Ultimate Strength of Plates and Stiffened Panels …...Ultimate Strength of Plates and Stiffened...
Transcript of Ultimate Strength of Plates and Stiffened Panels …...Ultimate Strength of Plates and Stiffened...
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Ultimate Strength of Plates and Stiffened Panels
by
Professor Jeom Paik
The LRET Research CollegiumSouthampton, 11 July – 2 September 2011
Ultimate Strength of Plates and Stiffened Panels
Prof. Jeom Kee Paik, DirectorThe LRET Research Centre of Excellence
at Pusan National University, Korea
Overview
Aims and Scope
Rationally-Based Structural Design
Methods used for Benchmark Study
Theory of the ALPS/ULSAP Method• Ultimate Strength of Plates
• Ultimate Strength of Stiffened Panels
Benchmark Study• Target Structure: Unstiffened panel
• Ultimate Strength of Unstiffened Plates under Biaxial Compression
• Target Structure: Stiffened panel
• Nonlinear FEA Modeling
• Ultimate Strength of Stiffened Panels
Concluding Remarks
Aims and Scope
Stiffened panel structure Stiffened panel subject to a combined in-plane and lateral pressure load
Rationally-Based Structural Design(Optimum structural design procedure based on ultimate limit state)
Modeling of Structure & Loads
Structural Response AnalysisCalculate Load Effects, Q
Limit State AnalysisCalculate Limit Values
of Load Effects, QL
Evaluation(A) Formulate constraints (B) Evaluate adequacy
γ1 γ2 γ3 Q ≤QL Constraints satisfied?Objective achieved?
Optimization Objective
Methods Used for Benchmark Study
Candidate methods
• Nonlinear finite element method (ANSYS, MSC/MARC, Abaqus)
• ALPS/ULSAP method
• DNV/PULS method
Theory of the ALPS/ULSAP Method
- ALPS/ULSAP (Analysis of Large Plated Structures / Ultimate Limit State Assessment Program), developed by Prof. J.K.Paik, Pusan National University
Theory of the ALPS/ULSAP Method
Ship Structural Analysis and Design (2010)
Hughes & Paik
Ultimate Limit State Design of Steel-Plated Structures (2003)
Paik & Thayamballi
(a) Plasticity at the corners
(b) Plasticity at the longitudinal mid-edges
(c) Plasticity at the transverse mid-edges
Ultimate Strength of Plates: σu = min.(σu1, σu2, σu3)
2 2 21 3max max max maxeq x x y y Yσ σ σ σ σ τ σ= − + + =
2 2 22 3max max min mineq x x y y Yσ σ σ σ σ τ σ= − + + =
2 2 23 3min min max maxeq x x y y Yσ σ σ σ σ τ σ= − + + =
• : Expected plasticity locationT: TensionC: Compression
Mode I – overall collapse
Mode II – plate-induced collapse
Mode III – stiffener-induced collapse by beam-column type collapse
Mode V – stiffener-induced collapse by tripping
Mode IV – stiffener-induced collapse by web buckling
Mode VI: Gross yielding
Ultimate Strength of Stiffened Panels: 6 Types of Collapse Modes
σu = min.(σuI, σu
II, σuIII, σu
IV, σuV, σu
VI)
Benchmark Study
Candidate methods
• Nonlinear finite element method (ANSYS, MSC/MARC, Abaqus)
• ALPS/ULSAP method
• DNV/PULS method
• Yield stress of plate, σYp = 313.6 N/mm2
• Yield stress of stiffener, σYs = 313.6 N/mm2
• Elastic modulus, E = 205800 N/mm2
• Poisson’s ratio, ν = 0.3
• Plate length, a = 2550 mm
• Plate breath, b = 850 mm
• Plate thickness, tp = 11, 16, 22, 33 mm
• Under biaxial compressive loads
• All edges simply supported
• No residual stress
• No lateral pressure
Target Structure: Unstiffened Panel
Material and Geometric Properties
Trans. frames
Long
. stif
fene
rs
850
25502550 2550
850
850
Unit: mm
2 2 2 2 2 2 2 2
2 2 2 2 2 2
( / 1 / ) [( 1) / 1 / ]/ / ( 1) / /
m a b m a bm a c b m a c b
+ + +≤
+ + +
where, /y xc σ σ=
σx and σy are the component of the longitudinal and transverse axial buckling stress of the plate under combined biaxial loading.
σx,1 and σy,1 are the component of the longitudinal or transverse axial buckling stress of the plate under uniaxial loading.
Buckling half-wave number
2.00.0 0.5 1.5
0.5
1.5
2.0
1.0
1.0
σy/ σy,1 a/b=3
σx/ σx,1
m=1
m=2
m=3
-1.0
-1.0
Unstiffened Plates under Biaxial Compression (1/3)
0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
FEMALPS/ULSAPDNV/PULS
FEMALPS/ULSAPDNV/PULS
a×b = 2550×850(mm)tp= 11mm a×b = 2550×850(mm)tp= 11mm
σyu
/ σY
σxu/ σY
Unstiffened Plates under Biaxial Compression (2/3)
tp=11mm tp=16mm
0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
FEMALPS/ULSAPDNV/PULS
FEMALPS/ULSAPDNV/PULS
a×b = 2550×850(mm)tp= 16mm a×b = 2550×850(mm)tp= 16mm
σyu
/ σY
σxu/ σY
Unstiffened Plates under Biaxial Compression (3/3)
tp=22mm tp=33mm
0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
FEMALPS/ULSAPDNV/PULS
FEMALPS/ULSAPDNV/PULS
a×b = 2550×850(mm)tp= 22mm a×b = 2550×850(mm)tp= 22mm
σyu
/ σY
σxu/ σY
σyu
/ σY
σxu/ σY
0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEMALPS/ULSAPDNV/PULS
FEMALPS/ULSAPDNV/PULS
a×b = 2550×850(mm)tp= 33mm a×b = 2550×850(mm)tp= 33mm
Unit: mm
• Yield stress of plate, σYp = 313.6 N/mm2
• Yield stress of stiffener, σYs = 313.6 N/mm2
• Elastic modulus, E = 205800 N/mm2
• Poisson’s ratio, ν = 0.3
• Plate length, a = 4750 mm
• Plate breath, b = 950 mm
• Plate thickness, tp = 11, 12.5, 15, 18.5, 25, 37 mm
• Number of the stiffeners: 8 stiffeners in a panel
• No residual stress
Target Structure: Stiffened Panel (1/2)
Material and Geometric Properties
N. A. N. A. N. A.
b
tp
hw
tw
b
tp
hw
tw
b
tp
hw
tw
bf
tf
bf
tf
*N.A. = neutral axis
Flat bar Angle bar Tee bar
Flat bar (hwxtw) Angle bar (hwxbfxtw/tf) Tee bar (hwxbfxtw/tf)
Size 1 150x17 138x90x9/12 138x90x9/12
Size 2 250x25 235x90x10/15 235x90x10/15
Size 3 350x35 383x100x12/17 383x100x12/17
Size 4 550x35 580x150x15/20 580x150x15/20
Target Structure: Stiffened Panel (2/2)
Dimensions of the Stiffeners
xA'''
z
y
AA'
A''
D'
D''D'''
B
C
B'
C'Longi. gird
ers
D Trans. frames
Boundary Description
A-A''' and D-D'''
Symmetric condition with Rx=Rz=0 and
uniform displacement in the y direction (Uy=uniform),
coupled the plate part
A-D and A'''-D'''
Symmetric condition with Ry=Rz=0 and
uniform displacement in the x direction (Ux=uniform),
coupled with longitudinal stiffeners
A'-D', A''-D'',
B-B' and C-C' Uz=0
ANSYS Nonlinear FEA Modeling (1/2)
Extent of Analysis: Two bay/two span model
Boundary Conditions
ANSYS Nonlinear FEA Modeling (2/2)
Mesh Sizes Applied
Flat type(hw×tw)
150×17(mm) 250×25(mm) 350×35(mm) 550×35(mm)27600 elements 27600 elements 40400 elements 50000 elements
Angle type(hw×bf×tw/tf)
138×90×9/12(mm) 235×90×10/15(mm) 383×100×12/17(mm) 580×150×15/20(mm)30800 elements 30800 elements 43600 elements 53200 elements
Tee type(hw×bf×tw/tf)
138×90×9/12(mm) 235×90×10/15(mm) 383×100×12/17(mm) 580×150×15/20(mm)30800 elements 30800 elements 43600 elements 53200 elements
Size 1 Size 2 Size 3 Size 4
MSC/MARC Nonlinear FEA Modeling by Prof. M. Fujikubo, Osaka University
Extent of Analysis: Two bay/two span model
Mesh Sizes Applied (22753 elements)
10 mesh
6 mesh6 mesh
x
z
y
Extent of Analysis: Three bay/one span model
Mesh Sizes Applied (7740 elements)
3 mesh1 mesh
z
y
x
Abaqus Nonlinear FEA Modeling by Dr. Amlashi Hadi, DNV
sin sinoc o
x yw Ba Bπ π
=
sin sinopl om x yw A
a bπ π
=
2 0.1 ; 0.0015 ; Ypo p o o
p
bA t B C at E
σβ β= = = =
Nonlinear FEA Modeling for ANSYS and MSC/MARC
ocw
iθ
osw
Plate Initial Deflection Column Type Initial Distortion of Stiffener
0 sinosw
z xw Ch a
π=
B
Ly
xwoc
wopl
wopl
woc
b
b
b
b
a aaa
Sideways Initial Distortion of Stiffener
x
z
y
Overall deflection with amplification factor of 50x
z
y
Local deflection with amplification factor of 20
Initial deflection with amplification factor of 20
Nonlinear FEA Modeling for ANSYS and MSC/MARC
Plate Initial Deflection
Column Type Initial Distortion of Stiffener
Sideways Initial Distortion of Stiffener
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode IIIIII III
III III III
σ xu/σ Y
eq
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
Panel C: hw×tw = 150×17 (mm) (F)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode III
IIIIII
III IV IV
σ xu/σ Y
eq
Panel C: hw×tw = 250×25 (mm) (F)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
Size 2Size 1
Ultimate Strength of Stiffened Panels (1/26)
Flat Bar Under Longitudinal Uniaxial Compression
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode IIIIII IV
IVII
II
σ xu/σ Y
eq
Panel C: hw×tw = 350×35 (mm) (F)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode III IV
IVIV IV II
σ xu/σ Y
eq
Panel C: hw×tw = 550×35 (mm) (F)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
Size 4Size 3
Ultimate Strength of Stiffened Panels (2/26)
Flat Bar Under Longitudinal Uniaxial Compression
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Mode III IIIIII
III
III IIIσ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (A)
Yp( / ) σ /pb t E
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode IIIIII
IIIV
σ xu/σ Y
eq
V
Panel C: hw×bf×tw/tf = 235×90×10/15(mm) (A)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
V
Size 2Size 1
Ultimate Strength of Stiffened Panels (3/26)
Angle Bar Under Longitudinal Uniaxial Compression
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode IIIIII
VV V V
σ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 383×100×12/17(mm) (A)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
VMode III
VII
II II
σ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 580×150×15/20(mm) (A)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
Size 4Size 3
Ultimate Strength of Stiffened Panels (4/26)
Angle Bar Under Longitudinal Uniaxial Compression
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
IIIMode IIIIII
III III
IIIσ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (T)FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
III
Mode III
IIIV V V
σ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 235×90×10/15(mm) (T)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
Size 2Size 1
Ultimate Strength of Stiffened Panels (5/26)
Tee Bar Under Longitudinal Uniaxial Compression
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
Mode III V
V V
σ xu/σ Y
eq
VV
Panel C: hw×bf×tw/tf = 383×100×12/17(mm) (T)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
0 1 2 3 40.0
0.2
0.4
0.6
0.8
1.0
1.2
Yp( / ) σ /pb t E
VMode V
VII
II II
σ xu/σ Y
eq
Panel C: hw×bf×tw/tf = 580×150×15/20(mm) (T)
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Design Formula (DNV/PULS)
FEA (ABAQUS)
Size 4Size 3
Ultimate Strength of Stiffened Panels (6/26)
Tee Bar Under Longitudinal Uniaxial Compression
Angle bar
Ultimate Strength of Stiffened Panels (7/26)
Under Longitudinal Uniaxial Compression
σ xu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Flat bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4
Size 3
Size 2
Size 1 σ xu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Angle bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4
Size 3
Size 2
Size 1
Flat bar
Tee bar
σ xu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Tee bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4
Size 3
Size 2
Size 1
All stiffener types
Ultimate Strength of Stiffened Panels (8/26)
Under Longitudinal Uniaxial Compression
σ xu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Flat Angle TeeFEA (ANSYS)
Design formula (ALPS/ULSAP)
Size 4
Size 3
Size 2
Size 1
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×tw = 150×17 (mm) (F)
Mode I
III
III
III IIIIII
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×tw = 250×25 (mm) (F)
Mode III
III
III
IV IVIII
Size 2Size 1
Ultimate Strength of Stiffened Panels (9/26)
Flat Bar Under Transverse Uniaxial Compression
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×tw = 350×35 (mm) (F)
Mode III
III
IV
IV IVIV
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×tw = 550×35 (mm) (F)
Mode III
IV
IV
IV IVIV
Size 4Size 3
Ultimate Strength of Stiffened Panels (10/26)
Flat Bar Under Transverse Uniaxial Compression
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (A)
Mode III
III
III
III IIIIII
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 235×90×10/15(mm) (A)
Mode III
III
III
V VV
Size 2Size 1
Ultimate Strength of Stiffened Panels (11/26)
Angle Bar Under Transverse Uniaxial Compression
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 383×100×12/17(mm) (A)
Mode III
V
V
IV IVIV
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 580×150×15/20(mm) (A)
Mode V
IV
IV
IV IVIV
Size 4Size 3
Ultimate Strength of Stiffened Panels (12/26)
Angle Bar Under Transverse Uniaxial Compression
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (T)
Mode III
III
III
III IIIIII
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 235×90×10/15(mm) (T)
Mode III
III
III
V VV
Size 2Size 1
Ultimate Strength of Stiffened Panels (13/26)
Tee Bar Under Transverse Uniaxial Compression
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 383×100×12/17(mm) (T)
Mode III
V
V
IV IVIV
σ yu/σ Y
eq
Yp( / ) σ /pb t E0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
FEA (ANSYS)Design Formula (ALPS/ULSAP)
Panel C: hw×bf×tw/tf = 580×150×15/20(mm) (T)
Mode V
IV
IV
IV IVIV
Size4Size 3
Ultimate Strength of Stiffened Panels (14/26)
Tee Bar Under Transverse Uniaxial Compression
Angle barFlat bar
Ultimate Strength of Stiffened Panels (15/26)
Under Transverse Uniaxial Compression
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Flat bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4 Size 3 Size 2
Size 1
σ yu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Angle bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4 Size 3 Size 2 Size 1
σ yu/σ Y
eq
All stiffener typesTee bar
Ultimate Strength of Stiffened Panels (16/26)
Under Transverse Uniaxial Compression
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Tee bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)
Size 4 Size 3 Size 2 Size 1
σ yu/σ Y
eq
Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2 Flat Angle TeeFEA (ANSYS)
Design formula (ALPS/ULSAP)
Size 3Size 4 Size 2 Size 1
σ yu/σ Y
eq
2 2 2 2 2 2 2 2
2 2 2 2 2 2
( / 1 / ) [( 1) / 1 / ]/ / ( 1) / /
m a b m a bm a c b m a c b
+ + +≤
+ + +
where, /y xc σ σ=
2.00.0 0.5 1.5
0.5
1.5
2.0
1.0
1.0
σy/ σy,1 a/b=5
σx/ σx,1
m=1m=2
m=3
m=4
m=5
-1.0
-1.0
σx and σy are the component of the longitudinal and transverse axial buckling stress of the plate under combined biaxial loading.
σx,1 and σy,1 are the component of the longitudinal or transverse axial buckling stress of the plate under uniaxial loading.
Ultimate Strength of Stiffened Panels (17/26)
Buckling half-wave number
Size 1 Size 2
Ultimate Strength of Stiffened Panels (18/26)
Under Biaxial Compression (Flat Bar, tp=18.5mm)
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Mode III
Design Formula (ALPS/ULSAP)
hw×tw = 150×17(mm) (F)
Panel C: tp=18.5mm
FEA (ANSYS)
0.0
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Mode III
0.0
Design Formula (ALPS/ULSAP)
hw×tw = 250×25(mm) (F)
Panel C: tp=18.5mm
FEA (ANSYS)
Size 3 Size 4
Ultimate Strength of Stiffened Panels (19/26)
Under Biaxial Compression (Flat Bar, tp=18.5mm)
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
Design Formula (ALPS/ULSAP)
hw×tw = 350×35(mm) (F)
Panel C: tp=18.5mm
FEA (ANSYS)
Mode III
Mode IV
Mode II σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
Design Formula (ALPS/ULSAP)
hw×tw = 550×35(mm) (F)
Panel C: tp=18.5mm
FEA (ANSYS)
Mode IV
Mode IV
Mode II
Mode III
Size 1 Size 2
Ultimate Strength of Stiffened Panels (20/26)
Under Biaxial Compression (Angle Bar, tp=18.5mm)
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
Design Formula (ALPS/ULSAP)
hw×bf×tw/tf = 138×90×9/12(mm) (A)
Panel C: tp=18.5mm
FEA (ANSYS)
Mode III
Mode IVσ y
u/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Mode III
0.0
Design Formula (ALPS/ULSAP)
hw×bf×tw/tf = 235×90×10/15(mm) (A)Panel C: tp=18.5mm
FEA (ANSYS)
Size 3 Size 4
Ultimate Strength of Stiffened Panels (21/26)
Under Biaxial Compression (Angle Bar, tp=18.5mm)
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
Design Formula (ALPS/ULSAP)
hw×bf×tw/tf = 383×100×12/17(mm) (A)Panel C: tp=18.5mm
FEA (ANSYS)
Mode III
Mode V
Mode II σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
Design Formula (ALPS/ULSAP)
hw×bf×tw/tf = 580×150×15/20(mm) (A)
Panel C: tp=18.5mm
Mode IV
Mode V
Mode II
FEA (ANSYS)
Mode III
Size 1 Size 2
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Mode III
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Panel C: tp=18.5mm hw×bf×tw/tf = 138×90×9/12(mm) (T)
0.0
σ yu/σ Y
eq
σxu/ σYeq
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Mode III
hw×bf×tw/tf = 235×90×10/15(mm) (T)Panel C: tp=18.5mm
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Ultimate Strength of Stiffened Panels (22/26)
Under Biaxial Compression (Tee Bar, tp=18.5mm)
Size 3 Size 4
σ yu/σ Y
eq
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
σxu/ σYeq
hw×bf×tw/tf = 383×100×12/17(mm) (T)Panel C: tp=18.5mm
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Mode III
Mode V
Mode II
σ yu/σ Y
eq
σxu/ σYeq
0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
hw×bf×tw/tf = 580×150×15/20(mm) (T)
Panel C: tp=18.5mm
Mode IV
Mode V
Mode II
FEA (ANSYS)
Design Formula (ALPS/ULSAP)FEA (MSC/MARC)
Ultimate Strength of Stiffened Panels (23/26)
Under Biaxial Compression (Tee Bar, tp=18.5mm)
p
p
Plate-sided Pressure
Stiffener-sided Pressure
Ultimate Strength of Stiffened Panels (24/26)
Under Combined Longitudinal Compression and Lateral Pressure Loads
N. A.
b
tp
hw
tw
bf
tf
Plate thickness, tp = 15 mm
hw×bf×tw/tf = 383×100×12/17(mm) (T)
Ultimate Strength of Stiffened Panels (25/26)
p (MPa)
σ xu/σ Y
eq
tp=15mm
0.0 0.1 0.2 0.3 0.40.0
0.2
0.4
0.6
0.8
1.0Design Formula (ALPS/ULSAP)FEA (ANSYS) with Plate-sided PressureFEA (ANSYS) with Stiffener-sided Pressure
Panel C: hw×bf×tw/tf = 383×100×12/17(mm) (T)
Mode VMode II Mode V
Mode III
Stiffener-sided Pressure
Plate-sided Pressure
Under Combined Longitudinal Compression and Lateral Pressure Loads
Plate thickness, tp = 15 mm
hw×bf×tw/tf = 383×100×12/17(mm) (T)
Ultimate Strength of Stiffened Panels (26/26)
Plate-sided Pressure(with p=0.25 MPa, amplification factor of 10)
Stiffener-sided Pressure(with p=-0.25 MPa, amplification factor of 10)
Under Combined Longitudinal Compression and Lateral Pressure Loads
Concluding Remarks
Concluding RemarksThe dimension and material properties of a real ship panel was selected as a standard panel
and a wider range of plating and stiffener dimensions were considered by varying the panel’s properties.
The objective of the benchmark study reported in this paper was to check the accuracy of the ALPS/ULSAP method’s use to calculate the ultimate strength of plate and stiffened panel, compared with nonlinear finite element method.
The ALPS/ULSAP method was found in a good agreement with the nonlinear finite element method computations through a wide range of panel dimensions and different loading conditions.
The ALPS/ULSAP method is based on design formulations, the computational time required is extremely short compared to the nonlinear finite element method. So, this will be of great advantage in the structures design and safety assessment of ship structures comprising a large number of plate and panels.
Ultimate Strength of Hull Girders
Prof. Jeom Kee Paik, DirectorThe LRET Research Centre of Excellence
at Pusan National University, Korea
OverviewOverview
1. Background2. Rationally-based structural design3. Presumed stress distribution-based method4. Methods applied for the ultimate hull strength analysis5. Analysis results6. Statistical analysis7. Concluding remarks
BackgroundBackground
- To develop the modified Paik-Mansour formula method for the ultimate strength calculations of ship hulls subject to verticalbending moments.
- To validate the accuracy and applicability of modified Paik-Mansour formula method by comparing with more refined other methods.
Modeling of Structure & Loads
Structural Response AnalysisCalculate Load Effects, Q
Limit State AnalysisCalculate Limit Values
of Load Effects, QL
Evaluation(A) Formulate constraints (B) Evaluate adequacy
γ1 γ2 γ3 Q ≤QL Constraints satisfied?Objective achieved?
Optimization Objective
RationallyRationally--based structural designbased structural design(Optimum structural design procedure based on ultimate limit sta(Optimum structural design procedure based on ultimate limit state)te)
Methods for the ultimate hull strength analysisMethods for the ultimate hull strength analysis
• Numerical- Nonlinear FEM- Intelligent supersize FEM- Idealized structural unit method
• Analytical- Design formula
• Experimental
Presumed stress distributionPresumed stress distribution--based method based method (1/8)(1/8)
Sagging Hogging
Caldwell’s original formula method (1965)
0xdAσ =∫ 1
1
n
xi i ii
u n
xi ii
a zg
a
σ
σ
=
=
=∑
∑
( )
1
nvu xi i i u
i
M a z gσ=
= −∑
Longitudinal bending stress distribution of tanker hullat ULS obtained by Nonlinear FEA
Presumed stress distributionPresumed stress distribution--based method based method (2/8)(2/8)
Linear elasticaround N.A.
Buckling collapsedat compressed part
Yielded attensiled part
Single hull VLCCin hogging
Double hull VLCCin sagging
Suezmax-class double hull VLCC in sagging
Longitudinal bending stress distribution of ship hullat ULS obtained by Nonlinear FEA
Presumed stress distributionPresumed stress distribution--based method based method (3/8)(3/8)
Dow’s frigate test hullin sagging
Container shipin hogging
Bulk carrierin hogging
Original Paik-Mansour formula method (1995)
Uxσ
Exσ
Exσ
Yxσ
①
②
③
④
+ -
+-
Tens.
Comp.D-gus
gus
z
①
②
③
④
Yxσ z
D-guh
guh
+-
Tens.
Comp.
+ -
Exσ
Exσ
Uxσ
Sagging Hogging
0xdAσ =∫ 1
1
n
xi i ii
u n
xi ii
a zg
a
σ
σ
=
=
=∑
∑
( )
1
nvu xi i i u
i
M a z gσ=
= −∑
Presumed stress distributionPresumed stress distribution--based method based method (4/8)(4/8)
Modified Paik-Mansour formula method
Presumed stress distributionPresumed stress distribution--based method based method (5/8)(5/8)
0xdAσ =∫ 1
1
n
xi i ii
u n
xi ii
a zg
a
σ
σ
=
=
=∑
∑
( )
1
nvu xi i i u
i
M a z gσ=
= −∑
Sagging Hogging
2 2 2 2 4
10.995 0.936 0.170 0.188 0.067
xu
Yeq
σσ λ β λ β λ
=+ + + −
Yeqa
r Eσ
λπ
= Ypbt E
σβ =
s
IrA
=
Plate-stiffener combination element (PSC)
Plate-stiffener separation element (PSS)
Presumed stress distributionPresumed stress distribution--based method based method (6/8)(6/8)
(Paik and Thayamballi, 1997)
Plate element: a/b≥1 (Paik at al. 2004)
Plate element: a/b<1 (Paik at al. 2004)
Ypbt E
σβ =
Ypat E
σα =
4 2*
2
0.032 0.002 1.0 for 1.51.274 / for 1.5 3.01.248 / 0.283 for 3.0
xu
Yp
α α ασ α ασ
α α
⎧− + + ≤⎪= < ≤⎨⎪ + >⎩
4 2
2
0.032 0.002 1.0 for 1.51.274 / for 1.5 3.01.248 / 0.283 for 3.0
xu
Yp
β β βσ β βσ
β β
⎧− + + ≤⎪= < ≤⎨⎪ + >⎩
*
2
0.475 1xu xu
Yp Yp
a ab b
σ σσ σ α
⎛ ⎞= + −⎜ ⎟⎝ ⎠
Presumed stress distributionPresumed stress distribution--based method based method (7/8)(7/8)
8182 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58
57 56 55 54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27262524232221
20
19181716151413121110987654321
83
84
85
86
87
88
89
177178 90
91
92
93
94
95
96
175176 97
98
99
100
101
102
173174103
104
105
106
107
108
109
110
111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
169
160
170
131
132
133
134
135
136
137
138
139
140
141
142
143
144164 163 162
145
146
147
148
149
150
151
152
167 166 165
153
154
155
156
157
158
161 160 159
171172
8182 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58
57 56 55 54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27262524232221
20
19181716151413121110987654321
83
84
85
86
87
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89
177178 90
91
92
93
94
95
96
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98
99
100
101
102
173174103
104
105
106
107
108
109
110
111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
169
160
170
131
132
133
134
135
136
137
138
139
140
141
142
143
144164 163 162
145
146
147
148
149
150
151
152
167 166 165
153
154
155
156
157
158
161 160 159
171172
1 14 15 16 17
18
19 20 21 22 23 24
25
26 27 28 29
30
31 32 33 34 35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
52
55
51
53
54
56
57
58
59
60
61
125
2
124
1236263646566
67
121686970
73
7172
111
110
109
108
107
106
105
104
103
102
101
100
99 116
98
97
96
95
94
93
92
91
90
89
88
87
86
85
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83 82 81 80
79
78 77119
118
76 75 74
3
4
5
6
7
8
9
126
10
11
12
117
122
120
112
113
114
115
11 1414 1515 1616 1717
1818
1919 2020 2121 2222 2323 2424
2525
2626 2727 2828 2929
3030
3131 3232 3333 3434 3535
3636
3737
3838
3939
4040
4141
4242
4343
4444
4545
4646
4747
4848
4949
5050
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5555
5151
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5757
5858
5959
6060
6161
125
22
124
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6767
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7373
71717272
111
110
109
108
107
106
105
104
103
102
101
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9898
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122
120120
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113113
114114
115115
1
2
3
4
5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
106
107 108 109 110 111 112 113 114 115 116
117
118
202
119 120 121
203
206
204
205
122 123 124 125 126 127 128 129 130 131
132 207
208
209210
105 104 103 102 101 100 99 98 97 96
93
169
170
171
92 9195 94
168
90 89 88 87 86 85 84 83 82 81 80 79 78 77
76 75 74 73 72
71
70
69
68
67
66
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
165
164
163
162
161
160
159
158
157
156
155
154
153
152
151
150
149
148
147
146
145
144
143
142
141
140
139
138
137
136
135
134
133
211 212 213
214 215 216
217 218 219
220
221
222
223
11
2
3
4
5
66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 3131 3232 3333 3434 3535 3636 3737 3838
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107107 108108 109109 110110 111111 112112 113113 114114 115115 116116
117117
118118
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119119 120120 121121
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204204
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122122 123123 124124 125125 126126 127127 128128 129129 130130 131131
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9393
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170170
171171
9292 91919595 9494
168168
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7070
6969
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6767
6666
6565
6464
6363
6262
6161
6060
5959
5858
5757
5656
5555
5454
5353
5252
5151
5050
4949
4848
4747
4646
4545
4444
4343
4242
4141
4040
3939
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173173
174174
175175
176176
177177
178178
179179
180180
181181
182182
183183
184184
185185
186186
187187
188188
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200200
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164164
163163
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160160
159159
158158
157157
156156
155155
154154
153153
152152
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150150
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148148
147147
146146
145145
144144
143143
142142
141141
140140
139139
138138
137137
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135135
134134
133133
211211 212212 213213
214214 215215 216216
217217 218218 219219
220220
221221
222222
223223
Modeling: Modified Paik-Mansour formula method
Dow’s Test Hull Container Ship Bulk Carrier D/H Suezmax
S/H VLCC D/H VLCC
PSC model for hogging PSS model for sagging
PSC model for hogging PSS model for saggingPSS model
PSC model PSC model PSC model
Presumed stress distributionPresumed stress distribution--based method based method (8/8)(8/8)
Methods applied Methods applied for the ultimate hull strength analysis (1/5)for the ultimate hull strength analysis (1/5)
• Nonlinear FEM: ANSYS• Intelligent supersize FEM: ALPS/HULL• Idealized structural unit method (Smith method): IACS CSR by Dr. C.H. Huang
(China Corporation Register of Shipping)• Modified PaikModified Paik--MansourMansour formula methodformula method
NLFEM model ISFEM model ISUM model
Hard corner elements
ModifiedP-M method
NLFEM(ANSYS)
ISUM/Smith Method(IACS CSR)
ISFEM(ALPS/HULL)
Geometricmodeling
Finite element model Plate-stiffener combination model
Plate-stiffener separation model
Formulation technique
: Numerical formulation
[D]: Numerical formulation
:Closed-form solution : Numerical formulation
[D]: Closed-form solution
Computational cost
Expensive Cheap Cheap
Feature (1) 2 and 3-dimensional 2-dimensional 2 and 3-dimensional
Feature (2)Can deal with interaction between local and global failures
Can not deal with interaction between local and global failures
Can deal with interaction between local and global failures
[ ] [ ][ ] volTB D B dσ = ∫Yσ σ= Φ
1 11 1
1 1
edge functionforforfor
εε ε
ε
Φ =
− < −⎧⎪= − < <⎨⎪ >⎩
[ ] [ ][ ] volTB D B dσ = ∫
Methods applied Methods applied for the ultimate hull strength analysis (2/5)for the ultimate hull strength analysis (2/5)
Extent of the analysis
Trans. bulkhead
Trans. bulkhead
Trans. frame
Trans. bulkhead
Trans. bulkhead
Trans. frame
(a) The entire hull model
(b) The three cargo hold model
(c) The two cargo hold model
(d) The one cargo hold model
(e) The two-bay sliced hull cross-section model
(f) The one-bay sliced hull cross-section model
Methods applied Methods applied for the ultimate hull strength analysis (3/5)for the ultimate hull strength analysis (3/5)
Initial imperfections
sin sinopl om x yw A
a bπ π
=
sin sinoc ox yw B
a Bπ π
= 2where, 0.1 ; 0.0015 ; Ypo p o o
p
bA t B C at E
σβ β= = = =
0 sinosw
z xw Ch a
π=
woc
wos
wopl
Methods applied Methods applied for the ultimate hull strength analysis (4/5)for the ultimate hull strength analysis (4/5)
Application of vertical bending moments keeping the hull cross-section plane
• g = neutral axis position from the baseline• zi = distance from the ship’s baseline
(reference position) to the horizontalneutral axis of the ith structural component
• σxi = longitudinal stress of the ith structuralcomponent following the presumed stressdistribution
• ai = cross-sectional area of the ith structuralcomponent
• n = total number of structural components
1
1
n
xi i ii
n
xi ii
a zg
a
σ
σ
=
=
=∑
∑
Displacement control with neutral axis changes
Methods applied Methods applied for the ultimate hull strength analysis (5/5)for the ultimate hull strength analysis (5/5)
NLFEM (ANSYS) ModelingNLFEM (ANSYS) ModelingDow’s Test Hull Container Ship Bulk Carrier
D/H Suezmax S/H VLCC D/H VLCC
Total number of elements: 36,432Elements distribution:Plate: 10 Web: 4 Flange: 2
Total number of elements: 262,630Elements distribution:Plate: 10 Web: 6 Flange: 2
Total number of elements: 271,680Elements distribution:Plate: 10 Web: 8 Flange: 2
Total number of elements: 76,992Elements distribution:Plate: 8 Web: 4 Flange: 1
Total number of elements: 297,888Elements distribution:Plate: 8 Web: 6 Flange: 2
Total number of elements: 222,858Elements distibution:Plate: 10 Web: 6 Flange: 1
ISFEM (ALPS/HULL) ModelingISFEM (ALPS/HULL) ModelingDow’s Test Hull Container Ship Bulk Carrier
D/H Suezmax S/H VLCC D/H VLCC
Total number of elements: 196Plate: 106 elementsBeam-column: 90 elements
Total number of elements: 605Plate: 367 elementsBeam-column: 238 elements
Total number of elements: 431Plate: 243 elementsBeam-column: 188 elements
Total number of elements: 389Plate: 231 elementsBeam-column: 158 elements
Total number of elements: 834Plate: 442 elementsBeam-column: 392 elements
Total number of elements: 453Plate: 341 elementsBeam-column: 112 elements
ISUM (CSR) Modeling by Dr. C. H. HuangISUM (CSR) Modeling by Dr. C. H. Huang(China Corporation Register of Shipping, Taiwan)(China Corporation Register of Shipping, Taiwan)
Dow’s Test Hull Container Ship Bulk Carrier
D/H Suezmax S/H VLCC D/H VLCC
Result Result -- Case I: Case I: DowDow’’s Test Hull s Test Hull (1/6)(1/6)Curvature versus vertical bending moments
Dow’stest hull
Design formula method MuANSYS(MNm)
MuALPS/HULL
(MNm)
MuCSR
(MNm)Mu(MNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 10.338 210.000 0.000 210.000 0.000 11.235 10.698 11.889Sagging 9.329 760.200 0.000 760.200 0.000 10.618 9.940 10.224
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
0.0 1.0 2.0 3.00
2
4
6
8
10
12
Test result
0.5 1.5 2.5
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
MN
m)
0.0 0.5 1.0 1.5 2.0 2.5 3.0Curvature(1/km)
0
2
4
6
8
10
12
ANSYSALPS/HULLCSRModified Paik-Mansour formula methodH
oggi
ng b
endi
ng m
omen
t(M
Nm
)
Result Result -- Case II: Case II: Container Ship Container Ship (2/6)(2/6)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500
1
2
3
4
5
6
7
8
9
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Hog
ging
ben
ding
mom
ent(
GN
m)
Curvature versus vertical bending moments
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500
1
2
3
4
5
6
7
8
9
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
GN
m)
Containership
Design formula method MuANSYS(GNm)
MuALPS/HULL
(GNm)
MuCSR
(GNm)Mu(GNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 6.400 698.800 0.000 698.800 0.000 6.969 6.916 8.040Sagging 7.077 10330.800 0.000 10330.800 0.000 6.951 6.635 7.843
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
Result Result -- Case III: Case III: Bulk Carrier Bulk Carrier (3/6)(3/6)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350
4
8
12
16
20
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Hog
ging
ben
ding
mom
ent(
GN
m)
Curvature versus vertical bending moments
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350
4
8
12
16
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
GN
m)
Bulkcarrier
Design formula method MuANSYS(GNm)
MuALPS/HULL
(GNm)
MuCSR
(GNm)Mu(GNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 16.576 - - 1654.100 13.700 17.500 16.602 17.941Sagging 14.798 17935.000 0.000 17935.000 0.000 15.800 15.380 14.475
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
Result Result -- Case IV: Case IV: Double Hull Double Hull SuezmaxSuezmax Class Tanker Class Tanker (4/6)(4/6)Curvature versus vertical bending moments
0.00 0.05 0.10 0.15 0.20 0.25 0.300
2
4
6
8
10
12
14
16
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Hog
ging
ben
ding
mom
ent(
GN
m) (PSC)
(PSS)
0.00 0.05 0.10 0.15 0.20 0.25 0.300
2
4
6
8
10
12
14
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
GN
m)
(PSS)
(PSC)
Double hullSuezmaxtanker
Design formula method MuANSYS(GNm)
MuALPS/HULL
(GNm)
MuCSR
(GNm)Mu(GNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 13.965 - - 12.100 2210.600 14.066 13.308 15.714Sagging 12.213 16078.500 0.000 16078.500 0.000 11.151 11.097 12.420
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
Result Result -- Case V: Case V: Single Hull VLCC Class Tanker Single Hull VLCC Class Tanker (5/6)(5/6)Curvature versus vertical bending moments
0.00 0.05 0.10 0.15 0.20 0.25 0.300
3
6
9
12
15
18
21
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Hog
ging
ben
ding
mom
ent(
GN
m)
(PSS)
(PSC)
0.00 0.05 0.10 0.15 0.20 0.25 0.300
4
8
12
16
20
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
GN
m)
(PSS)
(PSC)
Single hullVLCCtanker
Design formula method MuANSYS(GNm)
MuALPS/HULL
(GNm)
MuCSR
(GNm)Mu(GNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 18.701 7035.200 0.000 7035.200 0.000 17.355 17.335 19.889Sagging 17.825 15225.500 0.000 15225.500 0.000 16.179 17.263 17.868
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
Result Result -- Case VI: Case VI: Double Hull VLCC Class Tanker Double Hull VLCC Class Tanker (6/6)(6/6)Curvature versus vertical bending moments
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400
5
10
15
20
25
30
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Hog
ging
ben
ding
mom
ent(
GN
m) (PSC)
(PSS)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400
5
10
15
20
25
30
ANSYSALPS/HULLCSRModified Paik-Mansour formula method
Curvature(1/km)
Sagg
ing
bend
ing
mom
ent(
GN
m)
(PSS)
(PSC)
Double hullVLCCtanker
Design formula method MuANSYS(GNm)
MuALPS/HULL
(GNm)
MuCSR
(GNm)Mu(GNm)
Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)
Hogging 25.667 - - 15.900 3816.000 27.335 25.600 28.352Sagging 22.390 20240.700 0.000 20240.700 0.000 22.495 22.000 24.798
Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.
Result: Result: Analysis VideoAnalysis Video
Modified PModified P--M Formula Method M Formula Method versus ANSYS Nonlinear FEA (1/2)
Ship Mp
(GNm)
Hogging Sagging
Formula ANSYSFormula/ANSYS
Formula ANSYSFormula/ANSYSMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.010 0.772 0.011 0.840 0.920 0.009 0.697 0.011 0.793 0.879
Container ship 9.220 6.400 0.694 6.969 0.756 0.918 7.077 0.768 6.951 0.754 1.018
Bulk carrier 20.394 16.576 0.813 17.500 0.858 0.947 14.798 0.726 15.800 0.775 0.937
D/H Suezmax 17.677 13.965 0.790 14.066 0.796 0.993 12.213 0.691 11.151 0.631 1.095
S/H VLCC 22.578 18.701 0.828 17.355 0.769 1.078 17.825 0.789 16.179 0.717 1.102
D/H VLCC 32.667 25.667 0.786 27.335 0.837 0.939 22.390 0.685 22.495 0.689 0.995
Mean 0.966 1.004
S-D 0.061 0.088
COV 0.063 0.087
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (1/12)Mean and COV (1/12)
Modified PModified P--M Formula Method M Formula Method versus ANSYS Nonlinear FEA (2/2)
0.0 0.2 0.4 0.6 0.8 1.0(Mu/Mp)ANSYS
0.0
0.2
0.4
0.6
0.8
1.0
(Mu/M
p)Fo
rmul
a
Hog / Sag Mean : 0.966 / 1.004Standard deviation : 0.061 / 0.088COV : 0.063 / 0.087
Formula/ANSYS:
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
0 0.0125 10 15 20 25 30(Mu)ANSYS(GNm)
0
0.0125
10
15
20
25
30
(Mu)
Form
ula(G
Nm
)
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
Statistical analysis Statistical analysis -- Mean and COV (2/12)Mean and COV (2/12)
Modified PModified P--M Formula Method M Formula Method versus ALPS/HULL ISFEM (1/2)
Ship Mp
(GNm)
Hogging Sagging
Formula ALPSFormula/
ALPS
Formula ALPSFormula/
ALPSMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.010 0.772 0.011 0.799 0.966 0.009 0.697 0.010 0.743 0.939
Container ship 9.220 6.400 0.694 6.916 0.750 0.925 7.077 0.768 6.635 0.720 1.067
Bulk carrier 20.394 16.576 0.813 16.602 0.814 0.998 14.798 0.726 15.380 0.754 0.962
D/H Suezmax 17.677 13.965 0.790 13.308 0.753 1.049 12.213 0.691 11.097 0.628 1.101
S/H VLCC 22.578 18.701 0.828 17.335 0.768 1.079 17.825 0.789 17.263 0.765 1.033
D/H VLCC 32.667 25.667 0.786 25.600 0.784 1.003 22.390 0.685 22.000 0.673 1.018
Mean 1.003 1.020
S-D 0.055 0.061
COV 0.055 0.060
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (3/12)Mean and COV (3/12)
Modified PModified P--M Formula Method M Formula Method versus ALPS/HULL ISFEM (2/2)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mean : 1.003 / 1.020Standard deviation : 0.055 / 0.061COV : 0.055 / 0.060
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
Formula/ALPS:
(Mu/M
p)Fo
rmul
a
(Mu/Mp)ALPS/HULL
Hog / Sag
0 0.0125 10 15 20 25 30
0
0.0125
10
15
20
25
30
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
(Mu)
Form
ula(G
Nm
)
(Mu)ALPS/HULL(GNm)
Statistical analysis Statistical analysis -- Mean and COV (4/12)Mean and COV (4/12)
Modified PModified P--M Formula Method M Formula Method versus CSR ISUM (1/2)
Ship Mp
(GNm)
Hogging Sagging
Formula CSRFormula/
CSR
Formula CSRFormula/
CSRMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.010 0.772 0.012 0.888 0.870 0.009 0.697 0.010 0.764 0.912
Container ship 9.220 6.400 0.694 8.040 0.872 0.796 7.077 0.768 7.843 0.851 0.902
Bulk carrier 20.394 16.576 0.813 17.941 0.880 0.924 14.798 0.726 14.475 0.710 1.022
D/H Suezmax 17.677 13.965 0.790 15.714 0.889 0.889 12.213 0.691 12.420 0.703 0.983
S/H VLCC 22.578 18.701 0.828 19.889 0.881 0.940 17.825 0.789 17.868 0.791 0.998
D/H VLCC 32.667 25.667 0.786 28.352 0.868 0.905 22.390 0.685 24.798 0.759 0.903
Mean 0.887 0.953
S-D 0.051 0.054
COV 0.058 0.056
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (5/12)Mean and COV (5/12)
Modified PModified P--M Formula Method M Formula Method versus CSR ISUM (2/2)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mean : 0.887 / 0.953Standard deviation : 0.051 / 0.054COV : 0.058 / 0.056
Formula/CSR:
(Mu/M
p)Fo
rmul
a
(Mu/Mp)CSR
Hog / Sag
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
0 0.0125 10 15 20 25 30
0
0.0125
10
15
20
25
30
(Mu)
Form
ula(G
Nm
)
(Mu)CSR(GNm)
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
Statistical analysis Statistical analysis -- Mean and COV (6/12)Mean and COV (6/12)
ANSYS Nonlinear FEA versus ALPS/HULL ISFEM (1/2)
Ship Mp
(GNm)
Hogging Sagging
ANSYS ALPSALPS /ANSYS
ANSYS ALPSALPS /ANSYSMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.011 0.840 0.011 0.799 0.952 0.011 0.793 0.010 0.743 0.936
Container ship 9.220 6.969 0.756 6.916 0.750 0.992 6.951 0.754 6.635 0.720 0.955
Bulk carrier 20.394 17.500 0.858 16.602 0.814 0.949 15.800 0.775 15.380 0.754 0.973
D/H Suezmax 17.677 14.066 0.796 13.308 0.753 0.946 11.151 0.631 11.097 0.628 0.995
S/H VLCC 22.578 17.355 0.769 17.335 0.768 0.999 16.179 0.717 17.263 0.765 1.067
D/H VLCC 32.667 27.335 0.837 25.600 0.784 0.937 22.495 0.689 22.000 0.673 0.978
Mean 0.962 0.984
S-D 0.026 0.045
COV 0.027 0.046
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (7/12)Mean and COV (7/12)
ANSYS Nonlinear FEA versus ALPS/HULL ISFEM (2/2)
0 0.0125 10 15 20 25 30
0
0.0125
10
15
20
25
30
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
(Mu)
AL
PS/H
UL
L (G
Nm
)
(Mu)ANSYS(GNm)0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mean : 0.962 / 0.984Standard deviation : 0.026 / 0.045COV : 0.027 / 0.046
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
ALPS/ANSYS:
(Mu/M
p)A
LPS
/HU
LL
(Mu/Mp)ANSYS
Hog / Sag
Statistical analysis Statistical analysis -- Mean and COV (8/12)Mean and COV (8/12)
ANSYS Nonlinear FEA versus CSR ISUM (1/2)
Ship Mp
(GNm)
Hogging Sagging
ANSYS CSRCSR/
ANSYS
ANSYS CSRCSR/
ANSYSMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.011 0.840 0.012 0.888 1.058 0.011 0.793 0.010 0.764 0.963
Container ship 9.220 6.969 0.756 8.040 0.872 1.154 6.951 0.754 7.843 0.851 1.128
Bulk carrier 20.394 17.500 0.858 17.941 0.880 1.025 15.800 0.775 14.475 0.710 0.916
D/H Suezmax 17.677 14.066 0.796 15.714 0.889 1.117 11.151 0.631 12.420 0.703 1.114
S/H VLCC 22.578 17.355 0.769 19.889 0.881 1.146 16.179 0.717 17.868 0.791 1.104
D/H VLCC 32.667 27.335 0.837 28.352 0.868 1.037 22.495 0.689 24.798 0.759 1.102
Mean 1.090 1.055
S-D 0.056 0.091
COV 0.052 0.086
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (9/12)Mean and COV (9/12)
ANSYS Nonlinear FEA versus CSR ISUM (2/2)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mean : 1.090 / 1.055Standard deviation : 0.056 / 0.091COV : 0.052 / 0.086
CSR/ANSYS:
(Mu/M
p)C
SR
(Mu/Mp)ANSYS
Hog / Sag
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
0 0.0125 10 15 20 25 30
0
0.0125
10
15
20
25
30
(Mu)
CSR
(GN
m)
(Mu)ANSYS(GNm)
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
Statistical analysis Statistical analysis -- Mean and COV (10/12)Mean and COV (10/12)
ALPS/HULL ISFEM versus CSR ISUM (1/2)
Ship Mp
(GNm)
Hogging Sagging
ALPS CSRCSR/ALPS
ALPS CSRCSR/ALPSMuh
(GNm)Muh/Mp
Muh
(GNm)Muh/Mp
Mus
(GNm)Mus/Mp
Mus
(GNm)Mus/Mp
Dow's test hull 0.013 0.011 0.799 0.012 0.888 1.111 0.010 0.743 0.010 0.764 1.029
Container ship 9.220 6.916 0.750 8.040 0.872 1.163 6.635 0.720 7.843 0.851 1.182
Bulk carrier 20.394 16.602 0.814 17.941 0.880 1.081 15.380 0.754 14.475 0.710 0.941
D/H Suezmax 17.677 13.308 0.753 15.714 0.889 1.181 11.097 0.628 12.420 0.703 1.119
S/H VLCC 22.578 17.335 0.768 19.889 0.881 1.147 17.263 0.765 17.868 0.791 1.035
D/H VLCC 32.667 25.600 0.784 28.352 0.868 1.108 22.000 0.673 24.798 0.759 1.127
Mean 1.132 1.072
S-D 0.038 0.087
COV 0.034 0.081
Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation
Statistical analysis Statistical analysis -- Mean and COV (11/12)Mean and COV (11/12)
ALPS/HULL ISFEM versus CSR ISUM (2/2)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mean : 1.132 / 1.072Standard deviation : 0.038 / 0.087COV : 0.034 / 0.081
CSR/ALPS:
(Mu/M
p)C
SR
(Mu/Mp)ALPS/HULL
Hog / Sag
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
0 0.0125 10 15 20 25 30
0
0.0125
10
15
20
25
30
(Mu)
CSR
(GN
m)
(Mu)ALPS/HULL (GNm)
Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC
Statistical analysis Statistical analysis -- Mean and COV (12/12)Mean and COV (12/12)
Concluding Remarks(1/2)Concluding Remarks(1/2)
- Four methods, namely NLFEM (ANSYS), ISFEM(ALPS/HULL), ISUM(CSR method), and Modified P-M formula method have been considered.
- Modified P-M formula method calculations are in good agreement with ANSYS nonlinear FEA and ALPS/HULL progressive collapse simulations.
Concluding Remarks(2/2)Concluding Remarks(2/2)
- Statistical analysis of the hull girder ultimate strength based on comparisons among the various computation is carried out in terms of their mean values and coefficient of variation.
ShipFormula/ANSYS
Formula/ALPS
Formula/CSR
ALPS/ANSYS
CSR/ANSYS
CSR/ALPS
Hog Sag Hog Sag Hog Sag Hog Sag Hog Sag Hog Sag
Dow's test hull 0.920 0.879 0.966 0.939 0.870 0.912 0.952 0.936 1.058 0.963 1.111 1.029
Container ship 0.918 1.018 0.925 1.067 0.796 0.902 0.992 0.955 1.154 1.128 1.163 1.182
Bulk carrier 0.947 0.937 0.998 0.962 0.924 1.022 0.949 0.973 1.025 0.916 1.081 0.941
D/H Suezmax 0.993 1.095 1.049 1.101 0.889 0.983 0.946 0.995 1.117 1.114 1.181 1.119
S/H VLCC 1.078 1.102 1.079 1.033 0.940 0.998 0.999 1.067 1.146 1.104 1.147 1.035
D/H VLCC 0.939 0.995 1.003 1.018 0.905 0.903 0.937 0.978 1.037 1.102 1.108 1.127
Mean 0.966 1.004 1.003 1.020 0.887 0.953 0.962 0.984 1.090 1.055 1.132 1.072
S-D 0.061 0.088 0.055 0.061 0.051 0.054 0.026 0.045 0.056 0.091 0.038 0.087
COV 0.063 0.087 0.055 0.060 0.058 0.056 0.027 0.046 0.052 0.086 0.034 0.081