In-Plane Buckling of Tubular High Strength Steel Trusses with Semi-Rigid Joints

169 Pages·2014·16.15 MB·English

by  Äli Haakana

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ÄLI HAAKANA
IN-PLANE BUCKLING AND SEMI-RIGID JOINTS OF TUBULAR
HIGH STRENGTH STEEL TRUSSES
Master of Science Thesis
Examiner: Professor Markku
Heinisuo
Examiner and topic approved by the
Council of the Faculty of Business
and Built Environment on 07 May
2014

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ABSTRACT
TAMPERE UNIVERSITY OF TECHNOLOGY
Master’s Degree Programme in Civil Engineering
HAAKANA, ÄLI: In-Plane Buckling and Semi-Rigid Joints of Tubular High
Strength Steel Trusses
Master of Science Thesis, 94 pages, 67 Appendix pages
August 2014
Major: Structural Design
Examiner: Professor Markku Heinisuo
Keywords: Buckling, tubular, truss, girder, hollow section, semi-rigid
This Master of Science thesis investigates buckling of hollow section members in
tubular trusses. The existing codes and instructions do not take into account several
factors that have been indicated to affect buckling lengths in tubular trusses.
Furthermore, the existing formulae give -in many cases- buckling length factors that are
excessively conservative or even underestimated results. Thus, buckling length of the
bracing and chord members is investigated. The emphasis is on the in-plane buckling of
K-joints. The influence of dimensional properties of truss members to the joint stiffness
is examined.
In general, obtaining buckling length is simple in the cases of fully rigid or hinged
connections. Since braces are usually welded to the chords in steel girders, the
connections can be semi-rigid. This makes the calculation of buckling challenging,
because the stiffness of the connection needs to be determined. In this thesis, the the
joint stiffness is determined by FE-modeling.
Recently a research has been conducted for development of new formulae for
calculation of buckling length factors. The aim of this thesis is to confirm a wider
applicability range for the new formulae by comparison of factors obtained with the
new formulae and FE modeling. The models are validated and verified, after which joint
stiffnesses of new joints are derived. The validation is done with high strength steel,
grade S500, joints. In some cases, the weld sizes are also determined using high strength
steels. Buckling length factors are analytically calculated with the obtained joint
stiffnesses.
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TIIVISTELMÄ
TAMPEREEN TEKNILLINEN YLIOPISTO
Rakennustekniikan koulutusohjelma
HAAKANA, ÄLI: Korkealujuusteräksisten putkiristikoiden puolijäykät liitokset ja
tasossa nurjahtaminen
Diplomityö, 94 sivua, 67 liitesivua
Elokuu 2014
Pääaine: Rakennesuunnittelu
Tarkastaja: professori Markku Heinisuo
Avainsanat: Nurjahtaminen, ristikko, putki, puolijäykkä
Tämä diplomityö tutkii nurjahdusilmiötä teräksisissä putkiristikoissa. Putkiristikon
uumasauvojen ja paarteiden nurjahdusta tutkitaan, sillä nykyisin käytössä olevat
suunnitteluohjeet ja -koodit eivät ota huomioon monia tekijöitä, joilla on osoitettu
olevan vaikutusta nurjahdukseen. Useissa tapauksissa ne myös antavat joko
huomattavan ylimitoitettuja tai jopa epävarmalla puolella olevia nurjahduspituuksia.
Työssä keskitytään erityisesti K-liitosten uumasauvojen nurjahtamiseen tasossa, ja
käsitellään rakenneosien dimensioiden vaikutusta liitosten jäykkyyteen.
Jotta sauvan nurjahduspituus voitaisiin laskea, tulee sen päiden liitosjäykkyydet
tuntea. Nurjahduspituuden laskeminen on yksinkertaista tapauksissa, joissa liitokset
ovat joko täysin jäykkiä tai nivelellisiä. Teräsrakenteisten putkipalkkien liitokset ovat
yleensä hitsiliitoksia, jotka voivat olla puolijäykkiä. Puolijäykkien liitosten sauvojen
nurjahduspituuksien laskenta on haasteellista, koska liitoksen jäykkyyden
määrittäminen on monimutkaista. Tässä työssä liitosten jäykkyyksiä tutkitaan FEM -
mallinnusta hyödyntäen.
Hiljattain on tehty tutkimus, jossa on kehitetty uusia kaavoja putkiristikoiden
rakenneosien nurjahduspituuden kertoimien laskemiseen. Työssä selvitetään näiden
uusien kaavojen pitävyys ja mahdollinen pätevyysalue vertailemalla FEM-mallinnuksen
avulla saatuja kertoimia uusilla kaavoilla laskettuihin kertoimiin. Mallit validoidaan ja
verifioidaan, minkä jälkeen voidaan mallintaa vapaasti valittujen liitoskombinaatioiden
liitosjäykkyyksiä. Validoinnissa käytetään korkealujuuksisia S500- luokan liitoksia.
Myös hitsien mitat määritetään käyttämällä korkealujuuksisia poikkileikkauksia.
Saatujen liitosjäykkyyksien avulla lasketaan analyyttisesti nurjahduspituuden kertoimia.
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PREFACE
I would like to thank the supervisor of this Master of Science Thesis Professor Markku
Heinisuo from Tampere University of Technology for great guidance. For practical help
in the progress of the research, I would like to thank also Teemu Tiainen and Timo
Jokinen from Tampere University of Technology. I thank Niko Tuominen from
Lappeenranta University of Technology for cooperation in validation process. Finally I
would like to thank Ilkka Lehtinen and Ilkka Sorsa from Ruukki Construction for
providing me the opportunity to make a contribution to this interesting subject.
25.08.2014, Tampere
Äli Haakana
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TABLE OF CONTENTS
1. Introduction ........................................................................................................... 1
1.1 Phenomenon of buckling ............................................................................... 2
1.2 Buckling behavior in lattice girders................................................................ 3
1.3 Investigation of buckling ............................................................................... 4
2. Literature review ................................................................................................... 5
2.1 Factors influencing buckling length ............................................................... 5
2.1.1 Influence of factors and ............................................................... 5
2.1.2 Influence of lateral supports .............................................................. 6
2.2 Studies on the influence of sectional dimensions ............................................ 9
2.3 Comparing FE results of Fekete to the Eurocode and CIDECT ...................... 9
3. Numerical investigation of Boel .......................................................................... 13
3.1 Defining connection stiffness ....................................................................... 14
3.1.1 In-plane rotational stiffness of the connection ................................. 15
3.1.2 Out-of-plane rotational stiffness of the connection .......................... 17
3.1.3 Torsional stiffness of the connection ............................................... 20
3.1.4 Axial stiffness of the connection ..................................................... 21
3.2 Beam-element model ................................................................................... 23
3.2.1 Deflection and stability ................................................................... 23
3.2.2 Connection stiffness ........................................................................ 25
3.2.3 Geometrical verification ................................................................. 27
3.3 Parameter study ........................................................................................... 29
3.3.1 Section combinations and length of the girder ................................. 29
3.3.2 Supports and section types .............................................................. 30
3.3.3 Interpretation of buckling shapes .................................................... 31
3.3.4 Influence of changes in and ....................................................... 32
3.3.5 Final comparison and testing ........................................................... 33
4. New formulae of Boel ......................................................................................... 35
4.1 Buckling of braces ....................................................................................... 35
4.1.1 In-plane buckling of bracing members ............................................ 35
4.1.2 Out-of-plane buckling of bracing members ..................................... 37
4.1.3 Summary of bracing members ........................................................ 38
4.2 Buckling of chord ........................................................................................ 39
4.2.1 In-plane buckling of chord .............................................................. 39
4.2.2 Out-of-plane buckling of chord ....................................................... 41
4.2.3 Summary of chord members ........................................................... 42
4.3 Range of applicability .................................................................................. 43
5. Research methods ................................................................................................ 45
6. Results ................................................................................................................ 48
6.1 Validation of the Abaqus model ................................................................... 48
6.1.1 Analysis method in Abaqus............................................................. 49
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6.1.2 Modeling of hollow section members ............................................. 49
6.1.3 Modeling of welds .......................................................................... 54
6.1.4 Joint no. 1 ....................................................................................... 55
6.1.5 Joint no. 2 ....................................................................................... 60
6.1.6 Selection of the material model ....................................................... 62
6.2 Verification with the results of Boel and deriving of analytical beam-models
62
6.3 Abaqus analyses varying ........................................................................... 67
6.3.1 Joint 1A .......................................................................................... 69
6.3.2 Joint 1B .......................................................................................... 72
6.3.3 Joint 1C .......................................................................................... 74
6.3.4 Joint 2A .......................................................................................... 75
6.3.5 Joint 2B .......................................................................................... 77
6.3.6 Joint 2C .......................................................................................... 78
6.3.7 Joint 3 ............................................................................................. 81
6.3.8 Summary of rotational stiffnesses of joints 1A-3 ............................. 82
6.4 Analytical deriving of buckling length factor ............................................... 83
6.4.1 Buckling length factor comparison of joints 1A, 1B and 1C ............ 85
6.4.2 Buckling length factor comparison of joints 2A, 2B and 2C ............ 86
6.4.3 Buckling length factor comparison of joint 3 .................................. 87
6.4.4 Summary of buckling length factor for braces of trusses with identical
chords 87
6.4.5 Buckling length factor comparison of braces of a joint with un-
identical chords ........................................................................................... 88
6.4.6 Buckling length factors of chords.................................................... 89
7. Discussion and Conclusions ................................................................................ 90
8. Recommendations ............................................................................................... 92
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LIST OF SYMBOLS AND ABBREVIATIONS
HSS Hollow structural section
FE Finite element
FEM Finite Element Method
Abaqus Software suite for finite element analysis by SIMULIA Abaqus FEA
SHS Square hollow section
RHS Rectangular hollow section
CHS Circular hollow section
CFSHS Cold formed square hollow section
CFRHS Cold formed rectangular hollow section
CFCHS Cold formed circular hollow section
CIDECT Comité International pour le Développement et l’Etude de la
Construction Tubulaire
LC Load case
K Buckling length factor
L System length
L Buckling length
cr
P Buckling load or critical load
cr
EI Flexural stiffness
b External width of a square chord member
0
d Diameter of a circular chord member
0
h External height of a rectangular chord member
0
t Wall thickness of a chord member
0
b External width of a square bracing member
1
d Diameter of a circular bracing member
1
h External height of a rectangular bracing member
1
t Wall thickness of a bracing member
1
The ratio of the width or diameter of the bracing member to that of the
chord
The ratio of the outer width or diameter of the chord to two times its wall
thickness
k Axial stiffness
C Torsional stiffness
tor
C In-plane rotational stiffness
in
C Out-of-plane rotational stiffness
out
1
1. INTRODUCTION
Currently buckling length factors and formulae of Eurocode (EN 1993-1-8) and
CIDECT (Comité International pour le Développement et l’Etude de la Construction
Tubulaire) are utilized to design lattice girders in Europe as well as in other parts of the
world. However, these codes and instructions do not take into account several factors
that have been indicated to affect buckling of the hollow section members in lattice
girders. Thus, excessively conservative or even unsafe buckling length factors are
provided in many cases.
The literature review of this thesis summarizes Master of Science Thesis “Buckling
Length Factors of Hollow Section Members in Lattice Girders” of Harm Boel (2010)
and introduces other relevant references. Important factors that are not taken into
account in current codes are highlighted and the numerical investigation of Boel (2010)
for developing better formulae for calculation of buckling length factors is introduced.
Due to the fact that the results of Boel (2010) are based only on FE-study and no
corresponding experimental study (of K-joints), a study with results obtained from
actual experiments is necessary. In this thesis, a recently conducted experimental study
(Tuominen & Björk, 2014) is utilized for validation of new FE-models. The fact that the
formulae developed by Boel are applicable for only a restricted range of symmetrical K-
joints (with identical brace sections and parallel identical chords) suggests that
applicability should be attempted to extend. Thus, in this thesis models are developed
for calculating buckling lengths for a wider range of K-joints (see Figure 1.1) of tubular
trusses. Verification of analytical models is conducted utilizing FE-models that are
validated with the results of experimental study.
Figure 1.1 On the left K-joint and on the right T-joint (EN 1993-1-8 p.102).
The aim is to optimize the design of hollow section truss members towards better
approximation of buckling length factors. The thesis of Boel (2010) resulted in new
2
formulae, applicable for a wider range of values of factor 1. The formulae take both
and 2 factors into account and they give more accurate buckling length factors than
CIDECT or Eurocode. Ideally, the buckling length factors will be obtained for yet a
wider range of joint combinations and geometries: trusses with un-identical chords, un-
identical braces as well as un-identical angles between braces and chords. Buckling
length factors are desired for regular steel and high strength steel. The buckling length
factors shall be less conservative, but still safe. More accurate buckling length factors
will lead to more efficient utilization of tubular trusses.
In this thesis, the phenomenon of buckling is introduced first. The factors are also
introduced that are of interest in order to study buckling of lattice girders. General
literature review is presented in Chapter 2, followed by numerical investigation of Boel
in Chapter 3, review of the results of Boel is presented in Chapter 4, the research
methods of this study are presented in Chapter 5, in Chapter 6 the reports as well as the
results are presented. Finally Chapter 7 concludes the thesis and recommendations are
given in Chapter 8.
1.1 Phenomenon of buckling
Buckling is a phenomenon that occurs when the compressive axial force in a member is
so high that the member cannot resist the axial force in combination with lateral
deflection. Therefore, the member loses its stable equilibrium. The axial load that needs
to be applied to a member -in order for it to buckle- is called the buckling load. When a
load equal to the buckling load is applied to a member it can either start buckling or stay
in un-deformed shape.
Effective length or buckling length describes a member’s ability to resist loading
before it starts to buckle. Buckling length L is generally calculated by multiplying the
cr
buckling length factor K by the system lengthL of the buckling member, as follows:
L K L. (1.1)
cr
The smaller the buckling length is the more the member can resist loading. In general,
the buckling load or the critical load P of a member is calculated as follows:
cr
2EI
P , (1.2)
cr L2
cr
whereEI is the flexural stiffness of the member (Boel 2010, p.14).
In lattice girders the system length of a brace is determined as the distance between
joints. However, it is not unambiguous. It can be defined as the distance between the
intersections of the center lines of the chords and the extensions of the center line of the
brace. It can also be the distance between the physical points where the brace is welded
to the chord or anything between these two (Figure 1.2).
1 is the ratio of the width or diameter of the bracing member to that of the chord, introduced in Ch. 2.
2 is the ratio of the outer width or diameter of the chord to two times its wall thickness, introduced in
Ch. 2.