STATIC STRENGTH OF TUBULAR DT JOINTS USING LUSAS FINITE
ELEMENT SOFTWARE
NORASHIDAH BINTI ABD RAHMAN
A project report submitted in partial fulfillment of requirement for the award of the
degree of Master of Engineering (Civil – Structure)
Fakulti Kejuruteraan Awam
Universiti Teknologi Malaysia
APRIL 2005
PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS
JUDUL:
STATIC STRENGTH OF TUBULAR DT JOINTS USING LUSAS FINITE
ELEMENT SOFTWARE
SESI PENGAJIAN:
Saya
2 0 0 4 /2 0 0 5
NORASHIDAH BINTI ABD RAHMAN
(HURUF BESAR)
mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan
Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1.
2.
3.
4.
Tesis adalah hakmilik Universiti Teknologi Malaysia.
Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan
pengajian sahaja.
Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara
institusi pengajian tinggi.
**Sila tandakan ( √ )
SULIT
TERHAD
√
(Mengandungi maklumat yang berdarjah keselamatan atau
kepentingan Malaysia seperti yang termaktub di dalam
AKTA RAHSIA RASMI 1972)
(Mengandungi maklumat TERHAD yang telah ditentukan
oleh organisasi/badan di mana penyelidikan dijalankan)
TIDAK TERHAD
Disahkan oleh
__________________________________
_____________________________________
(TANDATANGAN PENULIS)
(TANDATANGAN PENYELIA)
Alamat Tetap:
456, RUMAH KOS RENDAH SUNGAI
PROF. MADYA DR.SARIFFUDDIN BIN
PETAI, 21700 KUALA BERANG, HULU
SAAD
Nama Penyelia
TERENGGANU, TERENGGANU.
Tarikh:
CATATAN:
15 APRIL 2005
*
**
♦
Tarikh:
15 APRIL 2005
Potong yang tidak berkenaan.
Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak
berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu
dikelaskan sebagai SULIT atau TERHAD.
Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara
penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau
Laporan Projek Sarjana Muda (PSM).
“I declare that this project report entitled “ Static Strength of Tubular DT Joints
Using LUSAS Finite Element Software” is the result of my own research except as
cited in the references. The report has not been accepted for any degree and is not
concurrently submitted in candidature of any other degree”
Singnature
:
..............................................................
Name
:
NORASHIDAH BINTI ABD RAHMAN
Date
:
15 APRIL 2005
“I declare that I have read through this project report and to my opinion this project
report is adequate in term of scope and quality for the purpose of awarding the
degree of Master of Engineering (Civil – Structure)”.
Signature
:
Name of Supervisor :
....................................................
ASSOC. PROF. DR. SARIFFUDDIN BIN
SAAD
Date
:
15 APRIL 2005
iii
DEDICATION
To father and mother
Thank you for your support
&
To sisters and brothers
thank you for eveything
iv
ACKNOWLEDGEMENT
Alhmadulilah, Praise to Almighty Allah for the blessing and His permission, I
am able to complete my master project.
I wish to extent my greatest thank you and gratefulness to my supervisor,
Assoc. Prof. Dr. Sariffuddin Bin Saad for his valuable guidance, advice and
suggestions throughout this project. With his effort and concern, I am able to
complete my project. Thank you also to Mr. Koh Heng Boon of the Department of
Civil Engineering at KUiTTHO, for his help and advise.
I am also grateful to my most beloved parents for their love and kindness
towards me and for their strong support during my study period.
I wish to thank KUiTTHO and the Public Service Deparment for the financial
support during my stay at UTM.
Finally, a lot of thank you to all staff of Faculty of Civil Engineering,
University Teknologi Malaysia, Skudai, Johor and also for all my friends, student of
postgraduate of Structural and Material Department for their support and cooperation
throughtout my study.
Thank you very much.
v
ABSTRACT
Structural tubular are widely used in the construction of offshore structures.
As these structures are located in hostile environment, these joints represent
structural weak spots and so it is desirable to develop reliable methods of
determining their static collapse loads. This studies focus on the analysis of static
strength of tubular DT joints under brace compression loading by using LUSAS
finite element software. The numerical static strength result is compared with an
experimental test result obtained from the literature. The value of the static strength
obtained in this work is 56% lower than that of the experimental test. A parameter
study was performed to study the effect of the geometric parameters α, β, γ and τ as
well as the effect of the yield strength σy on the static strength of DT joint model.
Finally, a simple equation relating the static strength to the above parameters is
proposed.
vi
ABSTRAK
Struktur sambungan tubular lazimnya digunakan untuk pembinaan struktur
lepas pantai. Oleh kerana struktur ini terletak di persekitaran yang agresif, ia akan
menyebabkan sambungan tubular struktur tersebut menjadi lemah. Oleh itu, satu
kaedah yang baik adalah perlu untuk menentukan beban kegagalan statik bagi
sambungan tersebut. Oleh itu kajian ini tertumpu kepada analisis kekuatan statik bagi
sambungan DT bila brace dikenakan beban mampatan dengan menggunakan perisian
LUSAS. Nilai kekuatan statik ini kemudiannya telah dibandingkan dengan keputusan
ujian makmal yang diperolehi daripada literatur. Dalam kajian ini, nilai kekuatan
statik yang diperolehi adalah 56% lebih rendah daripada nilai ujian makmal. Kajian
parameter telah dijalankan untuk mengkaji kesan parameter geometri α, β, γ dan
τ serta juga kesan kekuatan alah σy kepada kekuatan statik sambungan model DT
tersebut. Akhirnya, satu formula mudah yang menghubungkan kekuatan statik
sambungan DT dengan parameter-parameter di atas telah dicadangkan.
vii
CONTENTS
CHAPTER
1
2
PAGE
TITTLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
CONTENTS
vii
LIST OF TABLE
x
LIST OF FIGURE
xi
INTRODUCTION
1
1.1
Introduction to the tubular structure
1
1.2
Problem of study
2
1.3
Objective of study
3
1.4
Scope of study
4
LITERATURE REVIEW
5
2.1
Introduction
5
2.2
Tubular Structure
5
2.3
Tubular Joint
6
2.4
Development of Static Strength Design Guidance
7
2.5
Previous Study of DT Tubular Joint
8
2.6
Finite Element Method (FEM)
12
2.6.1
14
2.7
Advantages and Disadvantages of FEM
BackGround of LUSAS
15
viii
2.7.1
LUSAS Software Characteristic
15
2.7.2
Procedure Analysis According to LUSAS
16
software
3
MODELLING DT TUBULAR JOINT USING THE
17
LUSAS SOFTWARE
3.1
Introduction
17
3.2
Dimensions and Geometric Parameter
17
3.3
Modelling Step for One eighth Model
19
3.3.1
New file
19
3.3.2
To Generate One eighth of The DT Joint
20
Model
3.4
4
Nonlinear Model
35
3.4.1
Meshing
35
3.4.2
Geometric Definition
37
3.4.3
Material Definition
38
3.4.4
Loading Definition
39
3.4.5
Support Definition
41
3.4.6
Nonlinear Control
43
ANALYSIS, RESULTS AND DISCUSSION
46
4.1
Introduction
49
4.2
One eighth Model Vs. Full Model
52
4.3
Type of supportt
67
4.4
Type of nonlinearity
68
4.5
Mesh Convergence studies
69
4.6
Parametric study
55
4.6.1 Relationship between failure load F and α
55
4.6.2 Relationship between failure load F and β
56
4.6.3 Relationship between failure load F and γ
57
4.6.4 Relationship between failure load F and τ)
58
4.6.5 Relationship between failure load F and σy
59
ix
5
CONCLUSION
63
5.1
Conclusion
63
5.2
Suggestion
64
REFERENCES
65
APPENDIX A ( The loading calculation)
x
LIST OF TABLES
TABLE
NO.
TITLE
PAGE
3.1
Dimensions (in mm) of the DT joint
18
3.2
Support condition for one eight model
42
4.1
Summary of Maximum Load with a Difference Type of
Nonlinearities
51
4.2
Result of Mesh Convergence Study
53
xi
LIST OF FIGURES
FIGURE.
NO.
TITLE
PAGE
1.1
A typical jacket structure
2
1.2
An elastic plastic response of the joint
4
2.1
Various type of tubular joint
6
2.2
A typical DT joint
7
2.3
DT joint test setup
11
2.4
Experimental load-displacement curves for DT joints under
brace/chord compression
11
2.5
A finite element model representing a real engineering
problem
12
2.6
A tubular joint finite element model
13
3.1
Model geometric
18
3.2
One eighth of the DT joint model
19
3.3
New Model start up
20
3.4
The dialogue box “Enter coordinates”
21
3.5
L1 Line
21
3.6
The sweep (rotate) dialogue box
22
3.7
Surface S1, line L2 and L3
22
3.8
Curve L3
23
3.9
Sweeping (translate) dialogue box
23
3.10
The overall chord view
24
xii
3.11
Dialogue box to divide the chord section
25
3.12
The two new chord surface (S2 and S3)
25
3.13
Line L12
26
3.14
The dialogue box used to rotate line L12
27
3.15
New surface, S4, for the top brace section
27
3.16
The sweep dialogue box
28
3.17
Surface S4 was created
28
3.18
The surface Splitting In Equal Divisions dialogue box
29
3.19
Two new surfaces of the brace member after the splitting
process
29
3.20
Model after intersection process
30
3.21
The new group command
31
3.22
The DT joint model after the deletion process
31
3.23
Line L34 was create after manifolding process
32
3.24
Line L4 and L10 must be separated at points P24 and P27
respectively
33
3.25
New surfaces S12 and S13
34
3.26
One-eighth of DT model joint
34
3.27
The dialogue box to define surface meshing
36
3.28
Model with the surface meshing definition
36
3.29
Surface Geometry dialogue box
37
3.30
Isotropic material dialogue box
38
3.31
Elastic plastic dialogue box
39
3.32
The structural loading Dataset dialogue box
40
3.33
Model with the loading at the brace end
40
3.34
Structural support dialogue box
41
xiii
3.35
Model with full support for the linear model
42
3.36
Model with the full support for non-linear model
43
3.37
Load Case properties dialogue box
44
3.38
The Nonlinear & Transient dialogue box
44
3.39
The advance nonlinear incrementation parameter dialogue
box
45
4.1
One eighth of DT joint Model A
47
4.2
An elastic perfectly plastic material model
48
4.3
Load-displacement graphs for Model A &
48
4.4
Full DT joint Model B
49
4.5
Load-displacement graph for both types of support
50
4.6
Load-displacement graph response for both nonlinearity types
52
4.7
Load-displacement graphs of DT joint with various number
of element division
53
4.8
Failure mode of FE model
54
4.9
Failure mode of model tested by Kang (1998)
54
4.10
Relationship between F and α
56
4.11
Relationship between F and β
57
4.12
Relationship between F and γ
58
4.13
Relationship between F and τ
59
4.14
Relationship between F and σy
60
xiv
NOTATION LIST
D
=
Chord outer diameter
d
=
Brace outer diameter
T
=
Chord thickness
T
=
Brace thickness
L
=
Total chord length
l
=
Total brace length
σy
=
Yield strength
N
=
Newton
α
=
Length parameter (2L/D)
β
=
Diameter ratio (d/D)
γ
=
Chord radius to thickness ratio (D/2T)
τ
=
Wall thickness ratio (t/T)
CHAPTER I
INTRODUCTION
1.1.
Introducing to The Tubular Structure
Tubular members are widely used in both onshore and offshore structures.
Their attributes such as the high strength-to-weight ratio, low drag coefficient, and
the ability to use their internal space have made them particularly useful in the
offshore industry over many years. A typical example of the use of tubular members
in an offshore situation is the fixed offshore platform (see Figure 1.1), where tubular
members form a space frame to support the topside structure. Tubular connection
design is a major factor in the design of a structure and can even be the limiting
factor in terms of the strength of the structure.
Circular hollow sections are widely used in the construction of offshore
structures in Malaysia. These sections offer many advantages over other sections.
The sections have the ability to distribute load consistently. From the architect point
of view, it has a minimum amount of surface area to unclean matter effect, rust and
other spoil. With a circular form, it has an advantage in reducing the effect of wind,
wave and blast loadings.
2
Figure 1.1: A typical jacket structure [1]
1.2.
Problem of Study
Structural tubular joints are widely used in the construction of offshore
structures. As these structures are located in hostile environment, these joints
represent structural weak spots and so it is desirable to develop reliable methods of
determining their static collapse loads.
It is impractical to test actual joints due to their massive sizes and also in
view of the associated testing costs. Testing small-scale steel joint models of various
3
shapes was widely carried out in the past. However, the manufacture of these joint
models needs highly skilled welders and the exact shape of fillet welds is not
repeatable.
An attractive alternative is to carry out finite element analysis using a suitable
software to obtain the static strength results. If the results are good, this method can
be used to performed a parameter study to investigate the effect various geometric
parameters on a joint static strength.
1.3.
Objectives of Study
The static strength of tubular DT joints will be studied using LUSAS finite
element software [2]. Objectives of the study are:
a)
to create a good finite element DT joint model.
b)
to carry out a mesh convergence study.
c)
to define the maximum load attained during the elastic plastic
response of the joint.
d)
to compare the static strength results of tubular DT joint between
finite element software and previous experimental test.
e)
to performed parameter study to investigate the effect of the various
geometric parameters on the static strength of DT joints.
f)
to develop a simple formula to calculate the static strength of DT
joints.
4
1.4.
Scope of Study
The LUSAS finite element software will be used to determine the static
strength of tubular DT joint. In this study, the static strength of a tubular DT joint is
defined as the maximum load attained during the elastic plastic response of the joint
and this is shown in Figure 1.2. Data for the analysis are taken from a previous
experimental testing on a similar DT joint performed by Kang et al.[3].
Load
Static strength
Displacement
Figure 1.2: An elastic plastic response of the joint
To obtain the static strength by using LUSAS software, the dimensions of the
DT joint finite element model had been based on the dimensions and data of the
actual joint test performed by Kang et al.[3]. Before the comparison of the static
strength result predicted by the LUSAS software and that of the actual test, a mesh
refinement was conducted by performing non-linear analysis of the DT joint model
under brace compression loading using different element density applied to the chord
area near the brace wall.
CHAPTER II
REVIEW OF LITERATURE
2.1.
Introduction
Tubular joint constitute one of the main problems and high cost areas in the
design, construction and maintenance of steel structures and have been the subject of
considerable research effort. The Department of Energy commissioned a study in
1980 of the various design documents, with particular emphasis on the static strength
of tubular joints [4].
2.2.
Tubular Structure
A tubular structure consists of a framework of hollow pipes made from steel.
There are two types of hollow section used, circular and rectangular. However,
circular hollow sections are more generally used in offshore structure construction. It
is because these sections have a small surface area, can minimise the wind and wave
load and also have a high ecstatic value.
6
2.3.
Tubular Joint
A tubular joint is a joint between the brace and the chord. Figure 2.1 shows
the various types of joint widely used for offshore construction work.
Figure 2.1: Various types of tubular joint [5]
7
Figure 2.2 shows a typical tubular DT joint showing the definition of the
various geometric factors
α
=
2L/D
β
=
d/D
γ
=
D/2T
τ
=
t/T
Figure 2.2: A typical DT joint [3]
2.4.
Development of Static Strength Design Guidance
Early development of offshore technology was on a trial and error basis.
Brace were welded to the jacket legs, which served as the chord member without any
reinforcement. The first attempts at tubular joint design in the late 1950s were based
on elastic analysis of the tubular shells. It quickly became apparent from a few tests
in the early 1960s that there was little correlation between ultimate strength and
elastic shell analysis.
8
This led to a series of tests in the mid 1960s and covered a limited range of
joint types and geometries. These tests were recognised as mainly to investigate the
relative importance of factors such as β (ratio of brace diameter to chord diameter)
and γ (ratio of chord radius to chord wall thickness).
2.5.
Previous Study of DT Tubular Joint
The earliest investigation on chord stress effects on DT joints were carried
out by Togo [6] and Washio et al. [7][8]. A series of small-scale joints (D = 101.6
mm, β = 0.47 and γ = 16) were subjected to brace axial compression with various
levels of chord axial stresses in DT joints which was found to generally reduce the
joint capacity, whereas tension chord stresses have a minor effect on joint strength.
Following their work, a semi empirical formula was developed and a chord
stress factor Qf was introduced to account for the presence of chord stresses. The
Washio Qf expression was adopted by the API RP 2A code from 1975 to 1983 and
also by other design codes.
The work on chord stress effect conducted by Boone et al. [9], Weinstein and
Yura [10] and Sanders [11] at Texas University is the most complete. Boone et al.
carried out 10 tests (including three tests without chord load used as base test) on
large scale DT specimens (D = 407.7 mm), α = 17.5, β = 0.67, γ = 25.6 and τ = 0.8)
to study the influence of chord axial compression, in plane bending (IPB) and out
plane bending (OPB) on the joint strength. The test results showed that chord stress
effects were most significant for brace IPB followed by axial loading and OPB.
9
Weinstein and Yura [10] carried out 10 DT joint tests to assess the influence
of β on the chord stress effect. Seven specimens (with β = 1) were tested with either
brace axial compression, IPB or OPB and three specimens (β = 0.35) were tested
with brace axial compression. The chord geometry was identical to that used by
Boone et al. [2], i.e. with γ = 25.4. Again, chord axial compression and bending
stress were considered. For specimens with β = 1, the results showed that the chord
stress has similar strength reduction effects compared to IPB loaded smaller β joints.
However, for axially loaded or OPB loaded joints, the results showed that the
chord stress had no effect on the ultimate strength as only small deformations of the
chord wall occurred at the saddle regions. However, the ultimate strength for β =1
axially loaded joints with or without chord stress increased significantly compared to
smaller β joints since most of the load was transferred through the short lengths of
chord wall between the weld toes at the saddle locations.
For specimens subjected to brace OPB and chord axial compression, the joint
failed by instability. It was also shown by Sanders [11] that the axial chord
compression stress has no effect on β =1 tension loaded DT joints. Results from test
on β = 0.34 brace axially loaded specimens indicated that the strength reduction due
to chord stresses is higher than that for specimens with β = 0.67.
In 1998, Kang et al.[3] carried out tubular DT joint tests. The objective was to
assess the ultimate strength of DT joints under combined brace compression and
chord compression. The work was carried out both experimentally and numerically.
Two methods were used in the numerical work to apply the chord and brace
loading: (1) proportional loading and (2) nonproportional loading. The former
method was adopted in the experimental work. The numerical calculations were done
using the finite element analysis. The models were created using the P3/PATRAN
10
mesh generation program and the static strength of the models was assessed using
ABAQUS 5.4 finite element program.
Generally the results showed a significant and increasing reduction in the
strength, from both FE and test result, as the applied nominal chord stress was
increased. The FE models achieved higher ultimate loads than the corresponding
experimental models.
From the preceding data, the experimental and numerical results have
confirmed that the ultimate strength of DT joints under brace compressive loading
could be reduced significantly when chord axial stress is present. They also found
that, FE analysis could significantly over predicted the ultimate strength of such
joints. The discrepancy may be caused by an instability in the joints that was
accentuated at higher chord loads.
Figure 2.3 shows the DT joint test set up. The test of the DT joints was
conducted in a 250-kN servohyraulic test machine. The joint specimens were
mounted in the test facilities with the brace members in the vertical position and the
chord in horizontal position. This arrangement allowed the brace members to be
loaded in compression by test machine such that both the upper and lower brace were
pushed into the chord member. The load-displacement graph for the brace
compression test (without chord stresses) is shown in Figure 2.4 (Test A1).
11
Figure 2.3: DT joint test setup [3]
Figure 2.4: Experimental load-Displacement Curves for DT joints Under
Brace/Chord Compression [3]
12
2.6.
Finite Element Method
Basic ideas of the finite element method originated from advances in aircraft
structure analysis. In 1941, Hrenikoff presented a solution of elasticity problems
using the “frame work method.” Courant’s paper, which used piecewise polynomial
interpolation over triangular sub regions to model torsion problems, appeared in
1943 [12]. Turner, et al. derived stiffness matrices for truss, beam and other elements
and presented their findings in 1956 [12]. The term finite element was first coined
and used by Clough in 1960 [12].
In the early 1960s, engineers used the method for approximate solution of
problems in stress analysis, fluid flow, heat transfer and other areas.
Figure 2.5: A finite element model representing a real engineering
problem [2]
In 1970s, the finite element method was further consolidated by Zainkiewicz
and Cheung, when they used this method to solve the general problems using
Laplace and Poisson equation.[12]. Mathematicians developed the algorithm solution
until Rayleigh-Ritz method became a main solution in certain general problem.
Hinton and Crisfield give a big contribution in modelling and solution of non-linear
13
problem according to FEM. Figure 2.5 shows a finite element model of a real
engineering problem.
Solution of finite element can be summarised as involving the combination of
several nodes to produce a small total unit that balance each other. The combination
of many such units then form a model. Figure 2.6 shows a tubular joint finite element
model.
Figure 2.6: A tubular joint finite element model [5].
14
2.6.1. Advantages and Disadvantages of the FEM
The finite element method has several advantages;
a) it can model complicated geometry
b) it can be programmed into a computer software and this may
avoid the need to perform laboratory test.
c) it can analyse difference element characteristics in a matrix system
d) it can handle non-linear behaviour involving high deformation
and non-linear material.
e) it can take the boundary conditions into account.
But the finite element method has several disadvantages, i.e:
a) it needs a professional to model an exact situation.
b) it needs a computer with a high processor to run the analysis smoothly.
c) The method is mesh sensitive so that it is necessary to try various element
densities at critical areas before the results can be accepted.
15
2.7.
Background of LUSAS
LUSAS is computer software for structural analysis based on the finite
element method; it was built by FEA Limited at United Kingdom. This software can
be combined with the CAD function to show the modelling shapes, stress distribution
sand post-processing shape changes.
LUSAS is an associative feature-based modeller. The model geometry is
entered in terms of features which are sub-divided (discretised) into finite elements
in order to perform the analysis. Increasing the discretisation of the features will
usually result in an increase in accuracy of the solution, but with a corresponding
increase in solution time and disk space required. The features in LUSAS form a
hierarchy that is volumes are comprised of surfaces, which in turn are made up of
lines or combined lines, which are defined by points.
2.7.1. LUSAS Software Characteristic
LUSAS software can analysis and organise complex structure problems and
shapes including 3 dimensional structures. This software also can be used in dynamic
structural analyses with temperature changes. LUSAS software can solve problems
up to 5000 number of elements.
16
2.7.2. Procedure Analysis According to LUSAS Software
There are 3 steps in the finite element analysis using the LUSAS software,
which are as follows:
a) Pre-processing phase
Pre-processing involves creating a geometric representation of the structure,
then assigning properties, then outputting the information as a formatted data file
(.dat) suitable for processing by LUSAS.
b) Finite Element Solver
Sets of linear or nonlinear algebra equations are solved simultaneously to
obtain nodal results, such as displacement values at different nodes or temperature
values at different nodes in heat transfer problems.
c) Result-Processing
In this process, the results can be processed to show the contour of
displacements, stresses, strains, reactions and other important information. Graphs as
well as the deformed shapes of a model can be plotted.
CHAPTER III
MODELLING DT TUBULAR JOINT USING THE LUSAS SOFTWARE
3.1.
Introduction
This section explains the process to build the model and the process to run an
elastic plastic analysis using LUSAS software.
3.2.
Dimensions and Geometric Parameters
The actual model is shown in the Figure 4.1. The symbols used for the DT
joint in Figure 3.1 are defined as follows:
a) D = Chord diameter
b) d = brace diameter
c) L = chord length
d) l = brace length
18
Brace
T=7.30 mm
chord
I = 749.5 mm
D = 169.2 mm
d = 88.5 mm
L = 1400mm
Figure 3.1: Model Geometric
The dimensions of the DT joint tested by Kang et al. [3] are shown in Table
3.1.
Joint
DT
D
d
L
l
(mm)
(mm)
(mm)
(mm)
169.5
88.5
1400
749.5
Table 3.1: Dimensions (in mm) of the DT joint
19
3.3.
Modelling Step for One eighth Model
3.3.1
New File
The units used to generate the tubular DT joint model were Newton (N) and
Meter (m). This section will described in detail the way to produce a one eighth of
the overall DT joint as shown in Figure 3.2.
Y
X
Z
Figure 3.2: A one eighth surface of the DT joint model
First, a new file was created to model the joint. The command file > new was
chosen to create a new file as shown in Figure 3.3.
20
Figure 3.3: New model start up
3.3.2. To Generate One Eighth of The DT Joint Model
The Command Geometry > Line > coordinates was used to create a straight
line, L1. The dialogue box as shown in Figure 3.4 was displayed. Only two points
were needed to create a straight line, which were P1 (0,0,0) and P2 (0.0846,0,0).
These coordinates were entered into the coordinates dialogue box and line L1 was
created as shown in Figure 3.5.
21
Figure 3.4: The dialogue box “Enter coordinates”
Figure 3.5: Line L1
Next, line L1 was used to create a curve for the chord end. L1 was selected
by clicking the left button of the mouse at L1 and then, the command Geometry >
surface > by sweeping was used.
22
Figure 3.6: The sweep (rotate) dialogue box
In the sweep dialogue box (see Figure 3.6), the option “rotate” was chosen.
An angle of rotation of 90o in the XY plane was keyed in. A new surface, S1 was
produced along with lines L2 and L3 (Figure 3.7).
Figure 3.7: Surface S1, line L2 and L3
23
Surface S1, lines L1 and L2 must be deleted to create a hollow chord section.
The command Delete was used to delete these entities only. Curve L3 remained as
shown in Figure 3.8.
Figure 3.8: Curve L3
The next step is to produce part of the chord of length 0.7 m by using the
translation method. This was done by first selecting the Geometry > Surface > By
sweeping command. The sweep dialogue box appeared as shown in Figure 3.9 and
the translate option then chosen.
Figure 3.9: The sweeping (translate) dialogue box
24
A value of 0.7 m was filled in the box associated with a translation in the Z
direction. This represented part of the chord length. This is shown in Figure 3.10.
The right button of the mouse was clicked and the Labels command was selected to
label the lines and surface.
Figure 3.10: The overall chord view
The surface S1 need to be divided into two sections with a ratio of 0.75. The
process started by selecting the surface S1 and then the command Geometry >
Surface > By splitting > at parametric Distance was used. A dialogue box as shown
in Figure 3.11 was displayed. Figure 3.12 shows the two new surfaces for the chord
section, i.e surfaces S2 and S3.
25
Figure 3.11: The dialogue box to divide the chord surface
L3
L9
L10
Y
L11
L4
S2
Z
X
S3
L7
L8
Figure 3.12: The two new chord surface (S2 and S3)
The next step is to create the brace surface. This surface was created to
intersect the surface S3 with a length of 0.37475 m measured from the longitudinal
axis of the chord.
26
The upper surface of the brace was created first. The command used to create
the chord section was again used to create the upper brace section using a different
set of coordinates. The coordinates (0,0.37475,0.7) and (0.04425,0.7) were used to
form line L12 (see Figure 3.13). The command Dynamic Rotation can be used to
view the model from various angles.
Figure 3.13: Line L12
Then, the command Geometry > Surface > By sweeping was chosen to create
curve to form the top part of the brace. The rotation option in the dialogue box was
selected. A 90o rotation of line L12 were made in the XZ plane with the point
(0,0.37475,0.7) acting as origin (Figure 3.14). The new surface , S4, was displayed as
shown in Figure 3.15.
27
Figure 3.14: The dialogue box used to rotate line L12
L12
S4
L13
L14
L10
L9
L4
L11
L3
S3
S2
Y
Z
L8
L7
X
Figure 3.15: New surface, S4, for the top brace section
The surface S4 was no longer needed to form the overall brace surface. Line
L14 need to be translated downward along the Y-axis to produce the brace surface.
First, surface S4 was deleted by using the command Delete. Next, the command
28
Geometry > Surface > By Sweeping was selected. In the dialogue box, the option
“Translate” was selected as shown in Figure 3.16. Line L14 was translate a distance
of 0.34 m downward (hence –0.35 in Figure 4.16) along the y-axis. The new brace
surface S4 was fully created after the translation process as shown in Figure 3.17.
Figure 3.16: The sweep dialogue box
S4
Y
S3
S2
Z
X
Figure 3.17: Surface S4 was created
29
The chord member and the brace member must be joined together to form the
connection. These process only involved surfaces S3 and S4 only. First, the brace
surface, S4, was divided into two smaller surfaces along the brace length by selecting
the command Geometry > Surface > By splitting > At equal Distance (Figure 3.18).
Two new surfaces (S5 and S6) were created as shown in Figure 3.19.
Figure 3.18: The Surface Splitting In Equal Distance dialogue box
S5
S6
Y
S3
S2
Z
X
Figure 3.19: Two new surfaces of the brace member after the splitting process.
30
The joining process was done by selecting all three surfaces involved i.e S3,
S5 and S6. Then the command Geometry > Line > By Intersection was chosen and
the option “Split intersecting Features” and “Delete Features On Splitting” were
clicked. Figure 3.20 shows the model after the intersection process.
S7
S11
S9
S6
S5
S8
S12
S10
S3
Y
S2
Z
X
Figure 3.20: The model after the intersection process
Surfaces S13 and S14 were no longer needed. To delete these surfaces,
surfaces S2, S3, S7, S9, S13 and S15 were selected to make them invisible. Then the
commands Geometry > Group > New Group were used. The command invisible was
selected under the new group icon by clicking the right button of the mouse (Figure
3.21).
31
Figure 3.21: The new Group command
After that, all items on display that needed to be deleted were selected, then
the right button was clicked to delete these items. The right button was clicked once
again at the New Group icon to view the remaining features of the model after the
deletion process. The command visible was then selected. Figure 3.22 shows the
model after the deletion process.
Y
Z
X
Figure 3.22: The DT joint model after the deletion process.
32
The surface S3 was selected and then the right button of the mouse was
clicked to create a on the chord surface joining point P8 and P26. Then, the
command Selection Memory > Set was selected. After that, points P8 and point P26
were selected and the command Geometry Line > By > Manifolding taken from the
menu was chosen. Line L34 was created to connect these two points (Figure 3.23).
The surface S3 must be made inactive for other steps of the modelling process by
using the command Selection Memory > clear.
Figure 3.23: Line L34 was created after the manifolding process
Next the surface S3 must be separated into two sections. One surface was
bounded by points P5, P24, P26 and P8, while the other surface was bounded by
points P8, P9, P27 and P26. Surface S3 was deleted by clicking on it and, then the
Delete button was pressed at the keyboard. Line L4 must be divided into 2 lines i.e
lines L36 and L37 at point P24 (see Figure 3.24). To do this, the command Geometry
> Line > by splitting > At A point was used. The same step was used to divide the
line L10 into two i.e L38 and L39 at point P27 (see Figure 3.24). Then both lines L4
and L10 were deleted.
33
Figure 3.24: Line L4 and L10 must be separated at points P24 and P27 respectively
For defining the new surface with the boundaries defined by points P5, P24,
P26 and P8, lines L36, L24, L35, and L8 were selected by using Geometry > surface
> Line > General Surface command. The new surface, which is S12, was obtained a
result from the process. Once again, the same step was used to define the other new
surface with the boundaries defined by points P26, P27, P9 and P8. Figure 3.25
shows the new surface S13 that had been created.
34
Figure 3.25: New surface S12 and S13
Finally, the unused lines which were L42 and L44 were deleted. Figure 3.26
shows the geometry of one eighth of DT joint model that use for the analysis.
S7
S11
S12S13
S2
Y
Z
X
Figure 3.26: One eighth of DT model joint
35
3.4. Nonlinear Model
3.4.1. Meshing
There were two stages to define the meshing. The first stage was to define the
surface meshing and then followed by defining the line meshing. Surface meshing
gave a basic mesh to the model. For the analysis, line meshing was used for
modification purpose to obtain an optimum mesh.
The command Attributes > Mesh > surface was selected to define the surface
meshing and a dialogue box appeared as shown in Figure 3.27. (In the “Generic
element” Type box, “Thin Shell” was set and a “Regular mesh with Automatic
Division” was selected). Quadrilateral was set into the Element shape box and
Quadratic was set into the Interpolation order box to run non-linear analysis (for
linear analysis, linear must be used instead). The name of the dataset was given as
meshing and this was displayed in the treeview
.
The model was then selected by pressing the Ctrl-A button, then the surface
mesh file (i.e “meshing”) at the treeview was clicked and dragged to the worksheet
area. The DT joint model was now given with a basic mesh containing 4 divisions
for each line (see Figure 3.28).
36
Figure 3.27:The dialogue box to define surface meshing
Y
Z
X
Figure 3.28: Model with the surface meshing definition
The next stage was to define the line meshing where the aim was to indicate
the size of the element at any line. First, the command Attributes > Mesh > Line was
used. The “Feature Mesh definition” dialogue box was displayed. To set different
sizes of element, the option of uniform transition ratio of last to first element was
37
selected. The value represent the ratio between size of the element at the end of a line
to the size of element at the beginning of the line.
3.4.2. Geometric Definition
The thickness of model which is 0.0075 m for the chord and 0.00545 m for
brace can be defined by using the command Attributes > Geometric > Surface.
Figure 3.29 shows the way to define the chord thickness in LUSAS.
Figure 3.29: Surface Geometry dialogue box
38
3.4.3. Material Definition
The model material can be defined by using the command Attributes >
material > Isotropic. For this material, the value of Young modulus is 210 GN/m2
and a of poison’s Ratio of 0.3 was used (see Figure 3.30).
Figure 3.30: Isotropic material dialogue box
For the plastic material property, a value of uniaxial yield stress of 345
MN/m2 was used in all analysis. Figure 3.31 shows the way to set this value in
LUSAS. Since the material is considered to be elastic perfectly plastic, therefore the
hardening gradient was set to “0” and the ductility of the material was assumed as 1
(or at 100% plastic strain). Figure 3.31 shows the way to set these values into the
LUSAS software.
39
Figure 3.31: The Isotropic material dialogue box to define the nonlinear material
stress strain curve
3.4.4. Loading Definition
The command Attributes > Loading > structural > global distribution was
used to define the load while the option Unit length was clicked. A compression
pressure of load -899180 N/m (see Figure 3.32) was placed at brace end (L19 and
L20) as shown in Figure 3.33. However, LUSAS would apply this load in
incremental manner until the analysis stopped. The detail calculation to establish this
loading is given in Appendix A.
40
Figure 3.32: The structural Loading Dataset dialogue box
Y
Z
X
Figure 3.33: Model with the loading at the brace end.
41
3.4.5. Support Definition
The command menu Attributes > Support > structural was used to defined
the support condition of the model. A dialogue box Structural support appeared as
shown in Figure 3.34.
Figure 3.34: The Structural Support dialogue box
The support conditions set in the dialogue box were meant for all nodes lying
on lines L7 and L8 (see Figure 3.35). These nodes were prevented from moving
along the y-axis and at the same time they are also prevented from rotating about the
z-axis. A dataset name was given as shown in Figure 3.34 and this was placed by
LUSAS in the treeview. To apply the above restraint conditions to all nodes on lines
L7 and L8, lines L7 and L8 were selected using the left hand button of the mouse.
Then the
button was clicked, all the datasets in the treeview would appear on the
screen. Using the mouse, the dataset fix y rotation z was selected by clicking the left
hand button, dragged and “let lose” on the model. For all other nodes on the lines
shown in Table 3.2, a similar procedure was adopted to apply the relevant restraint
conditions on those nodes.
42
If an elastic analysis was run, the restraints conditions as shown in Figure
3.35 would appear in the computer screen. However, if an elastic plastic analysis was
performed, the restraint conditions will be a little different and these are shown in
Figure 3.36.
Node at Line
Prevented from
Prevented from
Dataset
translating in the
rotation about at
L7, L8
Y- axis
Z – axis
Fix Y, rotation Z
L9, L38
X – axis
Z – axis
Fix X, rotation Z
L32
X – axis
Y – axis
Fix X, rotation y
L25
Z - axis
Y – axis
Fix Z, rotation Y
L3
X, Y – axis
Free
Fix XY
L19, L20
Free
Free
Free
L36
Z – axis
XY – axis
Fix Z, rotation XY
Table 3.2 Support condition for one-eighth model
L20 L19
L25L27
L32
L24
L34 L38
L11
L36
L8
L9
L3
L35
Y
L7
Z
X
Figure 3.35: Model with restraint conditions after elastic analysis
43
L20L19
L25L27
L32
L24
L36
L8
L34L38
L11
L9
L3
L35
Y
L7
Z
X
Figure 3.36: Model with restrain conditions after elastic plastic analysis
3.4.6. Nonlinear Control
Nonlinear analysis control properties were defined as properties of a
loadcase. The nonlinear analysis help to determine the load at which the tubular joint
failed. In the treeview
the name load case 1 was given and the option “nonlinear
& transient” was selected as shown in Figure 3.37.
44
Figure 3.37: The properties dialogue box
Figure 3.38: The Nonlinear & Transient dialogue box
Figure 3.38 shows the next dialogue box which is “Nonlinear & Transient”.
In this dialogue box, the option nonlinear under the heading of “Incrementation” was
selected and automatic was set into the “incrementation” box. A starting load factor
of 0.05 was set. The “max change in load factor” of 0.1 was added to restrict the
second and subsequent load increment sizes to ensure sufficient points were obtained
45
in the load deflection behaviour of the joint. “Max total load factor” was set to 0
meaning no limit on the maximum load factor was imposed. The number of desired
“Iterations per increment” was changed to 4.
Then, the advance button in the “Incrementation” section was clicked and the
dialogue box as shown in Figure 3.39 appeared. Under the termination criteria
section, the “Terminate on value of limiting variable” option was selected and in the
point number option box, node 12 was selected from list of nodes. The “Variable
type” was set as V which represented the deflection of the selected node in the Y
direction and the analysis would be terminated when the deflection reached a value
of 10 m in the opposite direction of y.
Figure 3.39:The advance nonlinear incrementation parameters dialogue box
For geometric nonlinear analysis, option button under the “Incrementation”
heading of Figure 3.38 was clicked. The option geometric with Total Lagragian was
selected. The model now was now ready to undergo analysis. Run icon was clicked
to run the analysis using LUSAS solver.
CHAPTER IV
ANALYSIS, RESULT AND DISCUSSION
4.1.
Introduction
A number of preliminary investigations were performed to get a good finite
element model similar to the model tested by Kang et al. [3].
4.2.
One eight Model vs. Full Model.
Since there was symmetry in terms of joint geometry and loading, to take the
advantage of this aspect, only one eighth of the actual joint was generated and this is
shown in Figure 5.1. This model is called Model A.
47
Y
Z
X
Figure 4.1: One eighth of DT joint (Model A)
The use of Model A would not only same effort in generating the model but
also would save running time and disk space during elastic plastic analysis. All nodes
at the support were not allowed to move in x and y directions but they were allowed
to move in the z direction. Thin shells elements were used through out. The value of
Young’s Modulus E=210 GN/m2 and a Poisson’s ratio of 0.3 were used.
An elastic plastic analysis was run using Model A. Material nonlinearity was
included where the elastic perfectly plastic material stress strain curve as shown in
Figure 4.2 was used, where σy = 340 MN/m2 and a ductility at failure of 100% was
assumed.
48
σ
σy = 340
100%
ε
Figure 4.2: An elastic perfectly plastic material model
A axial compression pressure load was applied incrementally at the brace end
by LUSAS until a limit load was reached. The results (for Model A) of this analysis
is shown in Figure 4.3 with a limit load of 126 kN
Load displacement graph
test failure
load
=221.2 kN
250
Load (kN)
200
150
100
50
0
0
50
100
150
Displacement (mm)
Figure 4.3: Load displacement graphs for Model A.
Next, another analysis was carried out but using a full model (model B) (see
Figure 4.4). Model B produced a limit load of 138 kN.
49
Y
X
Z
Figure 5.4: Full DT joint model B
Clearly, the limit load of model A is 9% lower when comparison is made the
limit load of Model B. This shows that the one eighth DT joint can predict the failure
load sufficiently accurately and therefore it can be used for all subsequent
investigations. The use model A helped to reduce the running time for subsequent
investigations as well as it help to reduce the use of disk space during each analysis.
4.3.
Type of Support Conditions
In his paper, Kang et al. [3] did not mention clearly the type of support he
used for the ends of chord. Therefore further investigation was necessary to choose
which was the most effective between a simply supported chord and fully fixed
chord ends. Elastic-plastic analyses were performed to get the failure loads for both
cases. Only material nonlinearitiy was included.
50
The simply supported chord give a failure load of about 43% lower then the
test failure load. The chord with fixed supports, on the other hand, gave a failure
load, which is about 30% lower than the test value. Figure 4.5 show the loaddisplacement results for both type of supports. Clearly, the chord with fixed support
give a better comparison. This support type were used for subsequent investigations.
Load- displacement graph
test failure
load
=221.2 kN
250
Load (kN)
200
simply
supported
150
100
fixed
50
0
0
50
100
150
Displacement (mm)
Figure 4.5: Load-displacement graphs for both types of support
4.4.
Type of Nonlinearity
Two types of non-linearities were investigated
a) material nonlinearities
b) material plus geometric nonlinearities
51
The effect of these two types of nonlinearities on the failure load of DT joint
was investigated. In both cases, the chord was fixed at all nodes at its ends in terms
of translation and rotation.
The model with material nonlinearity only give a failure load of 156 kN i.e.
about 30% lower than the test failure load. However, when material and geometric
nonlinearity were included, the failure load is 102 kN which is about 54% lower
compared with the test failure load. Table 4.1 show the summary of the finite
element prediction loads compared with the test failure load.
Type of support
Maximum load with
Maximum load with material
material nonlinearity
plus geometric nonlinearity
(kN)
(kN)
156
Fixed
(30% lower than test
value)
102
(54% lower than test value)
Table 4.1: Summary of maximum load with a different type of nonlinearities
On the basis of the above findings, both material and geometric nonlinearities were included in subsequent analyses. Figure 4.6 shows the load
displacement response for both nonlinearity types.
52
Load vs.displacement graph
test failure
load
= 221.2 kN
250
Load (kN)
200
150
material
nonlinearity
material plus
geometric
100
50
0
0
20
40
60
Displacement (mm)
Figure 4.6: Load-displacement graph response for both nonlinearities type
5.5.
Mesh Convergence Study
A mesh convergence study was carried out by performing nonlinear analysis
of the DT joint model under brace compression pressure loading by increasing the
row of elements applied on the chord wall around the brace. Table 4.2 shows the
static strength results of the study. The load displacement curve for each analysis is
plotted in Figure 4.7. It can be seen that the results are very close with a maximum
difference of about 5% between 4 divisions of elements on the chord wall adjacent to
the brace and that of 10 divisions. Even though a mesh with 4 divisions was adequate
for use in the subsequence parameter study, a mesh with 9 divisions was used
instead. Running with 9 divisions of element on the chord wall around the brace
produced a failure load of 97 kN.
53
The experimental failure load result of a similar joint was 221.2 kN as
reported by Kang et al. [3] So, the difference between the LUSAS results (with 9
divisions) and the test results is only about 56%. The failure mode of the finite
element model (9 divisions) is shown in Figure 4.8. The failure mode of the model
tested by Kang et al. [3] is shown in Figure 4.9. From both of these figures, it can be
seen that both failure modes resemble each other quite well
Mesh division
Maximum load (kN)
4
102
5
100
6
99
7
98
8
98
9
97
10
97
Table 4.2: Result of mesh convergence study
Mesh convergence studies
test failure
load
= 221.2 kN
250
Load (kN)
200
150
100
50
0
0
20
40
div=4
div=5
div=6
div=7
div=8
div=9
div=10
60
Displacement (mm)
Figure 4.7: Load displacement graphs of DT joint with various number of finite
element division.
54
Figure 4.8: Failure mode of FE model.
Figure 4.9:Failure mode of DT joint model tested by Kang et al. [3]
55
4.6.
Parametric Study
In this section, the results of a parameter study are presented. The effects of
the geometric parameter α, β, γ and τ on the failure load F (i.e the static strength) of
the DT joint model were investigated where α, β, γ, τ are defined in Figure 2.2 on
page 7. Also, the effect of changing the yield stress σy of the material on the failure
load F of the DT joint model was studied. Finally, a simple equation for the failure
load F in terms of α, β, γ, τ and σy is proposed. In all analysis, the mesh with 9
divisions of elements on the chord arranged around the brace was used.
4.6.1
Relationship Between Failure Load, F and α (=2L/D)
Figure 4.10 shows the results of the failure load when α was varied. It can be
seen that as α increases, the failure load, F, decreases. This is to be expected that as
the length of the chord increases, the effect of overall (global) chord bending become
more and more significant which causes F to decrease. A straight line can be drawn
passing through most of the points. An equation connecting F and α can be proposed
as follows;
F = -2.7 α + 197.4
(4.1)
Equation (4.1) is valid within the following range of α i.e 11.8≤ α ≤23.5.
56
F (kN)
F vs α
140
120
100
80
60
40
20
0
F= -2.6873α + 197.4
10
12
14
16
18
20
22
24
26
α
Figure 4.10: Relationship between F and α
4.6.2
Relationship Between Failure Load, F and β (=d/D)
Figure 4.11 shows the failure load results when β (= d/D) was varied. An
increase in β means the chord diameter decreases. Hence, the moment of inertia of
the chord will decrease and this will lower the capacity of the chord to carry load.
Therefore, the trend of results as given in Figure 4.11 is to be expected. An equation
relating F and β can be proposed as follows,
F = -277.3 β + 292.4
(4.2)
Equation (4.2) is valid within the following range of β i.e 0.3 ≤ β ≤ 0.6.
57
F vs β
150
F (kN)
130
y = -277.28β + 292.35
110
90
70
50
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
β
Figure 4.11:Relationship between F and β
4.6.3
Relationship Between Failure Load, F and γ (=D/2T)
Figure 4.12 shows data involving the values of the failure load, F, at different
values of γ (=D/2T). As expected , a thicker chord (with a lower γ) have a bigger
failure load compared to a thinner chord (with a bigger γ).The best straight line can
be drawn connecting the points and an equation relating F and γ is proposed an
follows;
F = -12.3γ + 353
(4.3)
Equation (4.3) is valid within the following range of γ i.e 11 ≤ γ ≤ 30
58
F vs γ
120
F (kN)
100
80
F = -12.335γ + 352.99
60
40
20
0
10
15
20
25
30
35
γ
Figure 4.12: Relationship between F and γ
4.6.4
Relationship Between Failure Load, F and τ (=t/T)
The results of the failure load, F of the DT joint model when τ (=t/T) are
varied are shown in Figure 4.13. A thicker chord (with a low τ) will have a bigger
failure F than a thinner chord (with a bigger τ). However the results of F shown in
Figure 4.13 give the opposite trend. At present, it is difficult to explain the relation
between F and τ produced by LUSAS here. The best straight line is drawn through
the points and an equation relating F and τ ισproposed i.e
F = 66.3τ + 102
(4.4)
Equation (4.4) is valid within the following range of τ i.e 0.2 ≤ τ ≤ 0.6.
59
F (kN)
F vs τ
120
100
80
60
40
20
0
F = 66.314τ + 102.07
0.1
0.2
0.3
0.4
0.5
0.6
0.7
τ
Figure 4.13: Relationship between F and τ
4.6.5
Relationship Between Failure Load, F and σy
Figure 4.14 shows the effect of increasing the yield stress of the material on
the failure F of the DT joint model. As expected as the chord yield stress increases,
the failure load F will also increase as confirmed by the trend of results. An equation
relating F and σy is proposed as follows;
F = 0.19σy + 32.2
(4.5)
Equation (4.5) is valid within the following range of σ i.e 250 ≤ σy ≤ 650
60
F vs. σy
160
F = 0.1878σy+ 32.198
F (kN)
140
120
100
80
60
200
300
400
500
600
700
2
σy (MN/m )
Figure 5.14: Relationship between F vs. σy
Combining the first the four equations below together i.e
F = -2.7 α + 197.4
(4.1)
F = -277.3 β + 292.4
(4.2)
F = -12.3γ + 353
(4.3)
F = 66.3t + 102
(4.4)
F = 0.19σy + 32.2
(4.5)
The following equation will be obtained,
4F = (- 2.6873α -277.28β -12.335γ + 66.314τ + ) + (197.4+292.35+352.99+102.07)
F =- 0.672α -69.32β -3.08γ + 16.58τ + 236.2
(4.6)
61
Then Equation 4.6 is added to Equation 4.5
2F =(- 0.672α -69.32β -3.08γ + 16.58τ + 236.2) + (0.1878σy + 32.198)
F = - 0.336α -34.66β -1.54γ + 8.29τ + 0.09σy + 134.2
(4.7)
Equation 4.7 represents a simple equation relating the static strength of DT
joints with the geometric parameters α, β, γ, and τ and yield stress σy. Equation 4.7 is
valid within the following range of geometric parameter ratio i.e.
11.8 ≤ α ≤ 23.5
0.3 ≤ β ≤ 0.6
11 ≤ γ ≤ 30
0.2 ≤ τ ≤ 0.6
250 ≤ σy ≤ 650
Finally, it is necessary to compare the static strength of DT joint model
obtained by using Equation 4.7 with the test static strength obtained by Kang et al.[3]
and the static strength obtained using LUSAS.
The data of the DT joint model are listed again.
t = 5.45mm
d = 88.5mm
T = 7.3mm
D = 169.5mm
L = 1400mm
62
α
=
2L/D =
16.5192
β
=
d/D
0.5221
γ
=
D/2T =
11.6096
τ
=
t/T
=
0.7466
σy
=
340 MN/m2
=
From Equation 4.7 the failure load was obtained was 129.9 kN which is
41.3% less than the test failure load (i.e 221.2 kN) and 27.5% higher than that
predicted by LUSAS finite element software (i.e 98 kN).
CHAPTER V
CONCLUSION
5.1.
Conclusion
A finite element elastic plastic analysis was carried out using LUSAS software
to obtain the static strength of a tubular DT joint. From this study, it can be conclude
that:
i)
One-eighth model is considered suitable to predict the static
strength of tubular DT joint.
ii)
From the mesh convergence study, by comparing the static
strength results with difference divisions of element on the
chord wall arranged around the brace, the mesh with 9
divisions was chosen as the optimum mesh.
iii)
From the analysis the failure load (i.e the static strength) of the
DT joint obtained by LUSAS was 98 kN compared to the
64
experimental value, which is 221.2 kN. The difference is about
56%.
iv)
A simple equation is proposed to calculate the static strength of
a tubular DT joint model as follows:
F = - 0.336α -34.66β -1.54γ + 8.29τ + 0.09σy + 134.2
This equation is valid within the following range of geometric
parameter ratios i.e;
11.8 ≤ α ≤ 23.5
0.3 ≤ β ≤ 0.6
11 ≤ γ ≤ 30
0.2 ≤ τ ≤ 0.6
250 ≤ σy ≤ 650
5.2.
Suggestion
There are several suggestion for future studies;
i)
Other softwares such as ABAQUS or COSMOS-M can be used
to obtain the static strength result of a DT joint.
ii)
The analysis can be extended by having axial compression
loading on the chord and brace to compare with the
experimental results obtained by Kang et al. [3]
REFERENCES
1. Lecture Note MAB 1093, “ Analysis, design and construction of marine
structure,” 2004-2005.
2. LUSAS modeller User Manual (1999), LUSAS FEA Version 13
3. Kang, C.T., Moffat, D. G. and Mistry, J., “Strength of DT Tubular Joints With
Brace and Chord Compression”, Journal of Structural Engineering, Vol. 124, No.
7, 1998.
4. Wimpey Laboratories Limited, “Report on UEG Project definition study on
design guidance on tubular joints in steel offshore structure,’ Volumes I and II,
1980.
5. Wimpey Offshore, “ Background to new static strength guidance for tubular joints
in steel offshore structure,” Department of energy, Offshore Technology Report,
OTH 89 308, November 2003.
6. Togo, T. “Experimental study on mechanical behaviour of tubular joint,” Phd
dissertation, Osaka University, Osaka, Japan, 1967.
66
7. Washio, K., Togo, T., and Matsui, Y., “ Experimental studies on local failure of
chords in tubular truss joints: Part I,” Technology Report, Osaka University,
Osaka, Japan, 1968, 18(850).
8. Washio, K., Togo, T., and Matsui, Y., “ Experimental studies on local failure of
chords in tubular truss joints: Part I,” Technology Report, Osaka University,
Osaka, Japan, 1969, 19(874).
9. Boone, T. J., Yura, J. A, and Hoadley, P. W., ‘ Chord stress effects on the ultimate
strength of tubular joints,” PMFSEL rep, 82-1, University of Texas at Austin,
Austin, Texas, 1982.
10. Weinstein, R. M., and Yura, J. A., “The effect of chord stresses on the static
strength of DT tubular connection,” P. M. Furguson Structural Engineering, Lab
rep. 85I, Phase III, 1985.
11. Sanders, D. H,, “strength and behaviour of tubular joints in tension” Msc. thesis,
Univ. of Texas at Austin, Austin, Texas, 1986.
12. Chandrupatla, T. R, and Belegundu A, D, “ Introduction To Finite Elements In
Engineering, Third edition,” New Jersey, Pearson Education International, 2002.
Appendix A
(The loading calculation)
Maximum Load P (assumed)
= 250 x 106 N
Brace diameter, D
= 0.00545 m
Brace circumference L
= πD
= 0.278 m
Load acting on brace
= P/L
= 899180 N/m