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Example of a beam grillage calculation according to different methods - Part 1

Example of a beam grillage calculation according to different methods 

Comparison of the results - multi-criteria analysis

Editor : Didier GUTH - Arcadis - June 14th, 2020

1) Introduction

1.1 Objectives

In this document, we will model the same multi-beam deck using several approaches:

  • the Guyon-Massonnet method,

  • a plane grid approach,

  • a 3D grillage (modeled as a ladder beam)

  • a 3D model associating bars and shells, with two approaches. 

We will compare:

  • Support reactions,

  • Efforts, moments and shear.

In addition, we will perform two transverse bending calculations to highlight the differences and limitations of the methods.

We will test the incidence of a moderate skew (70 degrees), a more consequent skew (50 degrees) and the presence of cross girders.

A table, by way of conclusion, will attempt to give the reader some clues as to the advantages and disadvantages of each of the models.

The dimensions and applied loads are plausible for a structure deemed to be made of reinforced concrete.

We insist on the fact that each work is particular and that we find ourselves, in the context of this example, in a given configuration of flexural and torsional rigidity, and that consequently the conclusions cannot be generalized as such.

1.2 Bibliography

We invite the reader to refer to the following references:

[1] - Guide technique CHAMOA P CHaîne Algorithmique Modulaire Ouvrages d’Art – Apendix http://www.setra.fr/html/logicielsOA/Ponts_Types/CHAMOA-P/chamoa-p.html 

[2] - Guide pour l’utilisation des programmes de réseaux de poutres - PRP 75 - SETRA -1975

[3] - Compléments à la méthode de calcul des ponts à poutres multiples - C. Massonnet – ITBTP annals - January 1962

[4] - Le calcul des grillages de poutres et dalles orthotropes selon la méthode Guyon-MassonnetBarès - R. Barès et C. Massonnet - Dunod – 1966

[5] - Calcul des ponts à poutres multiples solidarisées par des entretoises – J. Courbon - Annales des ponts et chaussées - November-December 1941

[6] - Méthode de calcul des ponts nervurés sans entretoise intermédiaire – ITBTP annals – July-August 1970

[7] - Nouvelle formulation analytique de la flexion transversale d'une dalle orthotrope - A.L. Millan - Construction Métallique n°2 – 2004

[8] - Méthode de Guyon Massonnet Barès appliquée aux ouvrages à poutres d'inertie distincte - G. Bondonet et P. Corfdir - Revue Européenne de Génie Civil - Volume 9, n°9-10 – 2005

[9] – Calcul analytique de flexion des ponts à poutres de géométrie quelconque, calage des inerties de torsion transversale par comparaison à des calculs aux éléments finis – P. Perrin et G. Bondonet – Bulletin Ouvrages d’Art - n°71 – 2015

[10]- Emploi des éléments finis en génie civil (Tome 1) : La modélisation des ouvrages – sous la direction de Michel Prat

[11] - Contribution à l’étude des grillages de poutres – Pierre Perrin – Dir Est – sur le wiki de l’AFGC [https://wiki-gtef.frama.wiki/accueil-gtef:partie-3:exemple-c]

[12] - Flexion transversale d'un pont multipoutre – Benjamin Tritschler – Arcadis - – sur le wiki de l’AFGC [https://wiki-gtef.frama.wiki/accueil-gtef:partie-3:exemple-c]

[13] Guide pour l’évaluation structurale et la réparation des Viaducs à travées Indépendantes à Poutres Préfabriquées précontraintes par post-tension (VIPP) – CEREMA – (à paraître)

[14] Dossier PRAD 73 – SETRA

[15] Dossier VIPP 67 – SETRA

1.3 Possible complements 

To complete the study, in a non-exhaustive way, in the end we could add:

  • Modeling with 3D elements (see reference [11])

  • The study of a longitudinal and/or transverse phasing, taking into account the creep shrinkage, either as at a fixed rate or by using a calculation with behavioral laws,

  • A study using an improved "Guyon Massonnet" approach

  • Tests to find the optimal width of the cross bands

  • How to take into account geometric or material non-linearities,

And extend the study to cases of structures with flexible connections.

2) Description of the structure and loads 

2.1 Geometry

 It includes:

  • Eleven ribs of 40 cm x 100 cm ht, spaced at 0.90 m intervals.

  • Two 25 m spans,

  • A 25 cm thick hollow-core element,

It is made of C35 concrete, E=36000 MPa, ν=0.2 and rests on simple supports.

2.1 Studied load cases

The applied loads are:

  • Self-weight:

  • A fictitious superstructure load of 3.00 kN/m² on the entire surface of the hollow-core element and 5 kN/ml on the edges at the end of the cantilever:

  • Multiple operating loads

    • A linear load of 9 kN/m in span 1, on beams 1 to 3:

  • A linear load of 9 kN/m in span 1+2, on beams 1 to 3:

  • A distributed load from the abscissa 10.00 to 11.25 m, astride beams 6 and 7

(will be used for the transverse bending study)

  • A point load on the abscissa 1.25 m from an abutment on beam n°4:

(will be used to study support reactions)

  • A linear load of 100 kN/ml at the edge of the deck:

(will be used for the transverse bending study)

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