video training courses in offshore structures design
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Video Training Courses in Offshore Structures
Below
you
can
have
a
look
at
some
parts
of
video
course
notes
about
Onbottom
stability
of
jackets (Mudmat Design) , Design of Tubular members and Pile groups effects
Item
no.
Subject
of
Training
Course
Video
Duration
Remarks
1 Loads on offshore structures 2.5 hours These Video Courses are
collected
in
10
DVDs,
if
you
are
interested
in
provide
it
pls
contact
me
at
email
in
order
to
arrange
for
dispatching
DVDs
through
TNT
or
DHL
cash
on
delivery
Service.
Total
Cost
is
about
130
us$
(90
for
DVDs
+
40
for
Delivery)
Cash
on
delivery
Service
is
a
model
of
payment
under
which
you
pay
upon
you
received
the
order
2
Marine operation for jackets and topsides (loadout,
sailout,
installation)
2 hours
3 Design
of
Tublar
members
for
jackets 4 hours
4 Design of Tublar joints for jackets 8 hors
5 Inplace
analysis
of
jackets 1 hour
6 onbottom
stability
of
jackets
(mudmat
design) 1.5 horse
7 Basics of Soil Mechanics for Foundation of offshore
Structures
4.5 hours
8
Pile foundations for offshore structures (Design,
Analysis)
6 hours
9 Piles
installation
and
load
test 3 hors
10 Offshore
special
foundations 2 hours
11
Jackup
rig
analysis
and
design
3
hours
12 Sacs
modeling
for
offshore
Structures 3 hours
13
Sacs
analysis
of
offshore
structures
(inplace,
seismic,
Fatigue)
5 hours
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
1
Mudmat Concepts and Design
OUTLINE FOR SESSION 10
Mudmat
Concepts Stability Requirements
Design
Special Foundations
Bucket Foundations
Gravity Foundations
Mudmat Concepts and Design
Mudmat
Mudmats are temporary floor support for the
jacket immediately after the jacket has beenupended from floating horizontal position prior tosupported by piles.
Need to designed with adequate surface area andsufficient strength strength to avoid excessive
ttl t f th j k t
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Advantages of
FRP and Timber Mudmat
FRP and Timber mudmats are used when liftweight is a concern. They will reduce the weightconsiderably.
The design requirement for Cathodic Protectionwill also be reduced
Mudmat Concepts and Design
Large Timber Mudmat
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
FRP Mudmat
Mudmat Concepts and Design
MUDMAT CONCEPTS
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Jacket with Rectangular Mudmat
Mudmat Concepts and Design
Triangular Mudmat
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Rectangular Mudmat
Mudmat Concepts and Design
Circular Mudmat
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Triangular Mudmat
Mudmat Concepts and Design
Mudmat Panels
Mudmat panels can be any one of the following.
Flate Plate (Steel)
Corrugated Plate (Steel)
Timber Plank
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Flat Steel plate
Mudmat Concepts and Design
Timber Plank
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Corrugated Steel plate
Mudmat Concepts and Design
FRP PANEL
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Design Requirements
When the jacket is resting on seabed, it shallsatisfy following requirements
Stability against bearing
Stability against sliding
Stability against overturning
Structural members shall have adequate
strength
Mudmat Concepts and Design
Design Loads
Dead loads
Bouyancy Loads
Wave and Current Loads
Wind Loads
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Design Requirements
When the jacket is resting on seabed, it shall
satisfy following requirements (API RP 2A) Stability against bearing
Stability against sliding
Stability against overturning
Sometimes it is also called “Unpiled Stability” sincethis is prior to the piling of the jacket after which the
jacket is firmly fixed to the seabed by piles
Mudmat Concepts and Design
Stability Against Bearing
As explained earlier, stability against bearing is to
have adequate bearing area to avoid excessivesettlement of jacket / failure of mudmat. This hastwo parts.
Geotechnical Requirement
Structural Requirement
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Factor of Safety against Bearing
The Factor of Safety against bearing shall becalculated as below.
. . u
a
Q F O S
P
The minimum Factor of Safety shall be 2.0 forloads arising from dead weight of the jacket only
and 1.5 for dead weight + environmental loads.
Where Qu is the ultimate bearing capacity of soiland Pa is the applied pressure
Mudmat Concepts and Design
Applied Mudmat Pressure (Dead Load)
The applied mudmat pressure can be calculated for dead
loads alone very easily.
2S x S
a
M yy
W e W H P
A I
Where WS is the total submerged weight of the jacket
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Factor of Safety against Overturning
The Factor of Safety against Overturning shall becalculated as below (for each edge).
. . e
s
F h F O S
W x
Where x is the distance between the verticalload (jacket submerged weight) and the geometriccentre of mudmat system at mudline.
The minimum FOS of 1.5 shall be required.
Mudmat Concepts and Design
Jacket Settlement
Most of Settlement will take place immediately after the
jacket has been placed on seabed. Hence the only immediate settlement using elastic theorywill suffice.
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
W Fe
Mudmat Concepts and Design
Jacket Settlement
Settlement of jacket is an important criteria in designing
the mudmat system as excessive settlement woill leadsubmergence of bottom framing in to the soil. This will leadfollowing issues.
The mudline framing will be subjected to constantupward force on the members
The conductor guide if any will be submerged in to mud
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Jacket Settlement
Elastic settlement of jacket on to the seabed canbe calculated as below.
2(1 ) s
qB I
E
Where q is the uniform applied pressure, B is thewidth of the mudmat, E is the Modulus of the soil, is the poissons ratio and Is is the influence
coefficient and shall be calculated depending on theshape of the mudmat.
Mudmat Concepts and Design
Settlement of Circular Footing
Vertical settlement of circular footing is given by
QGR
41
QGR
uv
4
1 Where
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
bh Am 4
23
)2/2/(4
12
4b Bbh
hb I yy
yy xxm
sa
I
xM
I
yM
A
W P
)()(
23
)2/2/(412
4h H bh
bh I xx
Where x and y are co-ordinates of points at which the mudmat pressure is
required
Rectangular Mudmat system
Mudmat Concepts and Design
22
4 44 H DDI
Circular Mudmat system
2
4
4 D Am
yy xxm
sa
I
xM
I
yM
A
W P
)()(
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
23
32
22
36
4b Bbh
bh I yy
23
32
22
36
4 H bh
bh I xx
Triangular Mudmat system
24
bh Am
yy xxm
sa
I
xM
I
yM
A
W P
)()(
Mudmat Concepts and Design
23
3bh
Triangular Mudmat system
2
4bh
Am
yy xxm
sa
I
xM
I
yM
A
W P
)()(
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
BEARING CAPACITY OFMUDMATS
Mudmat Concepts and Design
BEARING CAPACITY
The ultimate bearing capacity (qu) isdefined as the least pressure which
would cause shear failure of the
supporting soil immediately below
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
MODES OF FAILURE
a) General failure
b) Local shear
c) Punching failure
The mode of failure depends on thefollowing
- Foundation type and geometry- Soil compressibility
Mudmat Concepts and Design
MODES OF FAILURE
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
THEORY OF PLASTICITY
A suitable failure mechanism shall befound by either inspection, trial or limit
theorems. Two bounds can be defined.
Lower Bound True failure load is large than the load
corresponding to an equilibrium system
Upper Bound The true failure load is smaller than the load
corresponding to a mechanism if that load isdetermined using the virtual work principle
Mudmat Concepts and Design
EQUILIBRIUM SYSTEM
An equilibrium system, or a statically admissible field
of stresses is a distribution of stresses that satisfiesthe following conditions
a) it satisfies the conditions of equilibrium in each pointof the body
b) it satisfies the boundary conditions for the stresses
) h i ld di i i d d i i f h
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Mechanism A mechanism, or a kinematically admissible field
of displacement is a distribution of displacementsand deformations that satisfies the followingconditions.
a) the displacement field is compatible, i.e. nogaps or overlaps are produced in the body(sliding of one part along another part isallowed)
b) it satisfies the boundary conditions for thedisplacements
c) wherever deformations occur the stressessatisfy the yield conditions
Mudmat Concepts and Design
IDEALIZED STRESS-STRAIN RELATIONSHIP
s t r e s s
Y’
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
STATE OF PLASTIC EQUILIBRIUM
Mudmat Concepts and Design
cos2)sin1()sin1(
)cot2(2
1
)(2
1
sin
13
31
31
c
c
)sin1(
2sin1
2
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
LOWER BOUND SOLUTION
Mudmat Concepts and Design
cq
c
)1(2)1(
)1(2)1(
0for12/45tan2/45
245tan22/45tan
1.31.2
2
2
31
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
qcq
BqB B Bc
B Bq
ult
ult
2
022
UPPER BOUND SOLUTION
Mudmat Concepts and Design
Simplified bearing capacity for a ø – c soil
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
yqcult
p
p p p
p
p
ult
p
ult
p p p p
H
O
H
O p
yBN N qcN q
K K yB K K
q K K
cq
P cA
H B y
Bq
K cH K H q K yH P
dz cq yz dz P
cos4coscos
2
0cossin
cos2
.22
.2..2
245tan2
245tan)()(
2
2
2
1
Mudmat Concepts and Design
FAILURE UNDER A STRIP FOOTING
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
FOOTING AT DEPTH D BELOW THE
SURFACE
Mudmat Concepts and Design
Width offoundation (B)not less than 1m. Water tableat least B belowbase offoundation
>600
200 – 600
300
100 – 300
Dense gravel or dense sand and gravel
Medium dense gravel or medium dense
sand and gravel
Loose gravel or loose sand and gravel
Compact sand
Medium dense sand
RemarksBearingvalue(kN/m²)
Soil type
PERSUMED BEARING VALUS (BS 8004: 1986)
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
factorscapacity bearingand,
Depth
Breadth
capacity bearingultimatethe2
1
qc
u
qcu
N N N
D
B
q
DN cN BN q
Mudmat Concepts and Design
tan)1(801N
factorscapacityBearing,
cot1
/2)45(tan)tan(exp 2
N
N N
)(N N
N
cq
qc
o
q
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
qc f DN cN BN q 2.14.0
Length
Breadth
capacity bearingultimateThe
2.13.0
L
B
q
DN cN BN q
f
qc f
Circular footing
Square footing
Mudmat Concepts and Design
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Skempton’s values of Nc
for øu = 0 (Reproduced
from A.W.Skempton (1951)
Proceedings of the BuildingResearch Congress,
Division 1, p.181, by
permission of the Building
Research Establishment, ©
Crown copyright)
Mudmat Concepts and Design
RECOMMENDED
BEARING
CAPACITY
FACTORS
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
ECCENTRICALLY-
LOADED FACTORS
Mudmat Concepts and Design
AREA REDUCTION
FACTORS
ECCENTRICALLY-
LOADED
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
42 – 5885 – 100Very dense> 50
25 – 4265 – 85Dense30 – 50
8 – 2535 – 65Medium dense10 – 30
3 – 815 – 35Loose4 – 10
0 – 30 – 15Very loose0 – 4(N
I
)60
Id
(%)ClassificationN Value
DENSITY INDEX OF SANDS
Mudmat Concepts and Design
Bearing capacity calculationsby Davis and Booker
The bearing capacity can be calculated when the soil profile
is varying linearly with depth
)1(4
ccuor u S B
N C F q
factor Shape
L
B
N
N S
c
c
NC= 5.14 for strip footing
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Fr - Shear Strength Facto r
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000
Rh o
Mudmat Concepts and Design
SPECIAL FOUNDATIONS
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30 May 2008 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Special Foundations
Suction Anchor(Bucket Foundation)
Gravity Foundation
Mudmat Concepts and Design
Suction Anchors (Piles)
A suction anchor is an inverted top capped hollow
cylinder of fairly large diameter with a length todiameter ratio (L/D) of 1.0 to 2.0 that is embeddedinto the sea bed. Self-weight and differential waterpressure can facilitate easy installation of this typeof anchor into the sea bed. This differential water
( ti ti ) b t d b
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
The main pile advantages of this anchor over tension piles aredue to the weight of the soil plug inside and the freely availablehigh ambient water pressure which offers two advantages; easyinstallation of the anchor with its active suction arrangement andmobilization of passive suction force at the anchor bottom during
uplift. Further, the large-diameter sealed top provides asubstantial space for additional ballast, which can increase thebreakout resistance
Mudmat Concepts and Design
Suction Breakout Factors
From the equilibrium considerations (referring tofigure 1) the uplift pullout capacity of the suction
anchor is given by
Pu = Wa + Fext + Ws + Wb + R b
Where
W i th i ht f th h
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Indian Institute of Technology Madras-36
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Mudmat Concepts and Design
Mudmat Concepts and Design
Pu = Wa + Ws + Fext + Rb
Rb1 = Pu – (Wa + Ws + Fext)
From consideration of rupture in clay under tensile loading (Vesic, 1971) the
bottom breakwater resistance is expressed in a non-dimensional form as
Fext = Cu Ase
From the plug equilibrium (refer to figure 13) equations can be written as:
Rb2 + Ws - Ps + Fint
Rb2 = Ps + Fint - Ws
Design of Tubular Members Buckling
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9/16/2015 Dr. S. NallayarasuDepartment of Ocean Engineering
Indian Institute of Technology Madras-36
1
CONTENTS Introduction
Necessity of tubular
Loading and Load types
Factors affecting strength
Method Tubular Fabrication
Steel Making process
Seam Less Pipes
Fabricated Pipes
Residual stresses
Material Properties
Yield and Tensile Strength Modulus of Elasticity
Imperfections
Out-of roundedness
Misalignment
Straightness deviation
Ultimate Strength
Factors affecting ultimate strength
Ultimate strength of sections and span
Buckling
Local Buckling
Global buckling (Euler)
Effective Length
Design Methods
Allowable Stress Design (ASD)
Load and Resistance Factor Design (LRFD)
API RP 2A - ASD
Applied stresses
Allowable stresses
Interaction
API RP 2A - LRFD Load and Resistance factors
Interaction
Hydrostatic Pressure
Hoop stresses
Interaction
Design examples
Tubular section
Ring stiffened cylinders
Design of Tubular MembersT b l M b
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Indian Institute of Technology Madras-36
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Tubular Members
Good Hydrodynamic Properties (Low Cd and Cm)
good buoyancy to weight ratio
Good resistance against hydrostatic pressure
Uniform property across the section
No torsional buckling Good Ultimate strength compared to others
Full moment connections possible
Tubulars or circular hollow sections (CHS) are
used for jacket structures commonly due totheir versatility in resisting various forces. Themajor reasons are listed below.
However, the tubular member connections aresusceptible to fatigue cracks and havefabrication difficulty due to non-linear surfacesat intersection !.
Design of Tubular Members
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Indian Institute of Technology Madras-36
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Load Categories
Gravity loads
Wind Loads
Wave and Current Loads
Seismic Loads
Drilling Loads
Following external forces are applied tothe structure which in turn induceinternal loads on the members.
The above forces shall be applied to thestructure in a three dimensional analysis.
The member internal loads shall beextracted from the analysis results.
Design of Tubular Members
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Indian Institute of Technology Madras-36
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Member internal loads
Design of Tubular Members
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Indian Institute of Technology Madras-36
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FREE BODY DIAGRAM
Following member internal loads mayneed to be considered
Following member internal loadsmay need to be considered
Axial (Compression or tension)
Bending (In-plane or Out-off plane)
Torsion
Shear (in-plane or Out-off plane)
External Pressure
Design of Tubular Members
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Material properties (E, Fy, Ft )
Imperfections and residual stresses
Production method of tubular
Boundary conditions Loading
Geometric proportions: L/D, D/t
Stiffeners: circumferential or longitudinal
Factors Affecting Strength
Following factors affect the strength of the member.
Design of Tubular Members
i l i ( l)
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Indian Institute of Technology Madras-36
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Density
7850 kg/m3 or 78.5 kN/m3
Tensile stress (Ft)
Varies between 490 to 600 MPa
Yield stress (Fy )
Is in the range of 250 – 400 MPa
Modulus of Elasticity (E)
Normally taken as 200000 – 210000 MPa
Strain in elastic range is 0.2%. Poisson Ratio is in the range of 0.3 to 0.4
Friction coefficient is around 0.3 to 0.4
Material Properties (Steel)
The physical and mechanical properties of steel used in the design are listedbelow.
Design of Tubular MembersImperfections
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Indian Institute of Technology Madras-36
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Imperfections
Variation is cross section
Variation in thickness
Residual stresses
Out-off roundedness
Out-off straightness
Misalignment across thickness
Misalignment along length
Imperfections in fabrication and assembly can
cause the reduction in the strength of thestructure and must be minimized. Hencematerial and fabrication specifications shallinclude control parameters to limit the same.This is called “Tolerances”. Following are some
of the imperfections that need to be included.
Design of Tubular MembersTubular Production Methods
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Indian Institute of Technology Madras-36
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Tubular Production Methods
Tubular or Circular Hollow Sections (CHS) can be made using any one of thefollowing methods.
Seamless tube production by piercing of heated bars andextruding techniques
Hot forming steel plate and induction welding along thelongitudinal direction
Cold forming methods coils of plate and resistance welding alonglongitudinal direction
Cold forming of coils of plate and resistance welding along radialdirection
Cold forming of flat plates and assemble to make pipes
Each method has its own limitations, advantages and disadvantages. Hencedepending on the availability and technical requirement, production methodshall be selected.
Design of Tubular Members
Steel Making Process an outlook
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01 August 13 Department of Ocean EngineeringIndian Institute of Technology Madras-36
10
BLAST FURNACE
STEEL MAKING
PROCESS
HEAT
TREATMENT
ROLLING
IRON ORE PIG IRON
PIG IRON INGOT, BILLETS
INGOT SLABS
SLABS PLATES & SHAPES
Steel Making Process – an outlook
Design of Tubular Members
Steel Making Process an outlook
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Steel Making Process – an outlook
Source : Nippon Steel Corporation, Japan
Design of Tubular Members
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Design of Tubular Members
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Design of Tubular Members
Pilger and Piercing
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Pilger and Piercing
The large size bars areused to produce pipes.
This has been in use forseveral decades in the
pipe producing mills.
Both thin and thick pipescan be made using this
method.
Limiting size for suchproduction depends onthe mill but generally
diameter larger than 20”is normally not availableby this method.
Design of Tubular MembersCold Forming Processes and Resistance welding
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g g
In this method, sheet coilof plates is used to formcircular sections usingrollers.
The folded section is thenwelded by resistancewelding.
The application of thismethod is also limited bydiameter and generally to20”.
Design of Tubular MembersHot forming and induction welding
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g g
This method is very similarto the forming and weldingmethod except that this isdone in hot condition.
The coils of plate is heatedfirst before it is bent androlled to the shape.
The folded section is thenwelded by inductionwelding.The application ofthis method is also limitedby diameter and generally to
20”.
Design of Tubular MembersCold Forming Processes
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In this method, the plate
sections of specific lengthand width will be rolled toshapes either in semi-circular shape or in quarterarc of a circle.
The rolled sections of thecircular arc is then joined byarc welding to form a longpipe. This method is very
commonly used for makingpipes of any diameter usedin the steel fabricationindustry. Using this method,pipes of any diameter can be
made for use.As an alternative to the plates, rolls of plate can be used to form the pipe usingspiral form and then welded, and it is called “Spirally welded pipes”. Pipesmanufactured using this method is normally not used in the primary structure.
Design of Tubular MembersFabrication tubulars
T b la can be fab icated f om flat plates No mall flat
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cold rolling a flat plate and weld at the seam toform a can (length up to 3m). The longitudinalseam may be one or more depending on the
width of the plate available. This one piece of pipemade from plates is called “Can”.
Several cans can be welded to form a long tube
The long seams shall be arranged such that theorientation in each can away by 90o.
Welding between Cans is called transverse seamor circumferential weld.
This method of fabrication introduces out-of-roundness, out of straightness imperfections andresidual stresses in both the longitudinal andcircumferential directions
Tubular can be fabricated from flat plates. Normally, flatplates are rolled to form circular arcs and welded toform circular section as shown in figure.
Design of Tubular MembersResidual Stresses
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Residual stresses developed during welding of plates to form pipes and
welding of two pieces of pipes to form length may affect the final strengthunless these stresses are relieved.
Bending plates to form circular arcs induces bending strain andstresses depending on the radius of bend and D/t ratio. Larger the
bending radius, smaller the stresses. Larger the D/t ratio, strain willbe smaller.
Heat induced stresses during welding could be large due torestraint provided by the joining components.
Stresses induced during joining of pipe segments due to restrictionon the expansion during welding.
Design of Tubular Members
Consideration of Residual Stresses in design equations
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Consideration shall be given to account for the residual stresses in
members in the design equation.
As these stresses exist even before the member is loaded, these
stresses shall be deducted from the allowable stresses. However,
it will not be practical to account for in each case.
Hence it is better to reduce the yield stress by certain percentage
to account for the residual stresses. DNV codes suggests a 5%
reduction in yield stresses to residual stresses of welded section
g q
Design of Tubular MembersEffective method of including Imperfections in design
The method to include the imperfections in fabrication is a difficult process as
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The method to include the imperfections in fabrication is a difficult process asthe imperfections will not be known at the stage of design.
Hence certain assumptions has to be made during the design with limitations ondeviations that can be tolerated both with respect to design aspects andoperational aspects.
Design aspects will include change in cross sectional area, moment of inertia,center of gravity and other geometric properties. On the other hand, theoperational aspects include deviation from verticality, sagging of beams which
affects the daily operation for which the structures are built.
Hence restrictions on these imperfections which may happen during theconstruction stage may have to be imposed during the design stage.
These restrictions are called “Construction Tolerances” which shall beincorporated in the design equations so that the design need not be revised ifthese deviations are within the design tolerances.
Design of Tubular MembersOut-of Straightness
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Out-of straightness tolerance o shall be
measured at all points along the length of themember and the maximum shall be taken forconsideration.
DNV (1982) specifies a maximumlimit of 0.0015L (L/666) as the limit
API Spec 2B specifies a maximumlimit of L/960 or 9.50mm in any12200mm length (L/1284) whichever
is lower
This tolerance is very important as thisdeviation will lead to eccentric load andcorresponding moment.
Design of Tubular MembersOut-of Roundedness
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Out-of roundedness tolerance for fabrication of
tubular sections can be calculated as shown infigure using Dmean, Dmax and Dmin.
The Dmax and Dmin shall be measured across
diagonals at any angle and not necessarily at 90degrees. Out-of roundedness is normallyspecified as
max min %mean
D D D D Dδ −=
API Spec 2B specifies that the above tolerance
shall not exceed 2% and DNV specifies that thetolerance shall not exceed 1%.
Design of Tubular MembersEccentricity due to variation in Wall thickness
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Maximum thickness variation = ∆t = tmax - tmin
Effective axial load eccentricity due to ∆t can be calculated and included inthe stress calculation.
Design of Tubular MembersMisalignment in Butt Joint
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Misalignment in butt joint is veryimportant as it induces additionaleccentricity in axial loads andstresses.
API allows an eccentricity “e” of
• 0.2t1• e < 3.2mm for welding from
one side
• e < 6.4 mm for welding fromboth side.
DNV allows an eccentricity of 0.15t1 (minimum thickness) or 4mm whichever is less.
When the eccentricity in construction exceeds this limit, the design must be reviedadequate modifications shall be carried out to assure the d=safety of design.
Design of Tubular Members
Ulti t t th f ti
Ultimate Strength
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Ultimate strength of a section or
member depends on the efficientlyof the section to redistribute thestresses when the stresses exceedyield. Increase load carrying
capacity after reaching elastic limitis called “Ultimate Strength”.
Premature failure before reachingelastic limit is called “Buckling”.
Buckling strength of a member isfound to be considerably less thanthe theoretical elastic capacity.
Hence in order to determine the ultimate strength, first it is necessary to establish
that the section / member has sufficient buckling capacity to reach elastic capacity.The ultimate strength of the section / member can be computed based on thesection property and member boundary conditions.
Design of Tubular MembersBuckling Theory
B kling is a phenomenon that the bif ation of eq ilib i m to nstable state
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Buckling is a phenomenon that the bifurcation of equilibrium to unstable state
under axial load when the slenderness exceeds 50. This was explained byLeonhard Euler in 1757 even if there is no axial load.
The column at its unstablebifurcation of equilibrium, fails dueto lateral displacement for aparticular load called “Critical Loador Buckling Load”.
The critical load differs if the endof the column is restrained inlateral direction. This is evidentfrom the photograph showing theexperiment.
Slenderness is the ratio of itslength to the radius of gyration of the section.
Design of Tubular MembersEffective Length Factors (K)
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Effective length factor is
defines as the ratio ofbuckling strength of a columnwith simple pin-pin endconditions to that of a actual
column with any otherboundary conditions.
Buckling capacity of a columnwith pin-pin end conditions isgiven by
( )
2
2cr
EI P
KL
π =
In which K is called Effective length factor and is 1.0 for pin-pin endconditions of the column. For other cases, it is shown in the table above.
Design of Tubular MembersLocal and Global buckling
Buckling of thin walled tubes (D/t > 20) can be
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Buckling of thin walled tubes (D/t > 20) can be
classified in to the following.
Local buckling – due to instability of local shell wall
Global buckling – due to slenderness
Local Global
In which the D is the diameter of the cylinder and tis the wall thickness.
Local buckling is governed by the D/T ratio and theglobal buckling is governed by the KL/r ratio. Local
buckling may also happen due to bending of largediameter tubular.
Design of Tubular MembersFactors influencing Ultimate strength
Following factors influences the ultimate strength of a column or beam
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Following factors influences the ultimate strength of a column or beam
Cross section
Boundary condition at the ends
Load distribution
Stress strain characteristics of the material
Cross section influences the redistribution of stresses while the boundarycondition affects the redistribution of stresses across the length.
The stress strain relationship affects the ultimate load depending on the strainhardening range of the material. i.e. the gap between the yield point and theultimate point the stress strain curve.
All the factors put together, a beam or column can sustain larger load compared
to its load capacity at elastic range.
Design of Tubular MembersELASTIC AND PLASTIC MOMENT CAPACITY – RECTANGULAR SECTION
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2 2
y F h P b=
22
2 2 3 6
y
y
F h h bhM b F
= =
2
22 4 4
p y y
h h bhM F b F
= =
2 p y
h F b=
Design of Tubular Members
ELASTIC AND PLASTIC MOMENT CAPACITY– CIRCULAR SECTION
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2
12 4
p y D P F π =
2 34
8 3 6 p y y
D D DM Pa F F π π
= = =
4
3
D
π
3
32 y
DM F
π =
Plastic moment capacity of solid cross section is give below.
Elastic moment capacity of solid crosssection is give below.
21
2 2 4
y F D P
π
=
Design of Tubular MembersPLASTIC MOMENT CAPACITY HOLLOW CIRCULAR SECTION
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2
Dds rd d φ φ = =a tds=
A hollow circular section of diameter Dand wall thickness t is divided in tofour symetric segments.
Consider a small arc of ds with area
of a in the first quadrant of the pipeas shown in figure.
The area of the segment can becalculated as tds where ds can be
calculated using small angleapproximation.
Using the symetry, the momentcapacity can be integrated for first
quadrant and multiplied by 4.
Design of Tubular MembersPLASTIC MOMENT CAPACITY– CIRCULAR HOLLOW SECTION
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p y P F dt π =
2
0
4 cos2
P y
DM AF
π
φ =
2
0
4 cos2 2
P y
D DM F t d
π
φ φ
=
22
0
cos P yM F D t d
π
φ φ =
2= P yM F D t
Design of Tubular MembersLoad category, Factors and combinations
Load category and the corresponding load factors are listed below
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• D1 – Dead Load 1, e.g. Self weight• D2 – Dead Load 2, e.g. equipment weight• L1 – Live Load 1, e.g. weight of fluids• L2 – Live Load 2, e.g. operating forces
• We – Extreme wind, wave and current loads• Wo – Operating wind, wave and current loads• Dn – Inertial Load correspond to Wo
• Dead Load: 0.9 to 1.3• Variable Load: 1.3 – 1.5• Environmental load: 1.3 – 1.4
• Factored gravity loads•1.3D1 + 1.3D2 + 1.5L1 + 1.5L2
• Wind, wave and current loads• 1.1D1 + 1.1D2 + 1.1L1 + 1.35(We + 1.25Dn)• 0.9D1 + 0.9D2 + 0.8L1 + 1.35(We + 1.25Dn)
•1.3D1 + 1.3D2 + 1.5L1 + 1.5L2 + 1.2(Wo + 1.25Dn)• Earthquake
•1.1D1 + 1.1D2 + 1.1L1 + 0.9E•0.9D1 + 0.9D2 + 0.8L1 + 0.9E
Load combinations and the associated load factors required as per API RP 2A LRFD
Load category and the corresponding load factors are listed below
Design of Tubular MembersComparison of ASD and LRFD a beam column design with uniformly
distributed lateral load and axial load
Design lateral Load w kN/m
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Design lateral Load = w kN/m
Axial Load = P kN Span = L m Self Wight = ρ kN/m Yield Strength = F y MPa
a
P L f
A
ρ +=
2
2b
wL f =
1 1 0.6a y F F φ φ = ≤
2 2 0.66b y F F φ φ = ≤
1.0a b
a b
f f
F F + ≤
Appliedstresses
Allowable Axial
stress AllowableBendingstress
Interaction
φ1 and φ2 are to be computed includingthe buckling and slenderness effects
1 2a
P L f
A
γ γ ρ +=
2
3
2b
wL f
γ =
0.85c c y c F F φ φ = =
0.95b b y b F F φ φ = =
1.0c b
c y b y
f f
F F φ φ + ≤
Applied
stresses
Allowable Axialstress
AllowableBendingstress
Interaction
φ1 and φ2 are to be computed including thebuckling and slenderness effects. γ 1, γ 2 and γ 3are load factors 1.5, 1.3 and 1.5 respectivelyfor live, dead and wind loads
Design of Tubular MembersASD DESIGN PROCEDURE FOR TUBULAR MEMBERSDivide the member in to sections and calculate the axial, bending and shear forces ineach section along the length At-least 3 sections shall be checked
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each section along the length. At-least 3 sections shall be checked.
The variation in section propertysuch as diameter or wall thicknessshall also be taken in toconsideration for calculating thesection property along the memberlength in each section.
The axial buckling capacity shall be
calculated using the variable crosssection along the length.
Variation of internal forces shall
also be computed for varioussections along the length.
Free Body Diagram with member internal forces
Design of Tubular MembersASD DESIGN PROCEDURE FOR TUBULAR MEMBERS Divide the member in to sections and calculate the axial, bending and shear forces in
each section along the length At-least 3 sections shall be checked
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each section along the length. At least 3 sections shall be checked.
Establish geometric properties such as sectional area, moment of inertia, effectivelength factors, radius of gyration for each section.
Calculate the applied axial(f a), bending(f bx , f by), hoop (f h) and shear stresses (f s)using the geometry of the section and the applied axial, bending, hydrostatic and
shear forces. Establish the slenderness ratio(kL/r) and calculate the allowable axial stress (Fa)
and calculate the elastic buckling stress (F xe) and inelastic buckling stress (F xc) Establish the D/t ratio and calculate the allowable bending stress (Fb) Compute the allowable stresses for hoop using Elastic Hoop buckling stress (F
he) and
critical hoop buckling stresses (Fhc). The combined effect of loads is obtained using interaction of these loads in an
appropriate manner using axial, bending, hoop and shear interaction formulae forthe following cases.
Axial Bending Shear Hoop
Axial and bending Axial and hoop Shear and bending
Design of Tubular Members
Following method shall be used in calculation of applied stresses in members.
Applied Stresses in Tubular members
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a P f A
=
and y x
bx by
xx yy
M Y M Y f f
I I
= =
0.5 s
V f
A=
2
h
h
P D
f t =
Axial Stress
Bending Stresses
Shear Stress
Hoop Stress
Properties of Tubular section( )( )22 24
D D t A
π − −=
( )( )44 264
xx yy
D D t I I
π − −= =
Where P, V, M x , M y and Ph (= h) are the axial load, shear, in-plane and out-ofplane moments and hydrostatic pressure respectively. Y is the half diameter.
Design of Tubular Members
Following method shall be used in calculation of allowable stresses in members.
Allowable Stresses for Tubular members
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Axial Stress – Allowable axial stress in compression shall include the effect of slenderness ratio (kL/r) to determine whether yielding or global buckling govern thedesign. This is applicable for compression where as in tension it is taken as 0.6F yThe effect of local buckling of tubular sections due to axial loads is taken in toconsideration by computing the limiting values of Fy using critical hoop bucklingstress (Fxc).
Bending Stresses – Allowable bending stress depends on the D/t ratio and the
maximum value is to be limited to 0.75F y.
Shear Stress – Allowable shear stress is to be taken as 0.4F y
Hoop Stress – The allowable hoop stress is computed based on local buckling
effects due to external hydrostatic pressure. This is done by computing criticalelastic buckling stress (Fhe) and inelastic buckling stress (Fhc).
Design of Tubular MembersAllowable Axial Stress(Compression)
Allowable AxialStress (Tension)
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The allowable axial compressive stress, Fashould be determined from the followingformulae for members with a D/t ratioequal to or less than 60. Effect of localbuckling shall be considered by
substituting Fy with local buckling stress.2
2
3
3
2
2
122
( / )1
2 for /
3( / ) ( / )
5 / 3 8 8
12 for /
23( / )
2
y
c
a c
c c
a c
c
y
KL r F
C F KL r C
KL r KL r
C C
E F KL r C
KL r
where
E C
F
π
π
−
= <
+ −
= ≥
=
Fy = Yield stress (or min (Fxe, Fxc))
E = Young’s Modulus of elasticity
K = effective length factor
L = unbraced length
r = radius of gyration
The allowable tensile stress, Fafor cylindrical memberssubjected to axial tensile loads
should be determined from0.6a y F =
To account for local bucklingand imperfections, Fy shall bereplaced by minimum of Fxeand Fxc.
Design of Tubular MembersLocal Buckling Stress Due to Axial Load
The local buckling stress for use with axial stress limits
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Elastic Local Buckling StressThe elastic local buckling stress, Fxe for columns subjected to axial loadswhen D/t ratio greater than 60 and less than 300 should be determined
from:
Fxe = 2CE t/D
Where
C = Critical elastic buckling coefficient to be taken as 0.3 (instead of 0.6) to
account for imperfections as per API Spec 2B.D = outside diameter
t = wall thickness
Inelastic Local Buckling Stress
The inelastic local buckling stress, Fxc, should be determined from:Fxc = Fy x [1.64 – 0.23 (D/t)
¼] FxeFxc = Fy for (D/t) 60
g
shall be calculated in stages using elastic buckling stress
Design of Tubular MembersEffective length factor K as specified in API RP 2A
Deck Truss webmembers
Deck Trusschord members
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members
SuperstructureLegs
chord members
Jacket Legs
Jacket Braces
Design of Tubular MembersAxial Tension and Hydrostatic Pressure
When member longitudinal tensile stress and hoop compressive stresses
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(collapse) occur simultaneously, the following interaction equation should besatisfied.
2 2 2 1.0 A B A Bν + + ≤(0.5 )
( )a b h x y
f f f A SF
F
+ −= )(SF F
f B h
hc
h=
stressncompressiohoopof valueabsolute
stress bendingactingof valueabsolute
stressaxialactingof valueabsolute0.3,ratiosPoisson'
=
=
===
h
b
a
f
f
f v
Load case Axial
Tension(SFx)
Bending Axial
Comp.
Hoop Comp.
(SFh)
Operating 1.67 Fy /Fb 1.67 to 2.00 2.00
Storm 1.25 Fy /1.33Fb 1.25 to 1.50 1.50
ncompressiohoopfor factor safety
tensionaxialfor factor safety
stresshoopcritical
StrengthYield
=
=
=
=
h
x
hc
y
SF
SF
F
F
Factor of Safety against Hydrostatic collapse with other loads
Design of Tubular MembersAxial Compression and Hydrostatic Pressure
When longitudinal compressive stresses and hoop compressive stresses occur
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simultaneously, the following equations should be satisfied.
0.1
0.1)()()5.0(
≤
≤++
hc
hh
h
y
b x
xc
ha
F f SF
SF F
f SF
F
f f
,
,
where
0.15.0
5.02
h
heha
x
xeaa
ha
h
haaa
ha x
SF
F F
SF
F F
F
f
F F
f f
=
=
≤
+
−
−
SF x = safety of factor for axial compression
SF b = safety of factor for bending
f x = f a+f b+(0.5 f h )
f x should reflect the maximum compressive stress combination
hafor f 0.5 x f >
Refer to Member Local Buckling stresses
F xe = Member elastic local buckling stress due
to axial compression
F xc = Member inelastic local buckling stress
due to axial compression
Design of Tubular Members
Circumferential stiffening ring size may be selected on the following
Ring Design
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approximate basis.
hec F E
tLD I
8
2
=
Where
Ic = required moment of inertia
for ring composite sectionL = ring spacing
D = diameter of pipe
t = thickness of pipe
Fhe = Elastic buckling stress
Design of Tubular Members
The ring spacing is defines as the distancebetween supports or between the actual
Ring Spacing
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ring location. Hence the following procedureshall be adopted in designing a ringstiffened cylinders against combined axialand hoop stress.
a) Compute the axial and bending stressesusing unstiffened cylinders
b) Assume the spacing of rings as initialmember length “L” between the supportsor nodal connection as shown in figure
c) Determine the critical elastic hoop stress(Fhe) and compute the inelastic hoopstress (Fhc).
d) Determine the interaction ratio usingappropriate factor of safety.
e) Repeat the above steps (b) to (d) using areduced spacing “S” and stop if the UC isless than 1.0
Design of Tubular Members
1.1b Dt =
Moment of inertia of Ring stiffeners
Effective
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eff
( ) ( ) ( )
( )
0.5 0.5 0.5eff f w f f f na
eff w f
b t h t t t h t h bt t y
b t t h bt
+ + + + +=
+ +
( )
( )
( )
32
32
32
0.512
0.512
0.512
eff
xx eff f na
f na
f
f na f
b t
I b t h t y t
thth h t y
bt bt y t
= + + − +
+ + + −
+ + −
shell width
Neutral axis
Moment of inertia
Design of Tubular Members
Verify a jacket brace of diameter 762mm x 15.88mm against axial loads of 1200 kN, andin-plane and out-of-plane bending moment of 800 and 600 kNm respectively. The unbraced length of the member is 15m and yield strength is 345 Mpa.
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DESIGN OF A TUBULAR MEMBER AS PER API RP 2A (WSD)INPUT DATA
Diameter of brace D 762 mm⋅:=
Wall thickness t 15.88 mm⋅:=
Yield Strength Fy 345 MPa⋅:=
Weight density ρ s 78.5kN
m3
⋅:=
Modulus of elasticity E 2.0 105
⋅MPa
⋅:=
Unbraced length Ls 15 m⋅:=
Effective length factors K y 0.9:= K z 0.9:=
Axial Load P 1200 kN⋅:=
Bending Moment about y axis My 800 kN⋅ m⋅:=
Bending Moment about z axis Mz 600 kN⋅ m⋅:=
Design of Tubular MembersGEOMETRIC PROPERTIES
Sectiona area Asπ
4D
2D 2 t⋅−( )
2−⋅:= As 3.7 10
4× mm
2⋅=
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Moment of inertia about y axis Iyπ
64D
4D 2 t⋅−( )
4−⋅:= Iy 2.6 10
9× mm
4⋅=
Section Modulus for y axis bending Zy2 Iy⋅
D:= Zy 6.8 10
6× mm
3⋅=
Radius of gyration for y axis bending R yIy
As:= R y 263.9 mm⋅=
Due to symetry, z axis properties Iz Iy:= Zz Zy:= R z R y:=
Slenderness ratio for y axis bending KLRy K y Ls⋅R y
:= KLRy 51.165=
Slenderness ratio for z axis bendingKLRz
K z Ls⋅
R z:= KLRz 51.165=
Euler buckling stress Fe 12 π
2
⋅ E⋅23 KLRz
2⋅
:= Fe 393.4 MPa⋅=
Moment reduction factor Cm 1:=
Design of Tubular Members
ALLOWABLE BENDING STRESS AS PER API RP-2A SECTION 3.2.3
D
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Diametr to wall thickness ratio Ratio Dt
:= Ratio 47.985=
Allowable bending stress F b 0.75 Fy⋅ Ratio10340
Fy
≤if
0.841.74 Fy⋅ D⋅
E t⋅−
Fy⋅
10340
FyRatio<
20680
Fy≤if
0.72
0.58 Fy⋅ D⋅
E t⋅−
Fy⋅20680
Fy Ratio≤ 300≤if
:=
F b 240.1 MPa⋅=
Design of Tubular MembersALLOWABLE AXIAL STRESS AS PER API RP-2A SECTION 3.2.2
Critical elastic buckling coeficient Ceb 0.3:=
El ti l l b kli t F 2 C b E
t
F 2501 MP
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Elastic local buckling stress Fxe 2 Ceb⋅ E⋅ D⋅:= Fxe 2501 MPa=
Inelastic local bukling stress Fxc FyD
t60≤if
min Fxe 1.64 0.23 Dt
1
4
⋅−
Fy⋅,
Dt
60>if
:=
Fxc 345 MPa=
Limiting Slenderness ratio Cc2 π
2⋅ E⋅
min Fy Fxc,( ):= Cc 107=
Allowable axial stress incompression
Fa
1KLRz
2
2 Cc2
⋅
−
min Fy Fxc,( )⋅
5
3
3 KLRz⋅
8 Cc⋅+
KLRz3
8 Cc
3
⋅
−
KLRz Cc
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Computed Bending Stress f byMy
Zy:=
f by 117.6 MPa⋅=
f bzMz
Zy
:= f bz 88.2 MPa⋅=Computed Bending Stress
Unity Check ratio UCf a
Fa
f by2
f bz2
+
F b+
f a
Fa0.15≤if
UC1f a
Fa
Cm f by2
f bz2
+⋅
1f a
Fe−
F b⋅
+←
UC2f a
0.6 Fy⋅
f by2 f bz2+
F b+←
UC max UC1 UC2,( )←
f a
Fa0.15>if
:=
UC 0.86=
Design of Tubular Members
DESIGN OF A INTERNAL RING STIFFENER FOR BOUYANCY TANKS
Verify a buoyancy tank of diameter 2000mm x 15mm for a hydrostatic pressure of 100mdepth. The spacing of rings is 2m and yield strength is 250 Mpa.
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DESIGN OF A INTERNAL RING STIFFENER FOR BOUYANCY TANKSInput
Water Depth Wd 100 m⋅:=
Outer Diameter D 2000 mm⋅:=
Thickness of shell t 15 mm⋅:=
Yield Strength of material Fy 250 MPa⋅:=
ρ s 78.5 kN
m3
⋅:= ρ w 10.25 kN
m3
⋅:=Density of steel and water
Young's Modulus E 2.0 105
⋅ MPa⋅:=
Assume Dia/Thickness ratio Dt
133.333=
Spacing of ring stiffeners Sp 2 m⋅:=
Design of Tubular MembersBuckling Coefficient
Maximum hydrostatic pressure ph ρ w Wd⋅:= ph 1.025 MPa⋅=
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f h ph D⋅
2 t⋅:=
Maximum hoop stress f h 68.3 MPa⋅=
Geometric parameter MSp
D
2 D⋅
t
0.5
⋅:=
M 16.33=
Buckling Coefficient Ch 0.44t
D⋅ M 1.6
D
t⋅≥if
0.44t
D⋅ 0.21
D
t
3
M4
⋅+
0.825D
t⋅ M≤ 1.6
D
t
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Fhe 2 Ch⋅ E⋅ D⋅:= Fhe 140.7 MPa⋅=Elastic Hoop BucklingStress
Critical HoopBuckling Stress
Fhc Fhe Fhe 0.55 Fy⋅≤if
0.45 Fy⋅ 0.18 Fhe⋅+ 0.55 Fy⋅ Fhe≤ 1.6 Fy⋅
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Since the thickness of shell is given as 16mm, the thickness of the stiffener shall not exceed 16mmdue to welding limitations.
Assume a stiffener thicknessand dimension as
ts 15 mm⋅:= ds 150 mm⋅:=
ds
ts10= Less than 10, hence OK
Width of shell as part of ring Beff 1.1 t D⋅( )0.5
⋅:= Beff 190.5 mm⋅=
Nutral axis distance from bottomy
0.5 ts⋅ ds2
⋅ Beff t⋅ ds 0.5 t⋅+( )⋅+
ts ds⋅ Beff t⋅+:= y 121.2 mm⋅=
Moment of inertia of webIwp
ts ds3
⋅
12ts ds⋅ 0.5ds y−( )
2⋅+:=
Moment of inertia of flange IfpBeff t
3⋅
12Beff t⋅ ds 0.5 t⋅+ y−( )
2⋅+:=
Moment of inertia provided I p Iwp Ifp+:= I p 1.284 107
× mm4
⋅=
Irq < I p. Hence the provided stiffeners are adequate.
Design of Tubular Members
1 Check the axial load on the jacket leg of diameter 1524mm and wall thickness
Questions
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1. Check the axial load on the jacket leg of diameter 1524mm and wall thicknessof 50mm with yield strength of 345 MPa. The bending moment acting on the legis 200 Tonne.m. The unsupported length is 15m. The effective length factor Kand moment reduction factors Cm shall be taken as 1.0.
2. Calculate safe axial load that can be carried by the jacket leg of diameter1524mm and wall thickness of 50mm with yield strength of 345 MPa. Thebending moment acting on the leg is 200 Tonne.m. The unsupported length is15m. The effective length factor K and moment reduction factors Cm shall be
taken as 1.0.
3. Design a buoyancy tank of 2.2m diameter subjected to hydrostatic pressureat design water depth of 120m. The maximum thickness of the tank shall notexceed 16mm and the spacing of rings shall not be less than 1m. The materialof construction is ASTM A36. The initial unsupported length shall be taken as20m.
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