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Guide for Buckling and Ultimate Strength Assessment for Offshore Structures
GUIDE FOR
BUCKLING AND ULTIMATE STRENGTHASSESSMENT FOR OFFSHORE STRUCTURES
APRIL 2004 Updated JUNE 2007
American Bureau of Shipping
Incorporated by Act of Legislature of
the State of New York 1862
Copyright 2004
American Bureau of Shipping
ABS Plaza
16855 Northchase Drive
Houston, TX 77060 USA
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ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 iii
Foreword
Foreword
This Guide for the Buckling and Ultimate Strength Assessment of Offshore Structures is referred to
herein as this Guide. This Guideprovides criteria that can be used in association with specificRules and Guides issued by ABS for the classification of specific types of Offshore Structures. The
specific Rules and Guides that this Guide supplements are the latest editions of the following.
Rules for Building and Classing Offshore Installations [for steel structure only]
Rules for Building and Classing Mobile Offshore Drilling Units (MODUs)
Rules for Building and Classing Single Point Moorings (SPMs)
Guide for Building and Classing Floating Production Installations (FPIs) [for non ship-type
hulls].
In case of conflict between the criteria contained in this Guide and the above-mentioned Rules and
Guides, the latter will have precedence.
These criteria are not to be applied to ship-type FPIs, which are being reviewed to receive a SafeHull-
related Classification Notation. (This includes ship-type FPIs receiving the SafeHull-Dynamic Load
Approach Classification Notation) In these vessel-related cases, the criteria based on the contents of
Part 5 of theRules for Building and Classing Steel Vessels (SVR) apply.
The criteria presented in this Guide may also apply in other situations such as the certification or
verification of a structural design for compliance with the Regulations of a Governmental Authority.
However, in such a case, the criteria specified by the Governmental Authority should be used, but
they may not produce a design that is equivalent to one obtained from the application of the criteria
contained in this Guide. Where the mandated technical criteria of the cognizant Governmental
Authority for certification differ from those contained herein, ABS will consider the acceptance of
such criteria as an alternative to those given herein so that, at the Owner or Operators request, bothcertification and classification may be granted to the Offshore Structure.
ABS welcomes questions on the applicability of the criteria contained herein as they may apply to a
specific situation and project.
ABS also appreciates the receipt of comments, suggestions and technical and application questions for
the improvement of this Guide. For this purpose, enquiries can be sent electronically to [email protected].
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ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 v
Table of Contents
GUIDE FOR
BUCKLING AND ULTIMATE STRENGTHASSESSMENT FOR OFFSHORE STRUCTURES
CONTENTS
SECTION 1 Introduction ............................................................................1
1 General ..................................................................................13 Scope of this Guide................................................................1
5 Tolerances and Imperfections ...............................................1
7 Corrosion Wastage ................................................................2
9 Loadings ................................................................................2
11 Maximum Allowable Strength Utilization Factors ..................3
SECTION 2 Individual Structural Members..............................................5
1 General ..................................................................................5
1.1 Geometries and Properties of Structural Members ...........5
1.3 Load Application.............................................................. ..5
1.5 Failure Modes ...................................................... ............. 6
1.7 Cross Section Classification............................................ 11
1.9 Adjustment Factor.......................................................... .11
3 Members Subjected to a Single Action................................12
3.1 Axial Tension.................................................................. .12
3.3 Axial Compression .......................................................... 12
3.5 Bending Moment...................................................... ....... 15
5 Members Subjected to Combined Loads.............................16
5.1 Axial Tension and Bending Moment................................ 16
5.3 Axial Compression and Bending Moment ....................... 17
7 Tubular Members Subjected to Combined Loads withHydrostatic Pressure............................................................18
7.1 Axial Tension, Bending Moment and HydrostaticPressure.......................................................................... 18
7.3 Axial Compression, Bending Moment and HydrostaticPressure.......................................................................... 19
9 Local Buckling......................................................................21
9.1 Tubular Members Subjected to Axial Compression ........21
9.3 Tubular Members Subjected to Bending Moment ........... 21
9.5 Tubular Members Subjected to Hydrostatic Pressure.....22
9.7 Plate Elements Subjected to Compression andBending Moment............................................................. 23
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vi ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
TABLE 1 Geometries, Properties and Compact Limits ofStructural Members......................................................7
TABLE 2 Effective Length Factor..............................................14
TABLE 3 Minimum Buckling Coefficients under Compression
and Bending Moment, ks ............................................25
FIGURE 1 Load Application on a Tubular Member.......................5
FIGURE 2 Effective Length Factor..............................................14
FIGURE 3 Definition of Edge Stresses........................................24
SECTION 3 Plates, Stiffened Panels and Corrugated Panels.............. 27
1 General ................................................................................27
1.1 Geometry of Plate, Stiffened Panel and CorrugatedPanels ........................................................ .....................27
1.3 Load Application..............................................................291.5 Buckling Control Concepts ..............................................30
1.5 Adjustment Factor ...........................................................31
3 Plate Panels.........................................................................31
3.1 Buckling State Limit.........................................................31
3.3 Ultimate Strength under Combined In-plane Stresses ....34
3.5 Uniform Lateral Pressure.................................................35
5 Stiffened Panels...................................................................36
5.1 Beam-Column Buckling State Limit .................................36
5.3 Flexural-Torsional Buckling State Limit ...........................40
5.5 Local Buckling of Web, Flange and Face Plate ...............427 Girders and Webs................................................................43
7.1 Web Plate........... .............................................................43
7.3 Face Plate and Flange ....................................................43
7.5 Large Brackets and Sloping Webs ..................................43
7.7 Tripping Brackets ............................................................44
7.9 Effects ofCutouts ............................................................44
9 Stiffness and Proportions.....................................................45
9.1 Stiffness of Stiffeners ......................................................45
9.3 Stiffness of Web Stiffeners ..............................................45
9.5 Stiffness of Supporting Girders........................................46
9.7 Proportions of Flanges and Faceplates...........................46
9.9 Proportions of Webs of Stiffeners....................................46
11 Corrugated Panels...............................................................47
11.1 Local Plate Panels...................................... .....................47
11.3 Unit Corrugation ..................................................... .........47
11.5 Overall Buckling ...................................................... ........49
13 Geometric Properties...........................................................50
13.1 Stiffened Panels ...................................................... ........50
13.3 Corrugated Panels .................................................. ........51
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ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 vii
FIGURE 1 Typical Stiffened Panel ..............................................28
FIGURE 2 Sectional Dimensions of a Stiffened Panel................28
FIGURE 3 Typical Corrugated Panel ..........................................29
FIGURE 4 Sectional Dimensions of a Corrugated Panel............29
FIGURE 5 Primary Loads and Load Effects on Plate andStiffened Panel...........................................................30
FIGURE 6 Failure Modes (Levels) of Stiffened Panel ...............31
FIGURE 7 Unsupported Span of Longitudinal ............................39
FIGURE 8 Effective Breadth of Platingsw....................................40
FIGURE 9 Large Brackets and Sloping Webs ............................43
FIGURE 10 Tripping Brackets.......................................................44
SECTION 4 Cylindrical Shells .................................................................53
1 General ................................................................................53
1.1 Geometry of Cylindrical Shells ........................................ 53
1.3 Load Application............................................................. .54
1.5 Buckling Control Concepts.............. ................................ 54
1.7 Adjustment Factor........................................................... 55
3 Unstiffened or Ring-stiffened Cylinders...............................56
3.1 Bay Buckling Limit State ................................................. 56
3.3 Critical Buckling Stress for Axial Compression orBending Moment............................................................. 57
3.5 Critical Buckling Stress for External Pressure......... ........ 58
3.7 General Buckling.......................... ................................... 59
5 Curved Panels .....................................................................59
5.1 Buckling State limit............. ............................................. 59
5.3 Critical Buckling Stress for Axial Compression orBending Moment............................................................. 60
5.5 Critical Buckling Stress under External Pressure............ 61
7 Ring and Stringer-stiffened Shells .......................................62
7.1 Bay Buckling Limit State ................................................. 62
7.3 Critical Buckling Stress for Axial Compression orBending Moment............................................................. 63
7.5 Critical Buckling Stress for External Pressure......... ........ 64
7.7 General Buckling.......................... ................................... 65
9 Local Buckling Limit State for Ring and StringerStiffeners..............................................................................65
9.1 Flexural-Torsional Buckling............................................. 65
9.3 Web Plate Buckling....................................................... ..67
9.5 Faceplate and Flange Buckling....................................... 67
11 Beam-Column Buckling .......................................................67
13 Stress Calculations ..............................................................68
13.1 Longitudinal Stress.......................................................... 68
13.3 Hoop Stress ......................................................... ........... 69
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viii ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
15 Stiffness and Proportions.....................................................70
15.1 Stiffness of Ring Stiffeners ..............................................70
15.3 Stiffness of Stringer Stiffeners.........................................71
15.5 Proportions of Webs of Stiffeners....................................71
15.7 Proportions of Flanges and Faceplates...........................72
FIGURE 1 Ring and Stringer-stiffened Cylindrical Shell .............53
FIGURE 2 Dimensions of Stiffeners............................................54
FIGURE 3 Typical Buckling Modes of Ring and StringerCylindrical Shells........................................................55
SECTION 5 Tubular Joints ...................................................................... 73
1 General ................................................................................73
1.1 Geometry of Tubular Joints .............................................73
1.3 Loading Application .........................................................74
1.5 Failure Modes.................................................................. 74
1.7 Classfication of Tubular Joints.........................................75
1.9 Adjustment Factor ...........................................................76
3 Simple Tubular Joints ..........................................................76
3.1 Joint Capacity........... .......................................................76
3.3 Joint Cans ....................................................... ................77
3.5 Strength State Limit.........................................................78
5 Other Joints..........................................................................79
5.1 Multiplanar Joints ............................................................79
5.3 Overlapping Joints.................................................... .......79
5.5 Grouted Joints ...................................................... ...........80
5.7 Ring-Stiffened Joints .......................................................81
5.9 Cast Joints........................................................... ............81
TABLE 1 Strength Factor, Qu.....................................................77
FIGURE 1 Geometry of Tubular Joints........................................73
FIGURE 2 Examples of Tubular Joint Categoriztion ...................75
FIGURE 3 Examples of Effective Can Length.............................78
FIGURE 4 Multiplanar Joints .......................................................79
FIGURE 5 Grouted Joints............................................................81
APPENDIX 1 Review of Buckling Analysis by Finite Element Method(FEM)..................................................................................... 83
1 General ................................................................................83
3 Engineering Model...............................................................83
5 FEM Analysis Model ............................................................84
7 Solution Procedures.............................................................84
9 Verification and Validation ...................................................85
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ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 1
Section 1: Introduction
S E C T I O N 1 Introduction
1 General
The criteria in this Guide are primarily based on existing methodologies and their attendant safety
factors. These methods and factors are deemed to provide an equivalent level of safety, reflecting
what is considered to be appropriate current practice.
It is acknowledged that new methods and criteria for design are constantly evolving. For this reason,
ABS does not seek to inhibit the use of an alternative technological approach that is demonstrated toproduce an acceptable level of safety.
3 Scope of this Guide
This Guide provides criteria that should be used on the following structural steel components or
assemblages:
Individual structural members (i.e., discrete beams and columns) [see Section 2]
Plates, stiffened panels and corrugated panels [see Section 3]
Stiffened cylindrical shells [see Section 4] Tubular joints [see Section 5]
Additionally, Appendix 1 contains guidance on the review of buckling analysisusing the finite element
method (FEM) to establish buckling capacities.
5 Tolerances and Imperfections
The buckling and ultimate strength of structural components are highly dependent on the amplitude
and shape of the imperfections introduced during manufacture, storage, transportation and installation.
Typical imperfections causing strength deterioration are:
Initial distortion due to welding and/or other fabrication-related process
Misalignments of joined components
In general, the effects of imperfections in the form of initial distortions, misalignments and weld-
induced residual stresses are implicitly incorporated in the buckling and ultimate strength
formulations. Because of their effect on strength, it is important that imperfections be monitored and
repaired, as necessary, not only during construction, but also in the completed structure to ensure that
the structural components satisfy tolerance limits. The tolerances on imperfections to which the
strength criteria given in this Guide are considered valid are listed, for example, in ABS Guide for
Shipbuilding and Repair Quality Standard for Hull Structures During Construction. Imperfections
exceeding such published tolerances are not acceptable unless it is shown using a recognized method
that the strength capacity and utilization factor of the imperfect structural component are withinproper target safety levels.
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Section 1 Introduction
2 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
7 Corrosion Wastage
Corrosion wastage is not incorporated into the buckling and ultimate strength formulations provided
in this Guide. Therefore, a design corrosion margin need not be deducted from the thickness of thestructural components. Similarly, when assessing the strength of existing structures, actual as-gauged
minimum thickness is to be used instead of the as-built thickness.
9 Loadings
Conditions representing all modes of operation of the Offshore Structure are to be considered to
establish the most critical loading cases. The ABS Rules and Guides for the classification of various
types of Offshore Structures typically define two primary loading conditions. In the ABS Rules for
Building and Classing Mobile Offshore Drilling Units (MODU Rules), they are Static Loadings and
Combined Loadings, and in the ABS Rules for Building and Classing Offshore Installations
(Offshore Installations Rules), the ABSRules for Building and Classing Single Point Moorings (SPMRules) and the ABS Guide for Building and Classing Floating Production Installations (FPI Guide)
they are Normal Operation and Severe Storm. The component loads of these loading conditions
are discussed below. The determination of the magnitudes of each load component and each load
effect (i.e., stress, deflection, internal boundary condition, etc.) are to be performed using recognized
calculation methods and/or test results and are to be fully documented and referenced. As
appropriate, the effects of stress concentrations, secondary stress arising from eccentrically applied
loads and member displacements (i.e., P- effects) and additional shear displacements and shear
stress in beam elements are to be suitably accounted for in the analysis.
The primary loading conditions to be considered in the ABSMODU Rules are:
i) Static Loadings. Stresses due to static loads only, where the static loads include operational
gravity loads and the weight of the unit, with the unit afloat or resting on the seabed in calmwater.
ii) Combined Loadings. Stresses due to combined loadings, where the applicable static loads, as
described above, are combined with relevant environmental loadings, including acceleration
and heeling forces.
The primary loading conditions to be considered in the ABS Offshore Installations Rules, ABS SPM
Rules and ABSFPI Guide are:
i) Normal Operations. Stresses due to operating environmental loading combined with dead
and maximum live loads appropriate to the function and operations of the structure
ii) Severe Storm. Stresses due to design environmental loading combined with dead and live
loads appropriate to the function and operations of the structure during design environmentalcondition
The buckling and ultimate strength formulations in this Guide are applicable to static/quasi-static
loads, Dynamic (e.g., impulsive) loads, such as may result from impact and fluid sloshing, can induce
dynamic buckling, which, in general, is to be dealt with using an appropriate nonlinear analysis.
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Section 1 Introduction
ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 3
11 Maximum Allowable Strength Utilization Factors
The buckling and ultimate strength equations in this Guide provide an estimate of the average strength
of the considered components while achieving the lowest standard deviation when compared with
nonlinear analyses and mechanical tests. To ensure the safety of the structural components, maximumallowable strength utilization factors, which are the inverse of safety factors, are applied to the
predicted strength. The maximum allowable strength utilization factors will, in general, depend on the
given loading condition, the type of structural component and the failure consequence.
The maximum allowable strength utilization factors, , are based on the factors of safety given in theABS Offshore Installations Rules, ABS MODU Rules, ABS SPM Rules and ABS FPI Guide, as
applicable. The maximum allowable strength utilization factors have the following values.
i) For aloading condition that is characterized as astatic loadingofa Mobile Offshore Drilling
Unit or normal operation of an Offshore Installation, Floating Production Installation and
Single Point Mooring:
= 0.60ii) For a loading condition that is characterized as a combined loading of a Mobile Offshore
Drilling Unitorsevere storm of an Offshore Installation, Floating Production Installation and
Single Point Mooring:
= 0.80
where
= adjustment factor, as given in subsequent sections of this Guide.
Under the above-mentioned Rules and Guides, it is required that both of the characteristic types of
loading conditions (i.e., static and combined, or normal operation and severe storm) are to be applied
in the design and assessment of a structure. The loading condition producing the most severe
requirement governs the design.
In the Sections that follow concerning specific structural components, different adjustment factorsmay apply to different types of loading (i.e., tension or bending versus pure compression). To represent
the values ofapplicable to the different types of load components, subscripts are sometimes added tothe symbol (e.g., in Section 2, 1 and 2, apply, respectively, to axial compression or tension/bendingin the individual structural member.).
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ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 5
Section 2: Individual Structural Members
S E C T I O N 2 Individual Structural Members
1 General
This Section provides strength criteria for individual structural members. The types of members
considered in this Section are tubular and non-tubular members with uniform geometric properties
along their entire length and made of a single material. The criteria provided in this Section are for
tubular and non-tubular elements, but other recognized standards are also acceptable.
The behavior of structural members is influenced by a variety of factors, including sectional shape,material characteristics, boundary conditions, loading types and parameters and fabrication methods.
1.1 Geometries and Properties of Structural Members
A structural member with a cross section having at least one axis of symmetry is considered. The
geometries and properties of some typical cross sections are illustrated in Section 2, Table 1. For
sections which are not listed in Section 2, Table 1, the required geometric properties are to be calculated
based on acceptable formulations.
1.3 Load Application
This Section includes the strength criteria for any of the following loads and load effects: Axial force in longitudinal direction,P
Bending moment,M
Hydrostatic pressure, q
Combined axial tension and bending moment
Combined axial compression and bending moment
Combined axial tension, bending moment and hydrostatic pressure
Combined axial compression, bending moment and hydrostatic pressure
The load directions depicted in Section 2, Figure 1 are positive.
FIGURE 1Load Application on a Tubular Member
P
M
z
yx
q
L t
P
M
q
z
y
D
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Section 2 Individual Structural Members
6 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
1.5 Failure Modes
Failure modes for a structural member are categorized as follows:
Flexural buckling. Bending about the axis of the least resistance.
Torsional buckling. Twisting about the longitudinal (x) axis. It may occur if the torsional rigidityof the section is low, as for a member with a thin-walled open cross section.
Lateral-torsional buckling. Synchronized bending and twisting. A member which is bent aboutits major axis may buckle laterally.
Local buckling. Buckling of a plate or shell element that is a local part of a member
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TABLE1
(con
tinue
d)
Geometr
ies,
Propert
iesan
dCompac
tLimitso
fStructura
lMem
bers
Geometry
SectionalShape
Geometrical
Parameters
Axis
Properties*
CompactLimits
3.Welded
boxshape
z
ytw
a b
b2
tf
d
d=Webdepth
tw=Webthickness
b=Flangewidth
tf=Flangethickness
b2=Outstand
Majory-y
Minorz-z
A=2(btf+dtw)
Iy=d2(3btf+dtw)/6
Iz=b2(btf+3dtw)/6
K=
+
w
f
td
ta
da
2
2
2
Io=Iy+Iz
=
)
(24
)
(
3
2
2
3
2
3
2
2
3
w
f
w
f
tda
tdb
t
da
tdb
+
0
5.1
,
E
td
ta
w
f
0
2
4.0
E
tbf
4.W-shape
z
y
tw
tf
b
d
d=Webdepth
tw=Webthickness
b=Flangewidth
tf=Flangethickness
Majory-y
Minorz-z
A=2btf+dtw
Iy=d2(6btf+dtw)/12
Iz=b3tf/6
K=(2btf3+dtw3)/3
Io=Iy+Iz
=d2b3tf/24
0
5.1
E
td w
0
8.0
E
tbf
Section 2 Individual Structural Members
8 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
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TABLE1
(con
tinue
d)
Geometr
ies,
Propert
iesan
dCompac
tLimitso
fStructura
lMem
bers
Geometry
SectionalShape
Geometrical
Parameters
Axis
Properties*
CompactLimits
5.Channel
z
ytf
tw
d
b
d=Webdepth
tw=Webthickness
b=Flangewidth
tf=Flangethickness
dcs=Distanceof
shearcenterto
centroid
Majory-y
Minorz-z
A=2btf+dtw
Iy=d2(6btf+dtw)/12
Iz=d3tw(btf+2dtw)/3
A
K=(2btf3+dtw3)/3
Io=Iy+Iz+A
2 csd
=
)
6(12
)
2
3(
3
2
w
f
w
f
f
dt
bt
dt
bt
tbd
+
+
0
5.1
E
td w
0
4.0
E
tbf
6.T-bar
z
y
tw
tf
b
d
d=Webdepth
tw=Webthickness
b=Flangewidth
tf=Flangethickness
dcs=Distanceof
shearcenterto
centroid
Majory-y
Minorz-z
A=btf+dtw
Iy=d3tw(4btf+dtw)/1
2A
Iz=b3tf/12
K=(btf3+dtw3)/3
Io=Iy+Iz+A
2 csd
=(b3tf3+4d3tw3)/144
0
4.0
E
td w
0
8.0
E
tbf
Section 2 Individual Structural Members
ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 9
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TABLE1
(con
tinue
d)
Geometr
ies,
Propert
iesan
dCompac
tLimitso
fStructura
lMem
bers
Geometry
SectionalShape
Geometrical
Parameters
Axis
Properties*
CompactLimits
7.Double
angles
z
y
twb
tf
d
d=Webdepth
tw=Webthickness
b=Flangewidth
tf=Flangethickness
dcs=Distanceof
shearcenterto
centroid
Majory-y
Minorz-z
A=2(btf+dtw)
Iy=d3tw(4btf+dtw)/3
A
Iz=2b3tf/3
K=2(btf3+dtw3)/3
Io=Iy+Iz+A
2 csd
=(b3tf3+4d3tw3)/18
0
4.0
E
td w
0
4.0
E
tbf
*Theformulationsfortheprope
rtiesarederivedassumingthatthesectionisthin-walled(i.e.,thicknessisrelativelysmall)where:
A
=
crosssectionalarea,cm2(in2)
Iy
=
momentofinertiaabouty-axis,cm4(in4)
Iz
=
momentofinertiaaboutz-axis,cm4(in4)
K
=
St.Venanttorsionconstantforthemember,cm4(in4)
I0
=
polarmomentofinertiaofthemember,cm4(in4)
=
warpingcon
stant,cm6(in6)
Section 2 Individual Structural Members
10 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
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Section 2 Individual Structural Members
ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004 11
1.7 Cross Section Classification
The cross section may be classified as:
i) Compact. A cross section is compact if all compressed components comply with the limits in
Section 2, Table 1. For a compact section, the local buckling (plate buckling and shell buckling)can be disregarded because yielding precedes buckling.
ii) Non-Compact. A cross section is non-compact if any compressed component does not comply
with the limits in Section 2, Table 1. For a non-compact section, the local buckling (plate or
shell buckling) is to be taken into account.
1.9 Adjustment Factor
For the maximum allowable strength utilization factors, , defined in Subsection 1/11, the adjustmentfactor is to take the following values:
For axial tension and bending[to establish 2 below]:
= 1.0
For axial compression (column buckling or torsional buckling) [to establish1 below]:
= 0.87 ifEAPr0
= EArP /13.01 0 ifEA >Pr0
where
EA = elastic buckling stress, as defined in 2/3.3, N/cm2 (kgf/cm2, lbf/in2)
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for
steel
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
For compression (local buckling of tubular members) [to establish xandbelow]:
= 0.833 ifCi 0.550
= 0.629 + 0.371Ci/0 ifCi > 0.550
where
Ci = critical local buckling stress, representing Cifor axial compression, as specifiedin 2/9.1,and Cfor hydrostatic pressure, as specified in 2/9.5, N/cm
2 (kgf/cm2,
lbf/in2)
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
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Section 2 Individual Structural Members
12 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
3 Members Subjected to a Single Action
3.1 Axial Tension
Members subjected to axial tensile forces are to satisfy the following equation:
t/20 1
where
t = axial tensile stress, N/cm2 (kgf/cm2, lbf/in2)
= P/A
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
P = axial force, N (kgf, lbf)
A = cross sectional area, cm2 (in2)
2 = allowable strength utilization factor for tension and bending, as defined in1/11and 2/1.9
3.3 Axial Compression
Members subjected to axial compressive forces may fail by flexural or torsional buckling. The
buckling limit state is defined by the following equation:
A/1CA 1
where
A
= axial compressive stress, N/cm2 (kgf/cm2, lbf/in2)
= P/A
P = axial force, N (kgf, lbf)
CA = critical buckling stress, N/cm2 (kgf/cm2, lbf/in2)
= ( )
>
FrEAEA
FrrF
FrEAEA
PPP
P
if11
if
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for
steel
F = 0, specified minimum yield point for a compact section
= Cx, local buckling stress for a non-compact section from Subsection 2/9
EA = elastic buckling stress, which is the lesser of the solutions of the followingquadratic equation, N/cm2 (kgf/cm2, lbf/in2)
0))(( 220 = csEAETEAEEA dA
I
E = Euler buckling stress about minor axis, N/cm2 (kgf/cm2, lbf/in2)
= 2
E/(kL/r)2
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ET = ideal elastic torsional buckling stress, N/cm2 (kgf/cm2, lbf/in2)
=0
2
06.2 I
E
kLI
EK
+
r = radius of gyration about minor axis, cm (in.)
= AI /
E = modulus of elasticity, 2.06 107N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
A = cross sectional area, cm2 (in2)
I = moment of inertia about minor axis, cm4 (in4)
K = St. Venant torsion constant for the member, cm4 (in4)
I0 = polar moment of inertia of the member, cm4 (in4)
= warping constant, cm6 (in6)
dcs = difference of centroid and shear center coordinates along major axis, cm (in.)
L = members length, cm (in.)
k = effective length factor, as specified in Section 2, Table 2. When it is difficult to
clarify the end conditions, the nomograph shown in Section 2, Figure 2 may be
used. The values ofG for each end (A and B) of the column are determined:
=g
g
c
c
L
I
L
IG
c
c
L
Iis the total for columns meeting at the joint considered and
g
g
L
Iis the
total for restraining beams meeting at the joint considered. For a column end that
is supported, but not fixed, the moment of inertia of the support is zero, and the
resulting value ofG for this end of the column would be . However, in practice,unless the footing was designed as a frictionless pin, this value ofG would be
taken as 10. If the column end is fixed, the moment of inertia of the support
would be , and the resulting value ofG of this end of the column would be zero.However, in practice, there is some movement and G may be taken as 1.0. If the
restraining beam is either pinned (G = ) or fixed (G = 0) at its far end,refinements may be made by multiplying the stiffness (Ig/Lg) of the beam by the
following factors:
Sidesway prevented
Far end of beam pinned = 1.5
Sidesway permitted
Far end of beam pinned = 0.5
Far end of beam fixed = 2.0
1 = allowable strength utilization factor for axial compression (column buckling), as
defined in1/11 and 2/1.9
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TABLE 2Effective Length Factor
Buckled shape ofcolumn shown by
dashed line
Theoretical value 0.50 0.70 1.0 1.0 2.0 2.0
Recommended kvalue when idealconditions are
approximated
0.65 0.80 1.2 1.0 2.1 2.0
End conditionnotation
Rotation fixed. Translation fixed
Rotation free. Translation fixed
Rotation fixed. Translation free
Rotation free. Translation free
FIGURE 2Effective Length Factor
GA k GB GA k GB
Sidesway Prevented Sidesway Permittted
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3.5 Bending Moment
A member subjected tobending moment may fail by local buckling or lateral-torsional buckling. The
buckling state limit is defined by the following equation:
b/2CB 1where
b = stress due to bending moment
= M/SMe
M = bending moment, N-cm (kgf-cm, lbf-in)
SMe = elastic section modulus, cm3 (in3)
2 = allowable strength utilization factor for tension and bending
CB
= critical bending strength, as follows:
i) For a tubular member, the critical bending strength is to be obtained from
the equation given in 2/9.3.
ii) For a rolled or fabricated-plate section, the critical bending strength is
determined by the critical lateral-torsional buckling stress.
The critical lateral-torsional buckling stress is to be obtained from the following equation:
C(LT) = ( )
>
FrLTELTE
FrrF
FrLTELTE
PPP
P
)()(
)()(
if11
if
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for
steel
E(LT) = elastic lateral-torsional buckling stress, N/cm2 (kgf/cm2, lbf/in2)
=2
2
)(kLSM
EIC
c
I = moment of inertia about minor axis, as defined in Section 2, Table 1, cm4 (in4)
SMe = section modulus of compressive flange, cm3 (in3)
=c
I
I = moment of inertia about major axis, as defined in Section 2, Table 1, cm4 (in4)
c = distance from major neutral axis to compressed flange, cm (in.)
C =2
2
6.2
)(
kL
I
K
I+
E = modulus of elasticity, 2.06 107N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
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F = 0, specified minimum yield point for a compact section
= Cx, local buckling stress for a non-compact section, as specified in 2/9.7
K = St. Venant torsion constant for the member, cm4 (in4)
= warping constant, cm6 (in6)
L = members length, cm (in.)
k = effective length factor, as defined in 2/3.3
5 Members Subjected to Combined Loads
5.1 Axial Tension and Bending Moment
Members subjected to combined axial tension and bending moment are to satisfy the following
equations at all cross-sections along their length:
For tubular members:
5.022
202
1
+
+
CBz
bz
CBy
byt
1
For rolled or fabricated-plate sections:
CBz
bz
CBy
byt
2202
++ 1
where
t = axial tensile stress from 2/3.1, N/cm2 (kgf/cm2, lbf/in2)
by = bending stress from 2/3.5about membery-axis, N/cm2 (kgf/cm2, lbf/in2)
bz = bending stress from 2/3.5 about memberz-axis, N/cm2 (kgf/cm2, lbf/in2)
CBy = critical bending strength corresponding to membersy-axis from 2/3.5, N/cm2
(kgf/cm2, lbf/in2)
CBz = critical bending strength corresponding to membersz-axis from 2/3.5, N/cm2
(kgf/cm2, lbf/in2)
2 = allowable strength utilization factor for tension and bending, as defined in1/11and2/1.9
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5.3 Axial Compression and Bending Moment
Members subjected to combined axial compression and bending moment are to satisfy the following
equation at all cross sections along their length:
For tubular members:When a/CA > 0.15:
5.02
1
2
121 )/(1
1
)/(1
11
+
+
Eza
bzmz
CBzEya
bymy
CByCA
a CC
1
When a/CA 0.15:
5.022
21
1
+
+
CBz
bz
CBy
by
CA
a
1
For rolled or fabricated-plate sections:
When a/CA > 0.15:
)/(1
1
)/(1
1
12121 Eza
bzmz
CBzEya
bymy
CByCA
a CC
+
+ 1
When a/CA 0.15:
CBz
bz
CBy
by
CA
a
221
++ 1
where
a = axial compressive stress from 2/3.3, N/cm2 (kgf/cm2, lbf/in2)
by = bending stress from 2/3.5about membery-axis, N/cm2 (kgf/cm2, lbf/in2)
bz = bending stress from 2/3.5about memberz-axis, N/cm2 (kgf/cm2, lbf/in2)
CA = critical axial compressive strength from 2/3.3, N/cm2 (kgf/cm2, lbf/in2)
CBy = critical bending strength corresponding to membery-axis from 2/3.5, N/cm2
(kgf/cm2, lbf/in2)
CBz = critical bending strength corresponding to memberz-axis from 2/3.5, N/cm2
(kgf/cm2, lbf/in2)
Ey = Euler buckling stress corresponding to membery-axis, N/cm2 (kgf/cm2, lbf/in2)
= 2E/(kyL/ry)2
Ez = Euler buckling stress corresponding to memberz-axis, N/cm2 (kgf/cm2, lbf/in2)
= 2E/(kzL/rz)2
E = modulus of elasticity, 2.06 107N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
ry, rz = radius of gyration corresponding to the membery- andz-axes, cm (in.)
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ky, kz = effective length factors corresponding to membery- andz-axes from 2/3.3
Cmy, Cmz = moment factors corresponding to the membery- andz-axes, as follows:
i) For compression members in frames subjected to joint translation
(sidesway):
Cm = 0.85
ii) For restrained compression members in frames braced against jointtranslation (sidesway) and with no transverse loading between their
supports:
Cm = 0.6 0.4M1/M2
but not less than 0.4 and limited to 0.85, whereM1/M2 is the ratio ofsmaller to larger moments at the ends of that portion of the member
unbraced in the plane of bending under consideration.M1/M2 is positivewhen the member is bent in reverse curvature, negative when bent in
single curvature.
iii) For compression members in frames braced against joint translation inthe plane of loading and subject to transverse loading between their
supports, the value ofCm may be determined by rational analysis.However, in lieu of such analysis, the following values may be used.
For members whose ends are restrained:
Cm = 0.85
For members whose ends are unrestrained:
Cm = 1.0
1 = allowable strength utilization factor for axial compression (column buckling), asdefined in1/11and2/1.9
2 = allowable strength utilization factor for tension and bending, as defined in1/11and2/1.9
7 Tubular Members Subjected to Combined Loads with
Hydrostatic Pressure
Appropriate consideration is to be given to the capped-end actions on a structural member subjected
to hydrostatic pressure. It should be noted that the equations in this Subsection do not apply unless thecriteria of 2/9.5 are satisfied first.
7.1 Axial Tension, Bending Moment and Hydrostatic Pressure
The following equation is to be satisfied for tubular members subjected to combined axial tension,
bending moment and hydrostatic pressure:
CB
bzby
T
tc
2
22
2
++ 1
where
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tc = calculated axial tensile stress due to forces from actions that include the capped-end actions due to hydrostatic pressure, N/cm2 (kgf/cm2, lbf/in2)
T = axial tensile strength in the presence of hydrostatic pressure, N/cm2 (kgf/cm2,
lbf/in2)
= Cq0
CB = bending strength in the presence of hydrostatic pressure, N/cm2 (kgf/cm2, lbf/in2)
= CqCB
CB = critical bending strength excluding hydrostatic pressure from 2/3.5
Cq = ]3.009.01[22 BBB +
B = /(C)
= 5 4C/0 = hoop stress due to hydrostatic pressure from 2/9.5, N/cm
2 (kgf/cm2, lbf/in2)
C = critical hoop buckling strength from 2/9.5, N/cm2 (kgf/cm2, lbf/in2)
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
2 = allowable strength utilization factor for tension and bending, as defined in1/11and2/1.9
= allowable strength utilization factor for local buckling in the presence ofhydrostatic pressure, as defined in 1/11and2/1.9
7.3 Axial Compression, Bending Moment and Hydrostatic Pressure
Tubular members subjected to combined compression, bending moment and external pressure are to
satisfy the following equations at all cross sections along their length.
When ac/CA> 0.15 and ac > 0.5:
5.02
1
2
1
215.0
15.0
1
15.0
+
+
Ez
ac
bzmz
Ey
ac
bymy
CBCA
ac CC
1
When ac/CA 0.15:
5.022
21
1
+
+
CB
bz
CB
by
CA
a 1
where
ac = calculated compressive axial stress due to axial compression that includes thecapped-end actions due to hydrostatic pressure, N/cm2 (kgf/cm2, lbf/in2)
= hoop stress due to hydrostatic pressure from 2/9.5, N/cm2 (kgf/cm2, lbf/in2)
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CB = critical bending strength in the presence of hydrostatic pressure from 2/7.1,N/cm2 (kgf/cm2, lbf/in2)
CA = axial compressive strength in the presence of hydrostatic pressure
=
>
)/1(if)/1(if
FFrEAF
FFrEAEA
PP
EA = elastic buckling stress in the absence of hydrostatic pressure from 2/3.3, N/cm2
(kgf/cm2, lbf/in2)
= 2/)4( 2 ++
= 1 Pr(1 Pr)F/EA /F
= 0.5(/F)(1 0.5/F)
Ey = Euler buckling stress corresponding to membery-axis from 2/5.3, N/cm2
(kgf/cm2, lbf/in2)
Ez = Euler buckling stress corresponding to memberz-axis from 2/5.3, N/cm2
(kgf/cm2, lbf/in2)
Cmy, Cmz = moment factors corresponding to the membery- andz-axes from 2/5.3
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for
steel
E = modulus of elasticity, 2.06 107N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
F = 0, specified minimum yield point for the compact section
= Cx, local buckling stress for the non-compact section from 2/9.7
1 = allowable strength utilization factor for axial compression (column buckling), asdefined in1/11and2/1.9
2 = allowable strength utilization factor for tension and bending, as defined in1/11and2/1.9
When x > 0.5Cand xx > 0.5C, the following equation is to also be satisfied:
2
5.0
5.0
+
CCCxx
Cx 1
where
x = maximum compressive axial stress from axial compression and bending moment,which includes the capped-end actions due to the hydrostatic pressure, N/cm2
(kgf/cm2, lbf/in2)
= ac + b
ac = calculated compressive axial stress due to axial compression from actions thatinclude the capped-end actions due to hydrostatic pressure, N/cm2 (kgf/cm2,
lbf/in2)
b
= stress due to bending moment from 2/3.5,N/cm2 (kgf/cm2, lbf/in2)
Cx = critical axial buckling stress from 2/9.1, N/cm2 (kgf/cm2, lbf/in2)
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C = critical hoop buckling stress from 2/9.5, N/cm2 (kgf/cm2, lbf/in2)
Cmy, Cmz = moment factors corresponding to the membery- andz-axes, as defined in 2/5.3
x = maximum allowable strength utilization factor for axial compression (local
buckling), as defined in1/11and2/1.9
= maximum allowable strength utilization factor for hydrodynamic pressure (localbuckling), as defined in 1/11 and 2/1.9
9 Local Buckling
For a member with a non-compact section, local buckling may occur before the member as a whole
becomes unstable or before the yield point of the material is reached. Such behavior is characterized
by local distortion of the cross section of the member. When a detailed analysis is not available, the
equations given below may be used to evaluate the local buckling stress of a member with a non-
compact section.
9.1 Tubular Members Subjected to Axial Compression
Local buckling stress of tubular members withD/tE/(4.50) subjected to axial compression may beobtained from the following equation:
Cx = ( )
>
00
0
0
if11
if
rExEx
rr
rExEx
PPP
P
where
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 forsteel
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
Ex = elastic buckling stress, N/cm2 (kgf/cm2, lbf/in2)
= 0.6Et/D
D = outer diameter, cm (in.)
t = thickness, cm (in.)
For tubular members withD/t>E/(4.50), the local buckling stress is to be determined from 4/3.3.
9.3 Tubular Members Subjected to Bending Moment
Critical bending strength of tubular members with D/tE/(4.50) subjected to bending moment maybe obtained from the following equation:
CB =
00
00
0
)/)](/(73.0921.0[
)/)](/(90.1038.1[
)/(
ep
ep
ep
SMSMEtD
SMSMEtD
SMSM
10.0)(for
10.0)(02.0for
02.0)(for
0
0
0
>
E/(4.50), the local buckling stress is to be determined from 4/3.3.
9.5 Tubular Members Subjected to Hydrostatic PressureTubular members with D/tE/(4.50) subjected to external pressure are to satisfy the following equation:
/C 1
where,
= hoop stress due to hydrostatic pressure
= qD/(2t)
q = external pressure
C
= critical hoop buckling strength, N/cm2 (kgf/cm2, lbf/in2)
= B
= plasticity reduction factor
= 1 for 0.55
= 18.045.0
+
for 0.55 < 1.6
=15.11
31.1
+for 1.6 < < 6.25
= 1/ for 6.25 = E/0
E = elastic hoop buckling stress
= 2CEt/D
C = buckling coefficient
= 0.44t/D for 1.6D/t
= 0.44t/D + 0.21(D/t)3/4 for 0.825D/t< 1.6D/t
= 0.737/( 0.579) for 1.5 < 0.825D/t
= 0.80 for
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= geometric parameter
= tDD /2/l
l = length of tubular member between stiffening rings, diaphragms or end
connections
D = outer diameter
t = thickness
E = modulus of elasticity, 2.06 107N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
0 = specified minimum yield point
= maximum allowable strength utilization factor for local buckling in the presenceof hydrostatic pressure, as defined in 1/11and2/1.9
For tubular members withD/t>E/(4.50), the state limit in 4/3.3 is to be applied.
9.7 Plate Elements Subjected to Compression and Bending Moment
The critical local buckling of a member with rolled or fabricated plate section may be taken as thesmallest local buckling stress of the plate elements comprising the section. The local buckling stressof an element is to be obtained from the following equation with respect to uniaxial compression andin-plane bending moment:
Cx = ( )
>
00
0
0
if11
if
rExEx
rr
rExEx
PPP
P
where
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 forsteel
0 = specified minimum yield point, N/cm2 (kgf/cm2, lbf/in2)
Ex = elastic buckling stress, N/cm2 (kgf/cm2, lbf/in2)
=
2
2
2
)1(12
stE
ks
E = modulus of elasticity, 2.06 107
N/cm
2
(2.1 106
kgf/cm
2
, 30 106
lbf/in
2
) forsteel
= Poissons ratio, 0.3 for steel
s = depth of unsupported plate element
t = thickness of plate element
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24 ABSGUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES .2004
ks = buckling coefficient, as follows:
i) For a plate element with all four edges simply supported, the bucklingcoefficient is to be obtained from following equation:
ks =
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TABLE 3Minimum Buckling Coefficients under Compression
and Bending Moment, ks*
Top Edge Free Bottom Edge Free
Loading Bottom EdgeSimply Supported
Bottom EdgeFixed
Top Edge SimplySupported
Top Edge Fixed
amin/amax = 1
(Uniform compression)
0.42 1.33 0.42 1.33
amin/amax = 1
(Pure Bending)
0.85 2.15
amin/amax = 0
0.57 1.61 1.70 5.93
*Note: ks
for intermediate value ofamin
/amax
may be obtained by linear interpolation.
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Section 3: Plates, Stiffened Panels and Corrugated Panels
S E C T I O N 3 Plates, Stiffened Panels and
Corrugated Panels
1 General
The formulations provided in this Section are to be used to assess the Buckling and Ultimate StrengthLimits of plates, stiffened panels and corrugated panels. Two State Limits for Buckling and Ultimate
Strength are normally considered in structural design. The former is based on buckling and the latteris related to collapse.
The criteria provided in this Section apply to Offshore Structures, SPMs, SEDUs, CSDUs and FPIs ofthe TLP and SPAR types, and it is not in the scope of this Guide to use the criteria with ship-typeFPIs. In this latter case, see Chapter 4, Section 2 of the ABSFPI Guide.
The design criteria apply also to stiffened panels for which the moment of inertia for the transversegirders is greater than the moment of inertia of the longitudinal stiffeners. It is not in the scope of thisGuide to use the criteria for orthotropically stiffened plate panels.
Alternatively, the buckling and ultimate strength of plates, stiffened panels or corrugated panels maybe determined based on either appropriate, well-documented experimental data or on a calibratedanalytical approach. When a detailed analysis is not available, the equations provided in this sectionshall be used to assess the buckling strength.
1.1 Geometry of Plate, Stiffened Panel and Corrugated Panels
Flat rectangular plates and stiffened panels are depicted in Section 3, Figure 1. Stiffeners in thestiffened panels are usually installed equally spaced, parallel or perpendicular to panel edges in thedirection of dominant load and are supported by heavier and more widely-spaced deep supportingmembers (i.e., girders). The given criteria apply to a variety of stiffener profiles, such as flat-bar,built up T-profiles, built up inverted angle profiles and symmetric and non-symmetric bulb profiles.The section dimensions of a stiffener are defined in Section 3, Figure 2. The stiffeners may havestrength properties different from those of the plate.
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Section 3 Plates, Stiffened Panels and Corrugated Panels
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FIGURE 1Typical Stiffened Panel
s
ss
s
lyz
x
Girder Stiffener
Longitudinal Girder
Bracket
Transverse Girder
Longitudinal Stiffener
Plate
s
FIGURE 2Sectional Dimensions of a Stiffened Panel
z
bf
b2
b1
tf
y0
dw
tw
z0
t
se
y
Centroid of
Stiffener
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Section 3 Plates, Stiffened Panels and Corrugated Panels
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Corrugated panels, as depicted in Section 3, Figure 3 , are self-stiffened and are usually corrugated inone direction, supported by stools at the two ends across the corrugation direction. They may act aswatertight bulkheads or, when connected with fasteners, they are employed as corrugated sheardiaphragms. The dimensions of corrugated panels are defined in Section 3, Figure 4. The buckling
strength criteria for corrugated panels given in Subsection 3/11are applicable to corrugated panelswith corrugation angle, , between 57 and 90 degrees.
FIGURE 3Typical Corrugated Panel
z
y
x
B
L
FIGURE 4Sectional Dimensions of a Corrugated Panel
z0
t
t
c
a
d
b
z
y
s
Centroid
1.3 Load Application
The plate and stiffened panel criteria account for the following load and load effects. The symbols foreach of these loads are shown in Section 3, Figure 5.
Uniform in-plane compression, ax, ay *
In-plane bending, bx , by
Edge shear,
Lateral loads, q
Combinations of the above
* Note: If uniform stress ax
oray
is tensile rather than compressive, it may be set equal to zero.
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FIGURE 5Primary Loads and Load Effects on Plate and Stiffened Panel
s
ymin
ymax
xmin
xmax
q
l
y
x
Edge Shear
Lateral PressureIn-plane Compression and Bendingymin = ayby
ymax
= ay
+ by
xmin
= ax
bx
xmax
= ax
+ bx
1.5 Buckling Control Concepts
The failure of plates and stiffened panels can be sorted into three levels, namely, the plate level, thestiffened panel level and the entire grillage level, which are depicted in Section 3, Figure 6. Anoffshore structure is to be designed in such a way that the buckling and ultimate strength of each level
is greater than its preceding level (i.e., a well designed structure does not collapse when a plate fails aslong as the stiffeners can resist the extra load they experience from the plate failure). Even if thestiffeners collapse, the structure may not fail immediately as long as the girders can support the extraload shed from the stiffeners.
The buckling strength criteria for plates and stiffened panels are based on the following assumptionsand limits with respect to buckling control in the design of stiffened panels, which are in compliancewith ABS recommended practices.
The buckling strength of each stiffener is generally greater than that of the plate panel it supports.
Stiffeners with their associated effective plating are to have moments of inertia not less than i0,given in 3/9.1.
The deep supporting members (i.e., girders) with their associated effective plating are to havemoments of inertia not less than Is, given in 3/9.5. In addition, tripping (e.g., torsional/flexuralinstability) is to be prevented if tripping brackets are provided, as specified in 3/7.7.
Faceplates and flanges of girders and stiffeners are proportioned such that local instability isprevented (see 3/9.7).
Webs of girders and stiffeners are proportioned such that local instability is prevented (see 3/9.9).
For plates and stiffened panels that do not satisfy these limits, a detailed analysis of buckling strengthusing an acceptable method should be submitted for review.
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FIGURE 6Failure Modes (Levels) of Stiffened Panel
Plate Level
Stiffened Panel Level
Deep Supporting
Member Level
Section 3, Figure 6 illustrates the collapse shape for each level of failure mode. From a reliabilitypoint of view, no individual collapse mode can be 100 percent prevented. Therefore, the bucklingcontrol concept used in this Subsection is that the buckling and ultimate strength of each level isgreater than its preceding level in order to avoid the collapse of the entire structure.
The failure (levels) modes of a corrugated panel can be categorized as the face/web plate bucklinglevel, the unit corrugation buckling level and the entire corrugation buckling level. In contrast tostiffened panels, corrugated panels will collapse immediately upon reaching any one of these threebuckling levels.
1.5 Adjustment Factor
For the maximum allowable strength utilization factors, , defined in 1/11, the adjustment factor is totake the following value:
= 1.0
3 Plate Panels
For rectangular plate panels between stiffeners, buckling is acceptable, provided that the ultimatestrength given in 3/3.5 of the structure satisfies the specified criteria. Offshore practice demonstratesthat only an ultimate strength check is required for plate panels. A buckling check of plate panels is
necessary when establishing the attached plating width for stiffened panels. If the plating does notbuckle, the full width is to be used. Otherwise, the effective width is to be applied if the platingbuckles but does not fail.
3.1 Buckling State Limit
For the Buckling State Limit of plates subjected to in-plane and lateral pressure loads, the followingstrength criterion is to be satisfied:
22
max2
max
+
+
CCy
y
Cx
x
1
where
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xmax = maximum compressive stress in the longitudinal direction, N/cm2 (kgf/cm2, lbf/in2)
ymax = maximum compressive stress in the transverse direction, N/cm2 (kgf/cm2, lbf/in2)
= edge shear stress, N/cm2 (kgf/cm2, lbf/in2)
Cx = critical buckling stress for uniaxial compression in the longitudinal direction,N/cm2 (kgf/cm2, lbf/in2)
Cy = critical buckling stress for uniaxial compression in the transverse direction,N/cm2 (kgf/cm2, lbf/in2)
C = critical buckling stress for edge shear, N/cm2 (kgf/cm2, lbf/in2)
= maximum allowable strength utilization factor, as defined in1/11and3/1.7
The critical buckling stresses are specified below.
3.1.1 Critical Buckling Stress for Edge Shear
The critical buckling stress for edge shear, C, may be taken as:
C=
( )
>
00
0
0
for11
for
rEE
rr
rEE
PPP
P
where
Pr = proportional linear elastic limit of the structure, which may be taken as0.6 for steel
0 = shear strength of plate, N/cm2 (kgf/cm2, lbf/in2)
=3
0
0 = specified minimum yield point of plate, N/cm2 (kgf/cm2, lbf/in2)
E = elastic shear buckling stress, N/cm2 (kgf/cm2, lbf/in2)
=( )
2
2
2
112
stE
ks
ks = boundary dependent constant
= 1
2
34.50.4 Cs
+
l
E = modulus of elasticity, 2.06 107 N/cm2 (2.1 106 kgf/cm2, 30 106lbf/in2) for steel
= Poissons ratio, 0.3 for steel
l = length of long plate edge, cm (in.)
s = length of short plate edge, cm (in.)
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t = thickness of plating, cm (in.)
C1 = 1.1 for plate panels between angles or tee stiffeners; 1.0 for plate panelsbetween flat bars or bulb plates; 1.0 for plate elements, web plate ofstiffeners and local plate of corrugated panels
3.1.2 Critical Buckling Stress for Uniaxial Compression and In-plane Bending
The critical buckling stress, Ci (i = x ory), for plates subjected to combined uniaxialcompression and in-plane bending may be taken as:
Ci =
( )
>
00
0
0
for11
for
rEiEi
rr
rEiEi
PPP
P
where
Pr = proportional linear elastic limit of the structure, which may be taken as0.6 for steel
Ei = elastic buckling stress, N/cm2 (kgf/cm2, lbf/in2)
=( )
2
2
2
112
stE
ks
For loading applied along the short edge of the plating (long plate):
ks =
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= ratio of edge stresses, as defined in Section 3, Figure 5*
= imin/imax
* Note: There are several cases in the calculation of ratio of edge stresses, :
If uniform stress ai (i =x,y) < 0 (tensile) and in-plane stress bi (i =x,y)= 0, buckling check is not necessary, provided edge shear is zero;
If uniform stress ai (i = x, y) < 0 (tensile) and in-plane bending stressbi (i =x,y) 0, then imax = bi and imin = bi, so that = 1;
If uniform stress ai (i = x, y) > 0 (compressive) and in-plane bendingstress bi (i =x,y) = 0, imax = imin = i, then = 1;
If uniform stress ai (i =x,y) >0 (compressive) and in-plane bending stressbi (i =x,y) 0, imax = ai + bi, imin = ai bi then 1 < < 1.
0 = specified minimum yield point of plate, N/cm2 (kgf/cm2, lbf/in2)
E = modulus of elasticity, 2.06 107 N/cm2 (2.1 106 kgf/cm2, 30 106
lbf/in2) for steel
= Poissons ratio, 0.3 for steel
l = length of long plate edge, cm (in.)
s = length of short plate edge, cm (in.)
t = thickness of plating, cm (in.)
C1 = 1.1 for plate panels between angles or tee stiffeners; 1.0 for plate panelsbetween flat bars or bulb plates; 1.0 for plate elements, web plate of
stiffeners and local plate of corrugated panels
C2 = 1.2 for plate panels between angles or tee stiffeners; 1.1 for plate panels
between flat bars or bulb plates; 1.0 for plate elements and web plates
3.3 Ultimate Strength under Combined In-plane Stresses
The ultimate strength for a plate between stiffeners subjected to combined in-plane stresses is to
satisfy the following equation:
22
maxmaxmax
2
max
+
+
UUy
y
Uy
y
Ux
x
Ux
x
1
where
xmax = maximum compressive stress in the longitudinal direction, N/cm2
(kgf/cm2
, lbf/in2
)
ymax = maximum compressive stress in the transverse direction, N/cm2 (kgf/cm2, lbf/in2)
= edge shear stress, N/cm2 (kgf/cm2, lbf/in2)
= coefficient to reflect interaction between longitudinal and transverse stresses(negative values are acceptable)
= 1.0-/2
Ux = ultimate strength with respect to uniaxial stress in the longitudinal direction,N/cm2 (kgf/cm2, lbf/in2)
= CxoCx
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Cx =
>
1for0.1
1for/1/2 2
Uy = ultimate strength with respect to uniaxial stress in the transverse direction, N/cm2
(kgf/cm2, lbf/in2)
= Cy0Cy
Cy = ( ) 1/1111.0 22 +
+ ll
ssCx
U = ultimate strength with respect to edge shear, N/cm2 (kgf/cm2, lbf/in2)
= ( ) ( ) CCC +++2/12
0 1/35.0
Cx = critical buckling stress for uniaxial compression in the longitudinal direction,specified in 3/3.1.2,N/cm2 (kgf/cm2, lbf/in2)
Cy = critical buckling stress for uniaxial compression in the transverse direction,specified in 3/3.1.2,N/cm2 (kgf/cm2, lbf/in2)
C = critical buckling stress for edge shear, as specified in 3/3.1.1
= slenderness ratio
=Et
s 0
E = modulus of elasticity, N/cm2 (kgf/cm2, lbf/in2)
l = length of long plate edge, cm (in.)
s = length of short plate edge, cm (in.)
t = thickness of plating, cm (in.)
0 = yield point of plate, N/cm2 (kgf/cm2, lbf/in2)
= maximum allowable strength utilization factor, as defined in1/11and 3/1.7.
, se and le are as defined in 3/3.3. Cx, Cy, 0, Cand are as defined in 3/3.1.
3.5 Uniform Lateral Pressure
In addition to the buckling/ultimate strength criteria in 3/3.1 through 3/3.3, the ultimate strength of a
panel between stiffeners subjected to uniform lateral pressure alone or combined with in-planestresses is to also satisfy the following equation:
qu2
02
2
0 11
10.4
+
e
s
t
where
t = plate thickness, cm (in.)
= aspect ratio
= l/s
l = length of long plate edge, cm (in.)
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s = length of short plate edge, cm (in.)
0 = specified minimum yield point of plate, N/cm2 (kgf/cm2, lbf/in2)
e = equivalent stress according to von Mises, N/cm2 (kgf/cm2, lbf/in2)
= 22
maxmaxmax2
max 3 ++ yyxx
xmax = maximum compressive stress in the longitudinal direction, N/cm2 (kgf/cm2, lbf/in2)
ymax = maximum compressive stress in the transverse direction, N/cm2 (kgf/cm2, lbf/in2)
= edge shear
= maximum allowable strength utilization factor, as defined in1/11and3/1.7
5 Stiffened Panels
The failure modes of stiffened panels include beam-column buckling, torsion and flexural buckling of
stiffeners and local buckling of stiffener web and faceplate. The stiffened panel strength against these
failure modes is to be checked with the criteria provided in 3/5.1 through 3/5.5. Buckling state limits
for a stiffened panel are considered its ultimate state limits.
5.1 Beam-Column Buckling State Limit
The beam-column buckling state limit may be determined as follows:
)/(1[)/( )(0 CEa
bm
eCA
a C
AA
+ 1
where
a = nominal calculated compressive stress, N/cm2 (kgf/cm2, lbf/in2)
= P/A
P = total compressive load on stiffener using full width of associated plating, N (kgf, lbf)
CA = critical buckling stress, N/cm2 (kgf/cm2, lbf/in2)
= E(C) forE(C)Pr0
=
)(
00 )1(1
CE
rr PP
forE(C) >Pr0
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for steel
E(C) = Eulers buckling stress
=2
22
l
eEr
A = total sectional area, cm2 (in2)
= As + st
As = sectional area of the longitudinal, excluding the associated plating, cm2
(in2
)
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Ae = effective sectional area, cm2 (in2)
= As +set
se = effective width, cm (in.)
= s when the buckling state limit of the associated plating from
3/3.1 is satisfied
= CxCyCxys when the buckling state limit of the associated plating from
3/3.1is not satisfied
Cx =
>
1for0.1
1for/1/2 2
Cy = ( )2
max2max 25.0115.0
+
Uy
y
Uy
y
*
* Note: A limit forCy is that the transverse loading should be less than the transverse ultimatestrength of the plate panels. The buckling check for stiffeners is not to be performed untilthe attached plate panels satisfy the ultimate strength criteria.
ymax = maximum compressive stress in the transverse direction, N/cm2 (kgf/cm2, lbf/in2)
Uy = ultimate strength with respect to uniaxial stress in the transverse direction, asspecified in 3/3.3, N/cm2 (kgf/cm2, lbf/in2)
Cxy =
2
0
1
= 1.0 /2
=Et
s 0
re = radius of gyration of area,Ae, cm (in.)
=e
e
A
I
Ie = moment of inertia of longitudinal or stiffener, accounting for the effective width,se, cm
4 (in4)
E = modulus of elasticity, 2.06 107 N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
0 = specified minimum yield point of the longitudinal or stiffener underconsideration. If there is a large difference between the yield points of alongitudinal or stiffener and the plating, the yield point resulting from theweighting of areas is to be used. N/cm2 (kgf/cm2, lbf/in2)
b = bending stress, N/cm2 (kgf/cm2, lbf/in2)
= M/SMw
M = maximum bending moment induced by lateral loads, N-cm (kgf-cm, lbf-in)
= qsl2/12
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Cm = moment adjustment coefficient, which may be taken as 0.75
q = lateral pressure for the region considered, N/cm2 (kgf/cm2, lbf/in2)
s = spacing of the longitudinal, cm (in.)
l = unsupported span of the longitudinal or stiffener, cm (in.), as defined in Section 3,Figure 7
SMw = effective section modulus of the longitudinal at flange, accounting for theeffective breadth,sw, cm
3 (in3)
sw = effective breadth, as specified in Section 3, Figure 8, cm (in.)
= maximum allowable strength utilization factor, as defined in1/11and3/1.7
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FIGURE 7Unsupported Span of Longitudinal
l
l
l
Supported by transverses
Supported by transverses
and flat bar stiffeners
Supported by transverses,
flat bar stiffeners
and brackets
Transverse
Flat Bar
dw/2
dw
a)
b)
c)
Transverse
Transverse Transverse
Flat Bar
Flat Bar Flat Bar
Transverse Transverse
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FIGURE 8Effective Breadth of Platingsw
l
cl
Bending Moment
Longitudinal
cl/s 1.5 2 2.5 3 3.5 4 4.5 and greater
sw/s 0.58 0.73 0.83 0.90 0.95 0.98 1.0
5.3 Flexural-Torsional Buckling State Limit
In general, the flexural-torsional buckling state limit of stiffeners or longitudinals is to satisfy theultimate state limit given below:
CT
a
1
where
a = nominal axial compressive stress of stiffener and its associated plating, N/cm2
(kgf/cm2, lbf/in2)
CT = critical torsional/flexural buckling stress with respect to axial compression of astiffener, including its associated plating, which may be obtained from thefollowing equations:
= ( )
>
00
0
0
if11
if
rETET
rr
rETET
PPP
P
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for steel
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ET = elastic flexural-torsional-buckling stress with respect to the axial compression ofa stiffener, including its associated plating, N/cm2 (kgf/cm2, lbf/in2)
= E
n
CI
nE
CnK
cL
20
0
20
2
6.2
+
+
+
l
l
l
K = St. Venant torsion constant for the stiffener cross section, excluding theassociated plating, cm4 (in4)
=3
33wwff tdtb +
I0 = polar moment of inertia of the stiffener, excluding the associated plating(considered at the intersection of the web and plate), cm4 (in4)
= Iy + mIz+As(y02 +z02)
Iy,Iz = moment of inertia of the stiffener about they- andz-axis, respectively, throughthe centroid of the longitudinal, excluding the plating (x-axis perpendicular to the
y-zplane shown in Section 3, Figure 2), cm4 (in4)
m =
f
w
b
du 1.07.00.1
u =fb
b121 , unsymmetrical factor
y0 = horizontal distance between centroid of stiffener,As, and web plate centerline (seeSection 3, Figure 2), cm (in.)
z0 = vertical distance between centroid of stiffener,As, and its toe (see Section 3,Figure 2), cm (in.)
dw = depth of the web, cm (in.)
tw = thickness of the web, cm (in.)
bf = total width of the flange/face plate, cm (in.)
b1 = smaller outstand dimension of flange/face plate with respect to webs centerline,cm (in.)
tf = thickness of the flange/face, cm (in.)
C0 =s
Et
3
3
warping constant, cm6 (in6)
36
332 wwwzf
tddmI +
Ixf
=
+
s
wwff
A
tdubt 23
0.30.112
, cm4 (in4)
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cL = critical buckling stress for associated plating corresponding to n-half waves,N/cm2 (kgf/cm2, lbf/in2)
= ( )2
222
112
+
s
t
n
nE
=s
l
n = number of half-waves that yield the smallest ET
E = modulus of elasticity, 2.06 107 N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
= Poissons ratio, 0.3 for steel
0
= specified minimum yield point of the material, N/cm2 (kgf/cm2, lbf/in2)
s = spacing of longitudinal/stiffeners, cm (in.)
As = sectional area of the longitudinal or stiffener, excluding the associated plating,
cm2 (in2)
t = thickness of the plating, cm (in.)
l = unsupported span of the longitudinal or stiffener, cm (in.)
= maximum allowable strength utilization factor, as defined in1/11and3/1.7
5.5 Local Buckling of Web, Flange and Face Plate
The local buckling of stiffeners is to be assessed if the proportions of stiffeners specified inSubsection 3/9 are not satisfied.
5.3.1 Web
Critical buckling stress can be obtained from3/3.1 by replacing s with the web depth and l
with the unsupported span, and taking:
ks = 4Cs
where
Cs = 1.0 for angle or tee bar
= 0.33 for bulb plates= 0.11 for flat bar
5.3.2 Flange and Face Plate
Critical buckling stress can be obtained from 3/3.1 by replacing s with the larger outstanding
dimension of flange, b2(see Section 3, Figure 2), and l with the unsupported span, and taking:
ks = 0.44
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7 Girders and Webs
In general, the stiffness of web stiffeners fitted to the depth of web plating is to be in compliance with
3/9.3. Web stiffeners that are oriented parallel to the face plate, and thus subject to axial compression,
are to also satisfy 3/3.1, considering the combined effects of the compressive and bending stresses inthe web. In this case, the unsupported span of these parallel stiffeners may be taken as the distance
between tripping brackets, as applicable.
The buckling strength of the web plate between stiffeners and flange/face plate is to satisfy the limits
specified in 3/3.1 through 3/3.5. When cutouts are present in the web plate, the effects of the cutouts
on the reduction of the critical buckling stresses should be considered (See 3/7.9).
In general, girders are to be designed as stocky so that lateral buckling may be disregarded and
torsional buckling also may be disregarded if tripping brackets are provided (See 3/7.7). If this is not
the case, the girder is to be checked according to Subsection 3/5.
7.1 Web Plate
The buckling limit state for a web plate is considered as the ultimate state limit and is given in 3/3.1.
7.3 Face Plate and Flange
The breadth to thickness ratio of faceplate and flange is to satisfy the limits given in 3/9.7.
7.5 Large Brackets and Sloping Webs
The buckling strength is to satisfy the limits specified in 3/3.1 for the web plate.
FIGURE 9
Large Brackets and Sloping Webs
Large Bracket
Sloping Plate
Sloping Web
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7.7 Tripping Brackets
To prevent tripping of deep girders and webs with wide flanges, tripping brackets are to be installed
with spacing generally not greater than 3 meters (9.84 ft).
FIGURE 10Tripping Brackets
P
TRIPPING BRACKET
The design of tripping brackets may be based on the force, P, acting on the flange, as given by the
following equation:
P= 0.02cl(bftf +3
1dw bw)
where
cl = critical lateral buckling stress with respect to axial compression between trippingbrackets, N/cm2 (kgf/cm2, lbf/in2)
= ce forcePr0
= 0 [1 Pr(1 Pr)0/ce] force >Pr0
ce = 0.6E[(bf/tf)(tw /dw)3], N/cm2 (kgf/cm2, lbf/in2)
Pr = proportional linear elastic limit of the structure, which may be taken as 0.6 for steel
E = modulus of elasticity, 2.06 107 N/cm2 (2.1 106 kgf/cm2, 30 106 lbf/in2) forsteel
0 = specified minimum yield point of the material, N/cm2 (kgf/cm2, lbf/in2)
bf,tf,dw,tw are defined in Section 3, Figure 2.
7.9 Effects of Cutouts
The depth of a cutout, in general, is to be not greater than dw /3, and the calculated stresses in the area
are to account for the local increase due to the cutout.
7.5.1 Reinforced by Stiffeners around Boundaries of Cut-outs
When reinforcement is made by installing straight stiffeners along boundaries of a cutout, the
critical buckling stresses of the web plate between stiffeners with respect to compression, in-
plane bending and shear may be obtained from 3/3.1.
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7.5.2 Reinforced by Face Plates around Contour of Cut-outs
When reinforcement is made by adding face plates along the contour of a cut-out, the critical
buckling stresses with respect to compression, bending and shear may be obtained from 3/3.1,