width for the Analysis of Composite Steel-Concrete Bridge Decks S.Carbonari (1) , L.Dezi (1) , F.Gara (1) , G.Leoni (2) (1) D.A.C.S., Università Politecnica delle Marche, Ancona, Italy (2) Dip. ProCAm, Università di Camerino, Ascoli Piceno, Italy closely spaced beams and cantilivered cross beams widely spaced beams 13.5 m 3.0 3.0 19.5 m 26.5 m 12.5 m var. 2.9 - 5.5 Viaducts in Mestre - Venice, Italy Serra Cazzola Viaduct - Sicily, Italy Typical composite bridge decks
Transcript
Load-Consistent Effective Width for the Analysis of Composite Steel-Concrete Bridge Decks
S.Carbonari(1), L.Dezi(1), F.Gara(1), G.Leoni(2)
(1) D.A.C.S., Università Politecnica delle Marche, Ancona, Italy
(2) Dip. ProCAm, Università di Camerino, Ascoli Piceno, Italy
closely spaced beams and cantilivered cross beams
widely spaced beams
13.5 m3.0 3.0
19.5 m
26.5 m
12.5 mvar.
2.
9 -
5.5
Viaducts in Mestre - Venice, Italy
Serra Cazzola Viaduct - Sicily, Italy
Typical composite bridge decks
- Analyses with plane (or solid) finite elements provide very accurate solutions
- The results are not synthetic and have to be post-processed
Analyses with shell finite elements
Refined analyses
0 L/4 L/2 3L/4 L0
Beam 1
Beam 2
2B
0
0
0
00
0
00
11
1
1
1
2
22
3
33
44
4
55
5
66
6
77
7
88
8
99
1010
p 125 KN/m, cs UDL + sh
Refined analyses
Analyses with suitable beam finite elements
- Analyses with one-dimensional (beam) finite elements provide accurate synthetic solutions
- Such elements are not included in the library of commercial computer programs
EC4-1Effective width method
Regular design
• Although not specified, the effective widths proposed are valid only for external vertical loads.
• For other kinds of actions (e.g., concrete shrinkage, thermal action and prestressing), no specific suggestions are given. This may induce some designers to believe that the effective slab width depends on the deck geometry and to use wrong formulas. In some cases, this may lead to non conservative results as for prestressing actions (Dezi et al. 2006 – J. Struct .Engrg. ASCE)
simplified method for the verification of twin-girder and single-box girder steel-concrete composite decks based on the definition of new effective widths consistently with the load case (uniformly distributed loads, traffic loads, support settlements and shrinkage).
In this paper
Parametrical analysis
Effective width formulas
Validation of the method
Parametrical analysis
Effective width formulas
Validation of the method
Three parabolic branches
This allows the description of the warping for any spacing of the beams
One-dimensional model (beam model)
The Newmark’s model (composite beam with flexible shear connection) was modified by introducing a warping of the slab that varies along the deck proportionally to a shear-lag function
warping function
Behaviour of materials
Steel
linear elasticSlab reinforcement
Shear connectionPrestressing cable
Concrete linear visco-elastic
Analytical model
Parametrical analysis
v2 v1 1 2
wc1
ws1
wc3
ws3
wc2
ws2 w1, f1 w3, f3w2, f2
½ Le ½ Le
v1
v2 1
2
Le * * *
f2 f1 f3
13 dof Longitudinal displacements
and SL function
Vertical displacement
One-dimensional finite element (Dezi et al. 2005)
The model used permits calculating the variation in time of displacements, stress resultants, and stress distribution in the concrete slab and in the steel beam, and is particularly straightforward in the calculation of the effective slab width.
Analytical model
Parametrical analysis
73500 73500
15
1300
80
60
240
0
1000
6000 9000
21000
6000
220 Es 210000 MPa Ec 32490 MPa = 0.15 12 kN/mm2
50 f.e.405 dof 5800 dof
Analytical model - validation
Parametrical analysis
The model was validated by refined finite element analyses performed by using shell elements.
6.0
3.0
0.0
9.0
c [MPa]
3.0
0.0
3.0
0.0
.0
0.0
6.0
1
2
3
4
73500
p 125 KN/m
1 2 3 4
Analytical model - validation
Parametrical analysis
c [MPa]
5 0.0
-4.0
-6.0
-8.0
-2.0
4 0.0
-4.0
-6.0
-8.0
-2.0
3 0.0
2.0
2 0.0
2.0
1 0.0
2.0
54390
Ftot 42000 KN
1 2 3 5
19110 4
UDL Longitudinal forces
Continuous beams
Simply supported and fixed beamsSchemes
Thermal action and concrete shrinkage
Prestressing (internal tendons, external cables, support settlement)
Loads (vertical, longitudinal, udl and concentrated, …)Actions
Steel beam geometry (web height, plate width and thickness)Geometry
Shear connection stiffnessStiffness
Parametrical analysis
Main results
Parametrical analysis
Shear connection stiffness
Reinforcing ratio
Beam flexural stiffness
Creep
Beff /B does NOT DEPEND on
maxc
A z
eff A
daBB c
2B2B1
Beff Beff
Main results
Parametrical analysis
B/L slab width to span length ratio
B1/B beam spacing to slab width ratio
Actions
Forces (vertical, longitudinal, udl and concentrated, …)Thermal action and concrete shrinkage
Slab prestressing (internal cables, external tendons, support settlement)
Beff /B DEPENDS onDeck geometry
maxc
A z
eff A
daBB c
2B2B1
Beff Beff
Parametrical analysis
Effective width formulas
Validation of the method
at internal supports
Beff
2B2B1
Beff
8
2
276
15
2
143
22
2
21
22 E
L
LEE
B
BE
B
BEE
L
BE
L
BE
B
BB
tottottot
,eff,eff
Beff,2
5
14
2
132
01
00 C
B
BC
B
BCC
L
BC
B
BB ,eff
,eff
at lateral supports
Beff,0
5
14
2
132
11
11 D
B
BD
B
BDD
L
BD
B
BB ,eff
,eff
at spans Beff,1
The formulas are obtained by linear and second order polynomial regressions by performing the least squares fit of data obtained from the parametrical analysis.
1. Calculation of the stress resultants for each load case by considering the real geometry of the deck
2. Definition of the effective widths for each load case
3. Calculation of the stress state for each load case(cross sectional analysis)
4. Superposition of the results
Method of analysis
Effective width formulas
Parametrical analysis
Effective width formulas
Validation of the method
Validation of the method
1300
120
1000
6000 9000
2B21000
6000
220
15
120
2800
Cross section
Actions Uniformly distributed loads (udl)
Traffic loads envelope
Thermal action on the slab
Support settlement
Comparisonsanalytical model proposed method
EC4
200 kN 200 kN
200 kN q1a
q1b 30 kN/m 30 kN/m
6.0 1.5 6.0 1.5
15.0
Italian Code of Practice
40 m 100 m 80 m 80 manalytical model proposed method
EC4 envelope EC4 zero bending moment method
Bef
f/B
c[M
Pa]
The proposed method gives a good approximation of Beff at span and at support sections
EC4 overestimates Beff at span section and especially at internal supports
The proposed method gives a very good approximation of the slab stresses all along the deck axis
EC4 underestimates the slab stresses especially at internal supports
0.5
1
2
2
Uniformly distributed load
Validation of the method
40 m 100 m80 m 80 m
0.5
1
2
2
Bef
f/B
c[M
Pa]
analytical model proposed method
EC4
The discrepancies between Beff of the proposed method and the EC4 method are larger
EC4 overestimates Beff at span sections and especially at internal supports
Proposed method gives a very good approximation of the slab stresses all along the deck axis
EC4 underestimates the slab stresses by about 10% at spans 25% at internal supports
Traffic load
Validation of the method
Support settlement
Validation of the method
2
2
0.5
1
40 m
100 m80 m 80 m
Bef
f/B
c[M
Pa]
The proposed method gives a good approximation of Beff all along the deck
EC4 overestimates Beff at internal supports
The proposed method gives a very good approximation of the slab stresses all along the deck axis
EC4 applied by considering the effective length calculated as the distance between points of zero bending moment gives good results
analytical model proposed method
EC4 zero bending moment method
Uniform thermal action
Validation of the method
2
2
0.5
1
40 m
T = -10°C
60 m 60 m 40 m60 m
Bef
f/B
c[M
Pa]
analytical model proposed method
The proposed method gives a good approximation of Beff and of the slab maximum stresses all along the slab
1300
var.
1000
6000 9000
2B21000
6000
220
var.
var.
var.
2,4
0
2,4
0
3,5
0
47,25 47,25 47,25 47,25
56,7094,5068,0449,14
269,38
0,500,50
2,4
0
2,4
0
3,5
0
C1 P2 P3 P4 C5
Twin girder composite deck
Slab width = 21 m
Four span continuous deck
Refined analysis performed by using shell finite elements
steel girders with variable depth
Max span length = 94.50 m
Pont sur la Nive - France
Application to a real case
UDL – self weight
Application to a real case
0.5
1
8
8
49.14 68.04 56.70 94.50
250 kN/m B
eff/
B c
[MP
a] The proposed method furnishes better estimation of the stresses at hogging regions than EC4
The proposed method gives Beff
smaller than those given by EC4 method
proposed method
EC4 FEM shell eleme
Traffic loads
Application to a real case
0.5
1
1.5
1.5
49.14 68.04 56.70 94.50
Traffic load - NTI
Bef
f/B
c[M
Pa]
The proposed method gives Beff
considerably smaller than those given by EC4 method
The proposed method furnishes better estimation of the stresses both at sagging and hogging regions than EC4
proposed method
EC4 FEM shell eleme
• A method for the evaluation of the stress state in slabs of steel-concrete composite decks at SLS and Elastic ULS has been proposed.
• The method is based on new effective widths depending on the loading conditions.
• The method, tested with refined shell finite element models, gives a good approximation for various loading conditions, i.e. uniformly distributed load, traffic load, support settlement, concrete shrinkage and uniform thermal action.
Conclusions
Load-Consistent Effective Width for the Analysis of Composite Steel-Concrete Bridge Decks
S.Carbonari(1), L.Dezi(1), F.Gara(1), G.Leoni(2)
(1) D.A.C.S., Università Politecnica delle Marche, Ancona, Italy
(2) Dip. ProCAm, Università di Camerino, Ascoli Piceno, Italy
