Third International Bridge Seminar
A “VIERENDEEL” GRILLAGE FOR
COMPOSITE PRESTRESSED
CONCRETE SLAB IN STAGED
CONSTRUCTION ANALYSIS
SERGIO SAIZ GARCÍA, IngZERO.
ANA IRENE LOREA ARNAL, IngZERO.
TBS Vierendeel grillage
Modeling a prestressed concrete slab into Midas Civil
Modeling needs:
• Composite action
• Out-of-plane and in-plane behaviour
• Prestressing Tendons
• Construction Stages Analysis
• Time dependent effects
3 Different approaches:
• 2D Plate elements + Virtual embebed elements
• Stringer+Pannels
• Isotropic Grillage (Typical bridge approach)
TBS Vierendeel grillage
2D Plate elements + Virtual embebed elements
Problems:
Interaction between virtual and plate stiffnesses
Virtual elements with nominal stiffness -> local deformations due to prestress
-> convergence issues in time analysis
C.J. Hoogenboom “Design of Structural Concrete walls”
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Stringer+Pannels
Aircraft industry Concrete walls models
Arrangement of two way beams + shear pannels
Advantadges:
Easy modeling
Well suited for concrete reinforcement
Disadvantadges:
Shear pannels not pressent in Civil
Need for nominal flexural stiffness
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Isotropic Grillage + “Vierendeel” in-plane behaviour
Out-of-plane work -> typical bridge analysis
In-plane work -> modeled by axial response and “Vierendeel” type distortion
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Verification- Pure shear load plate model v.s. Vierendeel model
Easy way in Civil -> section stiffness scale factor
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Verification- Pure shear load plate model v.s. Vierendeel model
2D Plate Vierendeel grillage
Displacements
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Construction Stage Analysis- Time dependent effects
Verification- Pure shear load plate model v.s. Vierendeel model
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H= total width of the deck n =number of divisions D=H/n u = Poisson’s ratio
Fictious beams inertia is about (1+n) more flexible
Impact of fictious in-plane inertias on global slab stiffness
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Comparison between Iz real and Iz model
Ratio Imod/Ireal v.s. nº divisions
Less than 10% error above 5 divisions
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The Arches
-Total lenght 80m (62+18) - Ab.deck 3.90m -U.deck 3.10m -> Slenderness =L/16
-Materials: Arch Stainless Steel 1.4462 + Steel S355J2G3 +Concrete HRC70
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The composite prestressed deck
-Total width 22.40+5.00m
-Thickness of the slab 0.22m
-Depth of the beam 1.20m
-Max. depth of the maingirders 1.30m
-Materials: Steel S-355 J2G3 Concrete HP-50
Steel beam
Elastic links (conection)
Vierendeel grillage (concrete slab)
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Construction Stage (I)
-Erection initial parts near abutment
-Temporary support (prop)
-Inner cast of the arch
-Crane erection arch+hangers+main girder
-Welding of joints
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Construction Stage (II)
-First group of transversal beams
-Dismantling of temporary support
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Construction Stage (III)
-Position of last transversal beams
-Filling up the arches
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Construction Stage (IV)
-Casting of the slab deck
-Pretension of the deck
-Positioning of steel ribs of the sidewalk
Evolution of Axial Loads During Construction
After pouring the concrete of the deck
Concrete + main girder
Stainless steel
Carbon steel
9498 kN
-2831 kN
-4584.kN
-3154 kN
N arch= - 10570 kN
Evolution of Axial Loads During Construction
After prestressing the deck
Concrete + main girder
Stainless steel
Carbon steel
2867 kN
-3134 kN
-4649 kN
-3385 kN
N arch= - 11169 kN
Evolution of Axial Loads During Construction
Force redistribution 10000days
Concrete+ main girder
Stainless steel
Carbon steel
-1273 kN
-5733 kN
-6118 kN
-4561 kN
N arch= - 16414 kN
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Lateral Introduction of Tension Load in the Slab
Plan of the deck “Vierendeel” grillage