Inelastic spatial stability of circular wide flange steel arches

109 Pages·2017·56.97 MB·English

Inelastic spatial stability of circular wide flange steel arches
Citation for published version (APA):
La Poutre, D. (2005). Inelastic spatial stability of circular wide flange steel arches. [Phd Thesis 1 (Research TU/e
/ Graduation TU/e), Built Environment]. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR585818
DOI:
10.6100/IR585818
Document status and date:
Published: 01/01/2005
Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be
important differences between the submitted version and the official published version of record. People
interested in the research are advised to contact the author for the final version of the publication, or visit the
DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page
numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
• You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please
follow below link for the End User Agreement:
www.tue.nl/taverne
Take down policy
If you believe that this document breaches copyright please contact us at:
[email protected]
providing details and we will investigate your claim.
Download date: 30. Jan. 2023
Inelastic spatial stability of circular wide flange
steel arches
Inelastic spatial stability of circular wide
flange steel arches
Dagowin Ia Poutre
Inelastic spatial stability of circular wide
flange steel arches
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
Rector Magnificus, prof.dr. R.A. van Santen, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op donderdag 27 januari 2005 om 16.00 uur
CIP-DATA
Dagowin Ia Poutre
Inelastic spatial stability of circular wide flange steel arches
ISBN 90-9018930-0
Subject headings: steel structures-stability I experimental research I structural
mechanics I finite element analysis
door
Trefwoorden: staalconstructies -stabiliteit I experimenteel onderzoek I
boogconstructies I constructief ontwerpen I eindige
elementen analyse
NUR: 955
Dagowin Bernolf Ia Poutre
Publisher: D.B. Ia Poutre (contact [email protected])
Illustration on the cover: overhead wire support of Brenner Railway, Austria.
geboren te Rotterdam
Cover design by K. Widmann
© 2005 Dagowin Ia Poutre
All rights reserved. No part of this material protected by this copyrights notice may be reproduced or utilized in any form or by any
means, electronic or mechanical, including photocopying, recording or by any information storage or retrieval system, without
written permission of the author
Dit proefschrift is goedgekeurd door de promotoren: Samenstelling promotiecommissie:
Rector Magnificus voorzitter
prof.ir. H.H. Snijder Prof.ir. H.H. Snijder Technische Universiteit Eindhoven
en
Prof. Dipl.-lng. Dr.techn. R. Greiner Technische UniversiUit Graz
prof.Dr.Dipl.-lng. R. Greiner
Dr.ir. J.C.D. Hoenderkamp Technische Universiteit Eindhoven
Copromotor:
Dr.ir. M.C.M. Bakker Technische Universiteit Eindhoven
dr.ir. J.C.D. Hoenderkamp
Prof.ir. F.S.K. Bijlaard Technische Universiteit Delft
Prof.dr.ir. J.G.M. Kerstens Technische Universiteit Eindhoven
Prof.dr.ir. J. Blaauwendraad Technische Universiteit Delft
Prof.dr. R. Maquoi Universite de Liege
Acknowledgements Table of contents
First of all, I would like to express my gratitude to Prof. Bert Snijder and Dr. Summary .......................................................................................... v
Hans Hoenderkamp for initiating this project and guiding it to successful Samenvatting ..................................................................................v i
completion. Their advice during the research and comments on the thesis were Kurzfassung ..................................................................................... vii
Glossary of terms ............................................................................. ix
invaluable. Secondly, I wish to acknowledge the guidance and the valuable
Notations ......................................................................................... x
contributions made by Prof. Richard Greiner at the TU Graz in Austria.
Abbreviations .................................................................................. xi
Furthermore, I would like to thank Dr. Monique Bakker and Prof. Frans Bijlaard
(TU Delft) for their contributions to the completion of the thesis.
Thanks are due to the Department of Structural Design of the Technische INTRODUCTION .............................................................. 1
Universiteit Eindhoven for the extensive facilities offered to carry out the
1.1 Arches .................................................................. 1
research. Experiments formed a large part of this work and it goes without
1 .1. 1 Classification of arches ................................................. 2
saying that I could not have completed them without the help of the laboratory
1.1.2 Bridges ......................................................................... 5
staff. In particular, the efforts of Thea van de Loo, Martien Ceelen and Eric Wijen
1.1.3 Buildings and other structures ........................................ 9
are greatly appreciated. I also would like to thank the student assistants Eelco
1 .2 Stability .............................................................. 12
Aartsma and Jaap Boon for carrying out the tensile tests and residual stress
1.2.1 Phenomena ................................................................ 12
measurements respectively.
1.2.2 Analyses ..................................................................... 14
Furthermore, I would like to thank all colleagues of the Department of
1.2.3 Design process ........................................................... 14
Structural Design for the pleasant working atmosphere during the past five
1 .3 Problem statement and objective ........................ 1 6
years. In particular, I would like to thank the research assistants Guillermo
1 .4 Research Approach ............................................ 1 6
Gonzalez, Steffen Zimmermann and Bright Ng'andu with whom I shared an
office. Our discussions both on and off the topic were helpful and motivating, 1 .5 Outline of thesis .................................................. 1 7
but most often simply hilarious. I would not forget to thank my partner Karin
Widmann for her endurance and support during this project, and for making 2 LITERATURE REVIEW ....................................................... 19
sure that the thesis looked pretty. Finally, I owe a debt of gratitude to many
2.1 Analytical eigenvalue for curved beams .............. 21
people, much too numerous to mention, who have contributed in one way or
2.2 Experimental work ............................................... 22
another.
2.2.1 Glossary of experiments .............................................. 23
Dagowin Ia Poutre 2.2.2 Dimensions of arches and cross sections ..................... 26
2.2.3 Boundary conditions ................................................... 27
Eindhoven, November 2004
2.2.4 Loading ...................................................................... 28
2.2.5 Materials and arch production .................................... 30
2.3 Nonlinear Finite element analyses ....................... 31
2.3.1 Curved beams ............................................................ 31
2.3.2 Arches ........................................................................ 33
STABILITY OF STEEL ARCHES CONTENTS iii
3 EXPERIMENTS ............................................................... 35 4 EFFECTS OF BENDING PROCESS ..................................... 99
3.1 Motivation and objectives .................................. 35 4.1 The bending process ........................................... 99
3.2 Test program ...................................................... 36 4.2 Tensile testing ................................................... 102
3.2.1 Selection of cross section ............................................ 36 4.2.1 Straight members ...................................................... 102
3.2.2 Selection of arches ..................................................... 39 4.2.2 Curved ribs ............................................................... 1 04
3.3 Model tests ........................................................ 41 4.3 Residual stresses ............................................... 106
3.3.1 Production of model sections ...................................... 41 4.3.1 Theoretical analysis ................................................... 1 07
3.3.2 Geometric similarity analysis ....................................... 43 4.3.2 Measuring residual stresses ....................................... 1 08
3.4 Design of test setup ............................................ 45 4.3.3 Discussion of residual stress ....................................... 110
4.4 Cross sectional measurements ........................... 111
3.4.1 Analysis of load case .................................................. 45
3.4.2 Testrig ........................................................................ 47 4.4.1 Dimensions and tolerances ....................................... 112
3.4.3 Load introduction ........................................................ 49 4.4.2 Shape deviations ...................................................... 115
3.4.4 Supports ...................................................................... 53 4.4.3 Section properties ..................................................... 117
3.4.5 Actuator guidance system ........................................... 55
3.4.6 Tilting load .................................................................. 57
5 FINITE ELEMENT ANALYSES ............................................ 121
3.4. 7 Axle for measuring arch radius .................................... 58
3.5 Imperfections and permanent deformations ........ 59 5.1 Modeling the cross section ................................ 1 21
3.5.1 Aligning the test setup ................................................. 59 5.1.1 Approach ................................................................. 1 22
3.5.2 Assembling the arch .................................................... 60 5.1 .2 Analytical section properties ..................................... 122
3.5.3 Influence of imperfections ........................................... 61 5.1 .3 Selection of element type ......................................... 1 24
3.5.4 Imperfections of the arch-rib ....................................... 62 5.1.4 Determining elastic FE-section properties .................. 1 25
3.5.5 Permanent deformations after testing .......................... 67 5.1.5 Results and discussion of modeling cross sections ..... 126
3.5.6 Categories of imperfections and permanent deformations .. 6 7 5.1.6 Final FE-model of cross section .................................. 127
5.1. 7 Plastic FE section properties ...................................... 130
3.6 Testing procedures and measurements ............... 70
5.2 Modeling the arch ............................................ 130
3.6.1 Testing procedures ...................................................... 70
3.6.2 Data acquisition .......................................................... 72 5.2.1 Arch-rib and imperfections ........................................ 130
3.6.3 Controlling the actuator .............................................. 73 5.2.2 Supports ................................................................... 131
3.6.4 Measuring frame ......................................................... 74 5.2.3 Load introduction ..................................................... 132
3.6.5 Correcting nonlinear effects ........................................ 75 5.3 Material modeling and residual stress ................ 133
3.6.6 Rigid body displacement of test setup ......................... 76
5.3.1 Material law .............................................................. 133
3.6.7 Lateral stiffness hinge-block ........................................ 78
5.3.2 Strain rate ................................................................. 1 34
3.6.8 Load ........................................................................... 80
5.3.3 Residual and assembly stress .................................... 135
3.6.9 Strain .......................................................................... 80
5.4 Analyses ........................................................... 13 7
3.6.10 Monitoring the hydrostatic bearing .............................. 82
5.4.1 Calibration ............................................................... 13 7
3. 7 Experimental results ............................................ 8 7
5.4.2 Results ...................................................................... 141
3. 7.1 Load-deformation graphs ............................................ 8 7
3.7.2 Ultimate loads ............................................................. 94
3.7.3 Stiffness ....................................................................... 96
3.8 Discussion of results ............................................ 97
iv STABILITY OF STEEL ARCHES Summary
6 DISCUSSION ON DESIGN METHOD ................................. 143
This thesis is on the inelastic out-of-plane stability of circular steel arches
6.1 Design method applied to arches tested ............ 143 loaded in bending and compression. Currently, for such structures, no design
6.1.1 Eigenvalue analysis ................................................... 144 equations are available in literature and in building standards. The objectives of
6.1.2 Plastic analysis .......................................................... 145 this research are to obtain experimental load-deformation relations, and to cali
6.1.3 Non-dimensional slenderness .................................... 147 brate a finite element model with the experimental data. The calibrated model is
6.1.4 Stability versus plastic strength .................................. 149
needed to be able to perform a parameter study to derive design equations.
6.2 Numerical Reduction factors for arches .............. 149 The experiments were performed on arches with wide flange ribs that were
6.3 Towards buckling curves for arches .................... 152 loaded by a single point load at the crown. A series of 15 tests was performed
in which the developed length of the arches was kept constant, but the sub
tended angle was varied between 90° and 180°. Of these tests, 12 were on full
7 CONCLUSIONS AND RECOMMENDATIONS ..................... 155
scale HEA 10 0-ribs and three on model arches with HEB 600 ribs. In the ex
7.1 Conclusions ...................................................... 1 55
periments, special attention was paid to the boundary conditions: at the crown,
7.2 Recommendations ............................................ 158 the load was introduced at the centroid of the arch-rib without giving any tor
sional support. This was accomplished with a spherical hydrostatic bearing.
REFERENCES ..................................................................... 161 The supports were so designed that they acted as hinges in-plane while they
provided fixity out-of-plane. As the arch deformed out-of-plane, the load tilted
but remained directed at the center of the chord between the supports.
APPENDIX A ...................................................................... 167
A finite element model was developed in a commercially available finite ele
A. 1 Design calculations hydrostatic bearing ............ 16 7 ment program to simulate the experiments. The cross section was composed of
A.2 Imperfections .................................................... 1 70 several shell-elements. Along the developed length, many elements were used.
A.3 Imperfections and permanent deformations ....... 1 72 Beam-elements were included to model the influence of the fillets on the tor
A.3.1 Lateral imperfections and deformations .................... 1 72 sional stiffness. The measured cross sectional dimensions of the specimens in
A.3.2 Radial imperfections and deformations ..................... 1 7 4 addition to their lateral and radial imperfections were used in the finite element
A.3.3 Twist imperfections and deformations ........................ 1 76 model. The actual material relation after bending, which varied over the cross
section, was determined experimentally and modeled in the material law. The
initial stress conditions, governed by residual stresses and assembly stresses,
APPENDIX 8 ...................................................................... 1 79
were determined experimentally and modeled as well.
8.1 Material law ...................................................... 1 79 The finite element model including all the above described features showed
8.2 Dimensions ........................................................ 183 moderate to very good agreement with the experiments. The underestimation in
8.3 Results of FEA .................................................... 184 ultimate load was within 8.3% and the overestimation within 6.1 %. The load
deformation curves of the experiments and simulations display good agreement.
With the calibrated FE-madel, the method of designing an arch with the
CURRICULUM VITAE ........................................................... 1 89
Overall Method of Eurocode 3, which is intended for use on structures under
general loading, was explored. It was found that the buckling curves, available
for columns and beams, are not applicable to the arches under investigation in
this thesis, and new buckling curves should be derived.
vi STABILI1Y OF STEEL ARCHES SUMMARY vii
Samenvatting Method) van Eurocode 3, die bedoeld is voor constructies onder willekeurige
belastingen. Hieruit bleek dat de huidige knikkrommen voor kolommen en bal
ken niet toepasbaar zijn voor de bogen onderzocht in dit proefschrift en dat
Dit proefschrift behandelt de plastische ruimtelijke stabiliteit van cirkelvormige nieuwe knikkrommen afgeleid zouden moeten worden.
stalen bogen belast op buiging en normaalkracht. Voor dit type constructies zijn
op het moment geen toetsingsregels beschikbaar, noch in de literatuur, noch in
Kurzfassung
norm- en regelgeving. De doelstellingen van dit onderzoek zijn het bepalen van
experimentele last-vervormingsdiagrammen en het kalibreren van een eindig
elementenmodel met deze gegevens. Het gekalibreerde model is nodig om een
parameterstudie uit te voeren waaruit een toetsingsregel voor boogconstructies Die vorliegende Arbeit befasst sich mit der Stabilitiit senkrecht zur Tragwerks
kan worden afgeleid. ebene, von Kreisbogen die auf Biegedruck beansprucht werden. Zur Bemessung
De experimenten zijn uitgevoerd op bogen met H-profiel als doorsnede die solcher Tragwerke liegen momentan weder in der Literatur noch in den entspre
werden belast door een puntlast aan de top van de boog. In totaal zijn chenden Normenwerken Bemessungsgleichungen vor. Die Zielsetzung dieser
15 proeven uitgevoerd waarbij de ontwikkelde lengte van de boog constant werd Arbeit ist zweigeteilt. So sollen in Experimenten Last-Verformungsbeziehungen
gehouden, maar de ingesloten hoek tussen goo en 180° werd gevarieerd. Twaalf ermittelt und mit Hilfe der daraus erhaltenen lnformationen ein Finite Elemente
proeven werden gedaan op ware grootte en met een doorsnede HEA 100 en drie Modell kalibriert werden. Das kalibrierte Modell wird benotigt, um Bogentrag
op schaal met een doorsnede HEB 600. Veel aandacht is besteed aan het ant werke hinsichtlich ihres Stabilitatsverhaltens bemessen zu konnen.
werp van de randvoorwaarden: de belasting werd aangebracht aan de top van Die experimentellen Untersuchungen wurden an Breitflansch - Bogentragern
de boog in het zwaartepunt van de doorsnede zonder dat enige torsiesteun werd durchgefOhrt. In einer Serie von 15 Versuchen wurden diese an ihrem Scheitel
verleend. Dit werd mogelijk gemaakt door de toepassing van een hydrostatisch durch eine nichtrichtungstreue Einzellast belastet. Hierbei wurde die abgewickel
bolscharnier. De opleggingen zijn zo ontworpen dat ze in het vlak van de boog te Lange der Bogentrager konstant gehalten, der Kreisausschnittswinkel jedoch
als scharnieren werken maar uit het vlak als inklemmingen. Bij het vervormen uit zwischen goo und 180° variiert. Zwolf der Versuche wurden an HEA 100-
het vlak van de boog veranderde de puntlast van richting met als richtpunt het Tragern im OriginalmaBstab und drei an skalierten HEB 600 Modellbogen
midden van de koorde tussen de opleggingen. durchgefOhrt. Besonderes Augenmerk wurde auf die Randbedingungen gelegt:
In een commercieel beschikbaar computerprogramma is een eindig elemen die auBere Last wurde so aufgebracht, dass einerseits die Wirkungslinie der
tenmodel ontwikkeld ten behoeve van het simuleren van de experimenten. In de einwirkenden Kraft und die Schwerelinie des Bogentragers zusammenfielen und
doorsnede en omtrek zijn schaalelementen gebruikt. Balkelementen zijn aan het andererseits keine Torsionsbehinderung auftreten konnte, was durch die Ver
model toegevoegd om de invloed van de afrondingstralen op de torsiestijfheid te wendung eines hydrostatischen Lagers am Lastangriffspunkt vermieden wurde.
modelleren. De werkelijke zijdelingse en radiale imperfecties en de afmetingen Die Widerlager waren so entworfen, dass der Trager in der Ebene gelenkig und
van de doorsnede, zoals die gemeten zijn in de proefopstelling, zijn gemodel aus der Ebene heraus eingespannt war. Sobald der Bogentrager aus der Trag
leerd. Het werkelijke materiaalgedrag is bepaald met trekproeven en bleek te werksebene ausknickt, kippt die einwirkende Last derart, dass sie nach wie vor
varieren over de doorsnede wat gemodelleerd is in de constitutieve relatie. De auf den Mittelpunkt des zwischen den Widerlagern angeordneten Untergurts
initiele spanningstoestand, bestaand uit rest- en montagespanningen, is experi zeigt.
menteel bepaald en gemodelleerd. Um die durchgefOhrten Versuche simulieren zu konnen, wurde in einem
Het eindige elementenmodel met bovengenoemde eigenschappen gaf goede kommerziell verfugbaren Finite Elemente Programm ein Modell entwickelt. Der
tot zeer goede resultaten in vergelijking met de experimenten. De gesimuleerde Tragerquerschnitt setzte sich aus einer Anzahl von Schalenelementen zusam
bezwijkbelastingen onderschatte de experimentele bezwijkbelastingen met men. Entlang der Tragerachse wurde eine groBe Anzahl von Elementen einge
maximaal 8.3% en overschatte deze met maximaal 6.1 %. Aile experimentele en setzt. Die Auswirkungen der Profilausrundungen auf die Torsionssteifigkeit wur
gesimuleerde last-vervormingsdiagrammen vertoonden een goede gelijkenis. den durch Balkenelemente berucksichtigt. Die seitlichen und radialen lmperfek
Met het gekalibreerde eindige elementenmodel is onderzocht hoe een boog tionen und die Querschnittsabmessungen wurden den tatsachlichen Gegeben
ontworpen zou kunnen worden met behulp van de Algemene Methode (Overall heiten entsprechend modelliert. Nach dem Biegevorgang wurden die Werkstoff-
Glossary of terms
Viii STABILITY OF STEEL ARCHES
beziehungen experimentell ermittelt und im Stoffgesetz beri.icksichtigt. Glei
Arch - plane structure curved in elevation and supported
chermaBen wurden die Spannungsanfangsbedingungen, die im Einzelnen durch
such that no spreading occurs
Eigenspannungen und ungewollte Vorspannung aufgrund von Montagetoleran
Abutment - support at the extreme end of an arch-rib
zen hervorgerufen werden, im Modell beri.icksichtigt.
Curved beam - structure curved in elevation and supported such that
Das Finite Elemente Modell, das aile oben angefi.ihrten Merkmale enthalt,
spreading can occur.
zeigte durchwegs gute bis sehr gute Obereinstimmung mit den Experimenten.
Cross section - section perpendicular to the longitudinal axis of a
Die Simulationen i.iber- beziehungsweise unterschatzten die tatsachliche Trag
beam or the tangential axis of an arch-rib
last maximal urn 6,1% beziehungsweise 8,3%. Aile simulierten Last
Direct stress - stress normal to the plane of the cross section
Verformungskurven stimmten in ihrer Gestalt mit den experimentellen i.iberein.
FE-model - model based on finite element method
Das kalibrierte Finite Elemente Modell wurde eingesetzt, urn zu untersuchen,
FE-program - computer program based on finite element method
ob die in Eurocode 3 fi.ir allgemein beanspruchte Konstruktion vorgeschlagene
Freestanding arch - arch supported only at its ends
Bemessungsmethode moglicherweise auf Bogentragwerke i.ibertragbar ist. Da
Gravity load - also conservative load, load that remains vertical in
bei wurde festgestellt, dass die vorhandenen Knicklinien auf die in dieser Arbeit
direction
untersuchten Bogentragwerke nicht angewendet werden konnen und neue
Mixed torsion -a combination of Saint Venant torsion and warping
Knicklinien entwickelt werden mi.issen.
restraint torsion
Model - scale model of prototype
Point load -also concentrated load, load acting at one point
Prototype - full-scale structure
Rib - curved structural element that constitutes the arch
Section -shape of the cross section i.e. structural shape, such
as !-section or wide flange beam
Support -location where one or more degree(s) of freedom
is/are restrained
Tied arch -also bow string arch, the horizontal reaction forces at
the abutments are transmitted to each other by means
of a connecting element (e.g. bridge deck)
Tilting load - also non-conservative load, load with a fixed orienta
tion which can change in direction
Wide flange beam - section with the shape of an I with wide flanges