A “VIERENDEEL” GRILLAGE FOR - Ingzero

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)


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”


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


Isotropic Grillage + “Vierendeel” in-plane behaviour

Out-of-plane work -> typical bridge analysis

In-plane work -> modeled by axial response and “Vierendeel” type distortion

Theoretical Model


Verification- Pure shear load plate model v.s. Vierendeel model



Easy way in Civil -> section stiffness scale factor



2D Plate Vierendeel grillage

Displacements


Shear flow


Construction Stage Analysis- Time dependent effects


model


Construction Stage Analysis- Deflections (first step)

model


Construction Stage Analysis- Deflections (last step)


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


Comparison between Iz real and Iz model

Ratio Imod/Ireal v.s. nº divisions

Less than 10% error above 5 divisions


One application:

Quinto Puente in San Sebastián


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


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)

Prestressed Concrete Deck

Family 1 (5+8) x 12 ud 16mm

Family 2 28 x 9 ud 16mm


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


Construction Stage (II)

-First group of transversal beams

-Dismantling of temporary support


Construction Stage (III)

-Position of last transversal beams

-Filling up the arches


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


After prestressing the deck

Concrete + main girder

Stainless steel

Carbon steel

2867 kN

-3134 kN

-4649 kN

-3385 kN

N arch= - 11169 kN


Force redistribution 10000days

Concrete+ main girder

Stainless steel

Carbon steel

-1273 kN

-5733 kN

-6118 kN

-4561 kN

N arch= - 16414 kN


Lateral Introduction of Tension Load in the Slab

Plan of the deck “Vierendeel” grillage


Lateral Introduction of Tension Load in the Slab

Evolution in time of shear flow between main girders and slab

Permanent loads (to) Permanent loads (too)

Documents

A “VIERENDEEL” GRILLAGE FOR - Ingzero