OFFSHORE TECHNOLOGY REPORT 2001/ · PDF fileCONTENTS 8.2 Differences ISO Versus NORSOK 20 8.1...

HSEHealth & Safety

Executive

Comparison of tubular member strengthprovisions in codes and standards

Prepared by Bomel Limitedfor the Health and Safety Executive

OFFSHORE TECHNOLOGY REPORT

2001/084

HSEHealth & Safety

Executive

Comparison of tubular member strengthprovisions in codes and standards

Bomel LimitedLedger House

Forest Green RoadFifield

MaidenheadBerkshire SL6 2NR

United Kingdom

HSE BOOKS

ii

© Crown copyright 2002Applications for reproduction should be made in writing to:Copyright Unit, Her Majesty’s Stationery Office,St Clements House, 2-16 Colegate, Norwich NR3 1BQ

First published 2002

ISBN 0 7176 2282 7

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This report is made available by the Health and SafetyExecutive as part of a series of reports of work which hasbeen supported by funds provided by the Executive.Neither the Executive, nor the contractors concernedassume any liability for the reports nor do theynecessarily reflect the views or policy of the Executive.

CONTENTS

208.2 Differences ISO Versus NORSOK

188.1 Interaction Formulae

18AXIAL COMPRESSION AND BENDING8



15AXIAL TENSION AND BENDING7

136.2 Partial Safety Factors

136.1 Design Criteria

13HYDROSTATIC PRESSURE6

115.2 Partial Safety Factors


11BENDING5


94.4 Axial Compressive Strength and Local Buckling Strength

84.3 Effective Length Factor

64.2 Partial Safety Factor


6AXIAL COMPRESSION4

4AXIAL TENSION3

2GENERAL COMPARISONS2

1INTRODUCTION1

Page No

iii

CONTENTS contd

36APPENDIX A LISTS OF SYMBOLS

35REFERENCES13

33CONCLUSIONS12

31DEFINITIONS OF CHARACTERISTIC EQUATIONS11



27AXIAL COMPRESSION, BENDING AND HYDROSTATIC PRESSURE10



23AXIAL TENSION, BENDING AND HYDROSTATIC PRESSURE9

Page No

iv

1. INTRODUCTION

The purpose of this Technical Note is to review and compare formulations for tubularmember strength given in the NORSOK standard for the design of Steel Structures [1],the 4th Edition Guidance Notes [2] and the draft of the forthcoming ISO standard forfixed steel offshore structures [3].

A general comparison is made first in Section 2, followed by detailed comparisonsbetween the provisions in the ISO and NORSOK standards, in terms of designresistances. These cover:

i. axial tension;ii. bending;iii. compression;iv. hydrostatic pressure;v. axial tension combined with bending;vi. axial compression combined with bending;vii. axial tension, bending and hydrostatic pressure;viii. axial compression, bending and hydrostatic pressure.

The reasons for limiting the detailed comparison to the ISO and NORSOK standardsare given in Section 2.

All the symbols and nomenclature used pertaining to the formulae set out in sections 3to 10 are defined in Appendix A

1

2. GENERAL COMPARISONS

Both the ISO and NORSOK standards involve modern limit state approaches to steeldesign. This involves the use of partial safety factors applied as multiples tocharacteristic loads to give design action effects, and divisors applied to characteristicresistances to give design resistances.

In considering the resistance partial safety factors, a principal difference between ISOand NORSOK is that ISO uses factors that are constant in value for the type ofresistance under consideration. NORSOK, on the other hand, in cases of loading thatgenerates compressive stresses, uses partial safety factors that vary and depend onthe severity of the loading and the slenderness of the component under design.

Both these codes have limits of applicability on the geometric slenderness - tubulardiameter to thickness (D/t) - to be < 120, and tubular wall thickness to be > 6mm. ISOalso limits the material yield strength and yield ratio (yield to ultimate strength) to 500MPa and 0.85, respectively. NORSOK argues that the use of steel with yield strengthin excess of 500 MPa must be justified.

The 4th Edition Guidance Notes (GNs) were not meant to be a code or a standard andwere intended to deliver guidance. As such direct quantitative comparison with ISOand NORSOK is not possible.

Section 21 of the GNs gives information on steel in material terms, and in terms ofsteelwork design. Clauses deal with allowable stresses in steel that should be inaccordance with the steel grade, and within the limits specified in an appropriate code.Tensile stress limits of 60% and 80% of yield are suggested for operating and extremeloading conditions, respectively.

In terms of compression, clauses indicate that bending of components must beconsidered including:

i. slender, tubular, chord and bracing elements of the structural frameworkii. flat stiffened panelsiii. ring-stiffened cylindrical shellsiv. end-closures to cylindrical shellsv. large diameter orthogonally stiffened cylinders.

Reference in the GNs is made to Appendix A21 for 'detailed guidance'. This,however, only relates to buckling. Each of the items i. to v., above, is dealt withtextually. Reference is made to other contemporaneous technical information (OTCpapers, journal papers, DNV guidelines, API/BSI Standards / Codes etc.), much of

2

which would now be outdated, superseded or incorporated into more current codesand standards. The guidance notes give no technical formulations for detailed design,but the principles therein remain valid however.

For these reasons, therefore, the comparisons in the remainder of this Technical Notefocus on the NORSOK and ISO provisions.

3

3. AXIAL TENSION

The design criteria for tubular members subjected to axial tensile loads, from the twostandards are set out in Table 3.1.

Hence, in comparing design resistances alone (i.e. not allowing for any differences inpartial safety factors applied to the actions) then the NORSOK design resistance is1.05 / 1.15 = 91% of the ISO design resistance. This difference is entirely due to thedifferences between the partial safety factors on resistance.

4

NSd Nt.Rd≤A fy⋅

γM

NSd = design axial force

A = cross-section area

fy = characteristic yield strength

γM = partial material factor [for axial tensile strength] = 1.15

ft

Fy

γRt≤

ft = axial tensile stress due to forces from factored actions

Fy = characteristic yield strength in stress units

γRt = partial resistance factor for axial tensile strength = 1.05

NORSOKISO

Table 3.1 Design Criteria for Axial Tension

5

4. AXIAL COMPRESSION

4.1 DESIGN CRITERIA

The design criteria for tubular members subjected to axial compressive loads, withouthydrostatic pressure, from the two standards are set out in Table 4.1.

Potential sources of difference between the two codes are discussed in the followingsubsections in respect of:

� partial safety factor� effective length factor� axial compressive strength and local buckling strength.

4.2 PARTIAL SAFETY FACTOR

Differences in the partial safety factors between the ISO and NORSOK standards existas follows:

cM = 1.15 for ks < 0.5

cM = 0.85 + 0.60 ks for 0.5 ñ ks ñ 1.0

cM = 1.45 for ks > 1.0

For the case of axial compression ONLY

ks2 =

fy

fcle

Hence,

ks = 1.291fy

E $ Dt

cRc = 1.18

NORSOKISO

It is clear from this that the difference in the partial safety factors depends on theproduct of the ratios fy/E and D/t. The NORSOK partial safety factor ranges between98% and 123% of the ISO one. The NORSOK standard becomes more conservativethan ISO when:

Fy

E $ Dt ISO

,fy

E $ Dt NORSOK

>0.181

6

k = effective length factorl = unbraced length of member in y- [in-plane] or z- [out-of-plane] direction

i = radius of gyration [of cross-section]

E = Young's modulus of elasticity

D = outside diameter [of cross-section]

t = wall thickness [of cross-section]

DK = effective length factorL = unbraced length of member in y- [in-plane] or z- [out-of-plane] direction

r = radius of gyration [of cross-section]

E = Young's modulus of elasticity

D = outside diameter [of cross-section]

t = wall thickness [of cross-section]

NSd Nc.Rd≤A fc⋅

γM

NSd = design axial force

fc 1.0 0.28 λ2

⋅−( ) fy⋅ for⋅ λ⋅ 1.34≤

fc0.9

λ2

fy⋅ for⋅ λ⋅ 1.34>

λk l⋅

π i⋅

fcl

E

0.5

⋅

fcl fy for⋅fy

fcle⋅ 0.170≤

fcl 1.047 0.274fy

fcle⋅−

fy⋅ for⋅ 0.170⋅fy

fcle<

fcle 2 Ce⋅ E⋅t

D

⋅ Ce = 0.3

fc

Fc

γRc≤

fc = axial compressive stress due to forces from factored actions

Fc 1.0 0.28 λ2⋅−( ) Fyc⋅ for⋅ λ⋅ 1.34≤

Fc0.9

λ2Fyc⋅ for⋅ λ⋅ 1.34>

λK L⋅

π r⋅

Fyc

E

0.5

⋅

Fyc Fy for⋅Fy

Fxe⋅ 0.170≤

Fyc 1.047 0.274Fy

Fxe⋅−

Fy⋅ for⋅ 0.170⋅Fy

Fxe< 1.911≤

Fyc Fxe for⋅Fy

Fxe⋅ 1.911>

Fxe 2 Cx⋅ E⋅t

D

⋅ Cx = 0.6 (theory); = 0.3 (recommended)

NORSOKISO

Table 4.1 Design Criteria for Axial Compression

7

4.3 EFFECTIVE LENGTH FACTOR

The effective length factors of the ISO and NORSOK standards (K and k, respectively)are derived in an identical fashion, according to the table given below. No differencesbetween the standards will be introduced into the design resistances through thismechanism.

0.7Secondary horizontals

0.8- Longer segment length of X-braces (3)

0.7- K-braces (3)

0.7- Primary diagonals and horizontals

Jacket braces

1.0- Ungrouted piling between shim points

1.0- Ungrouted jacket legs

1.0- Grouted composite section

Jacket legs and piling

see note below- Portal (unbraced)

1.0- Braced

Superstructure legs

K or kStructural element

Note: for both standards the effective length factors for unbraced superstructure legs are derived

from a commentary.

Table 4.2 Effective Length Factors

8

4.4 AXIAL COMPRESSIVE STRENGTH AND LOCAL BUCKLINGSTRENGTH

With study, it is clear from the equations given in Table 4.1 that the ISO and NORSOKcodes will give identical values for characteristic axial compressive strengths if

.Fy

E $ Dt =

fy

E $ Dt ñ 0.102

This is because, for this range of the product of these ratios, Fyc = Fy = fy and hence Fc

= fc.

A slightly different situation arises if the following obtains:

0.102 <Fy

E $ Dt =

fy

E $ Dt ñ 1.147

In this case the effective length factors are the same value for both codes, butbecause the ISO formula for characteristic axial compressive strength uses thecharacteristic local buckling strength (Fyc), whereas NORSOK uses the yield strength,then Fc (ISO)< fc (NORSOK). The characteristic local buckling strength degradeslinearly with the Fy/E, D/t product according to:

.Fyc

Fy= 1.047 - 0.457

Fy

E $ Dt

Given the limitations on Fy and D/t set by both the ISO and NORSOK standards of 500MPa and 120, respectively, this sets an upperbound of:

Fy

E $ Dt =

fy

E $ Dt ñ 0.286

At this upperbound, therefore, the NORSOK characteristic axial compressive strengthwill be about 109% of that calculated via the ISO standard.

The NORSOK standard is not clear, however, about the procedure to adopt when Fy/Ex D/t > 0.102. It may be that it is necessary to bring the calculations closer intoalignment with those of ISO in this situation.

4.5 DIFFERENCES ISO VERSUS NORSOK

Within the practical ranges of materials and slenderness parameters discussed in theproceeding subsection, and with reference to Table 4.1 (after some simplifyingalgebra), it can be shown that differences in the design resistance are caused by twoeffects:

9

a. partial safety factor computation; i.e. differences between γRc - ISO, and γM -NORSOK

b. use of the characteristic local buckling strength in the computation of thecharacteristic axial compressive strength; i.e. differences between Fc - ISO,and fc - NORSOK.

The individual differences depend on the value of Fy/E.D/t and contribute to the overalldifferences in the way set out in Table 4.3. This gives, for a range and specific valuesof Fy/E x D/t (or fy/E x D/t), the ratios of partial safety factors, characteristic axialcompressive strengths and factored axial resistances.

0.8550.9161.0710.286

1.0040.9790.9750.150

1.0261.0000.975 0.102ñ

fccM

$cRcFc

fcFc

cMcRc

Fy

E $ Dt or

fy

E $ Dt

Factored AxialResistances

b/a(NORSOK/ISO)

CharacteristicAxial Compressive

Strengthsb (see above)

Partial SafetyFactors

a (see above)

Ratio of NORSOK:ISO

Table 4.3 Design Resistance Ratios

It is worth noting that, whilst at the upper limits corresponding to Fy = 500 MPaand D/t = 120 the NORSOK design resistance is 15% less than the ISO value, inpractice D/t ratios are likely to be less than 60. This gives Fy/E.D/t for 350 MPa steeland 500 MPa steel as 0.100 and 0.143, respectively. Therefore, under these practicalcircumstances, the difference between ISO and NORSOK regarding design resistanceis negligible.

10

5. BENDING

5.1 DESIGN CRITERIA

The design criteria for tubular members subjected to bending alone are set out inTable 5.1. The difference between the two codes lies with the partial safety factors, asdiscussed below.

5.2 PARTIAL SAFETY FACTORS

Differences in the partial safety factors for bending between the ISO and NORSOKstandards exist as follows:

The same expressions as for axial

compression are used for γM (see Subsection4.2).

These become, upon simplification forbending only:

cM = 1.15 forfy

E $ Dt < 0.150

cM = 0.85 + 0.775fy

E $ Dt

for 0.150 ñfy

E $ Dt ñ 0.600

cM = 1.45 forfy

E $ Dt > 0.600

cRb = 1.05

NORSOKISO

The limitations on Fy (fy) and D/t set by both the ISO and NORSOK standards give anupper limit to Fy/E x D/t of 0.286. Noting that the only contribution to the differencebetween the two standards regarding bending is via the partial safety factors, thenthese differences can be quantified as set out in Table 5.2.

1.2040.286

1.095 0.150ñ

cMcRb

Fy

E $ Dt or

fy

E $ Dt

Table 5.2 Bending Partial Safety Factor Ratios

11

Z = [cross-section] plastic section modulus

W = [cross-section] elastic section modulus

Z = [cross-section] plastic section modulus

S = [cross-section] elastic section modulus

MSd MRd≤W fm⋅

γM

MSd = design bending moment

fmZ

W

fy⋅ for⋅fy

E⋅

D

t⋅ 0.0517≤

fm 1.13 2.58fy

E⋅

D

t⋅−

Z

W

⋅ fy⋅ for⋅ 0.0517⋅fy

E

D

t⋅< 0.1034≤

fm 0.94 0.76fy

E⋅

D

t⋅−

Z

W

⋅ fy⋅ for⋅ 0.1034⋅fy

E

D

t⋅< 120

fy

E⋅≤

fb

Fb

γRb≤

fb = bending stress due to forces from factored actions

FbZ

S

Fy⋅ for⋅Fy

E⋅

D

t⋅ 0.0517≤

Fb 1.13 2.58Fy

E⋅

D

t⋅−

Z

S

⋅ Fy⋅ for⋅ 0.0517⋅Fy

E

D

t⋅< 0.1034≤

Fb 0.94 0.76Fy

E⋅

D

t⋅−

Z

S

⋅ Fy⋅ for⋅ 0.1034⋅Fy

E

D

t⋅< 120

Fy

E⋅≤

NORSOKISO

Table 5.1 Design Criteria for Bending

12

6. HYDROSTATIC PRESSURE

6.1 DESIGN CRITERIA

The design criteria for tubular members subjected to hydrostatic pressure alone areset out in Table 6.1.

Thus, by observation, the differences between the ISO and NORSOK formulations forthe design resistances are due to the partial safety factors. These are dealt with in thenext subsection.

6.2 PARTIAL SAFETY FACTORS

Differences in the partial safety factors for hydrostatic pressure between the ISO andNORSOK standards are as follows.

cM = 1.15 for ks < 0.5

cM = 0.85 + 0.60 ks for 0.5 ñ ks ñ 1.0

cM = 1.45 for ks > 1.0

For the case of hydrostatic pressure ONLY

ks2 =

fy

fhe

cRh = 1.25

NORSOKISO

Hence, the NORSOK partial safety factor follows the complex expression for fhe

(elastic hoop buckling strength) given in Table 6.1. The difference between the ISOand NORSOK safety factors is set out indicatively in Table 6.2.

1.160 2 Chú

0.920 0.5 Chñ

cMcRh

Fy

E $ Dt or

fy

E $ Dt

Table 6.2 Hydrostatic Pressure Partial Safety Factors

13

L = length between stiffening rings, diaphragms or end connectionsL = length between stiffening rings, diaphragms or end connections

σp.Sd fh.Rd≤fh

γM

σp.Sd = design hoop stress due to hydrostatic pressure

fh fy for⋅ 2.44⋅ fy⋅ fhe<

fh 0.7 fy⋅fhe

fy

0.4

⋅ for⋅ 0.55⋅ fy⋅ fhe< 2.44 fy⋅≤

fh fhe for⋅ fhe⋅ 0.55 fy⋅≤

fhe 2 Ch⋅ E⋅t

D⋅

Ch 0.44t

D⋅ for⋅ 1.6⋅

D

t⋅ µ≤

Ch 0.44t

D⋅

0.21

µ4

D

t

3

⋅ for⋅ 0.825⋅D

t⋅+ µ≤ 1.6

D

t⋅<

Ch0.737

µ 0.579−for⋅ 1.5⋅ µ≤ 0.825

D

t⋅<

Ch 0.80 for⋅ µ⋅ 1.5<

µL

D

2 D⋅

t⋅

fh

Fh

γRh≤

fh = hoop stress due to forces from factored hydrostatic pressure

Fh Fy for⋅ 2.44⋅ Fy⋅ Fhe<

Fh 0.7 Fy⋅Fhe

Fy

0.4

⋅ for⋅ 0.55⋅ Fy⋅ Fhe< 2.44 Fy⋅≤

Fh Fhe for⋅ Fhe⋅ 0.55 Fy⋅≤

Fhe 2 Ch⋅ E⋅t

D⋅

Ch 0.44t

D⋅ for⋅ 1.6⋅

D

t⋅ m≤

Ch 0.44t

D⋅

0.21

m4

D

t

3

⋅ for⋅ 0.825⋅D

t⋅+ m≤ 1.6

D

t⋅<

Ch0.737

m 0.579−for⋅ 1.5⋅ m≤ 0.825

D

t⋅<

Ch 0.80 for⋅ m⋅ 1.5<

mL

D

2 D⋅

t⋅

NORSOKISO

Table 6.1 Design Criteria for Hydrostatic Pressure

14

7. AXIAL TENSION AND BENDING

7.1 INTERACTION FORMULAE

The two standards use formulae to compute interaction ratios in the case of combinedaxial tension and bending. The formulae from the two standards are given in Table7.1.

It is clear from these formulations and their contents that there are three sources ofdifference between the requirements of the two codes:

i. partial safety factors on actionsii. partial safety factors on resistancesiii. formulation differences in the interaction formulae.

The effects of item i cannot be dealt with here. Items ii and iii are combined andaddressed in the next subsection.


The differences between ISO and NORSOK are best illustrated by expressing theinteraction formulae in a common stress basis, in the manner described below.

cMt f t

fy

1.75+

cMb fbres

fmñ 1.0

fbres = as left

γMt = resulting material factor for tensionalone

γMb = resulting material factor for bendingalone

cRt f t

Fy+

cRb fbres

Fbñ 1.0

fbres = resulting bending stressdue to forces from factoredactions

NORSOKISO

The other terms have been defined in previous subsections and it should be noted that

Fy = fy and Fb = fm. As set out in previous subsections, γRt and γRb are constants (both1.05), and γMt is constant and equal to 1.15. γMb is not constant, however, and variesbetween 1.15 and 1.264 according to the values of fy/E x D/t (see Subsection 5.2).

15

The comparison between the interaction formulae is given in Figure 7.1, plotted astensile stress ratio (ft/Fy or ft/fy) versus bending stress ratio (fbres/Fb or fbres/fm). Two

curves for the NORSOK formulation are given, corresponding to γMb (denoted as psf inthe figure) of 1.15 and 1.264.

As can be seen from this figure, NORSOK is more conservative than ISO only forcases of mainly tension or mainly bending. Otherwise the opposite is true, although

for γMb (psf) = 1.264 the differences between ISO and NORSOK are small.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ISONORSOK psf=1.15NORSOK psf=1.264

Axial Tension plus Bending

Tensile stress ratio

Ben

ding

stre

ss ra

tio

Figure 7.1 ISO Versus NORSOK Interaction Diagrams for Combined Axial Tensionand Bending

16

NSd = design tensile axial force [including partial safety factor on actions]

My.Sd = design bending moment about member y-axis (in-plane) [including partial safety factor on actions]

Mz.Sd = design bending moment about member z-axis (out-of-plane) [including partial safety factor on actions]

fby = bending stress about member y-axis (in-plane) due to forces from factored actions

fbz = bending stress about member z-axis (out-of-plane) due to forces from factored actions

N Sd

N t.Rd

1.75M y.Sd

2M z.Sd

2+

M Rd+ 1.0≤

γ Rt f t⋅

F y

γ Rb f by2

f bz2

+⋅

F b+ 1.0≤

NORSOKISO

Table 7.1 Interaction Formulae for Combined Axial Tension and Bending

17

8. AXIAL COMPRESSION AND BENDING


The two standards use formulae to compute interaction ratios in the case of combinedaxial compression and bending. Each standard employs two formulae: one involving

overall compressive strength and P-δ amplified bending stress; and a second involvinglocal buckling strength and unamplified bending stress (see Table 8.1).

When expressed in stress terms, the corresponding formulae from each standard areidentical, except for the values of partial safety factors and expressions used forvarious characteristic strengths. The relevant formulae are as follows:

cMc fcd

fc+

cMb fbres*

fmñ 1.0

cMc fcd

fcl+

cMb fbres

fmñ 1.0

fcd = as left

fbres* = as left

fbres = as left

cRc fcd

Fc+

cRb fbres*

Fbñ 1.0

cRc fcd

Fyc+

cRb fbres

Fbñ 1.0

fcd = compressive stress due toforces from factored actions

fbres* resulting amplified bendingstress due to forces fromfactored actions

fbres = resulting unamplified bendingstress due to forces fromfactored actions

NORSOKISO

The other terms in the formulae have been defined in previous subsections, where it

should be noted that Fb = fm. As set out in previous subsections, γRc and γRb areconstants (1.18 and 1.05, respectively). In addition to this, over the practical range fy/Ex D/t 0.286, Fyc = fcl. Immediate comparisons between the formulae are renderedñ

difficult by the fact that, generally, Fc fc.!

18

fc = axial compressive stress due to forces from factored actions

NSd

Nc.Rd

1

MRd

Cmy My.Sd⋅

1NSd

NEy−

2Cmz Mz.Sd⋅

1NSd

NEz−

2

+

0.5

⋅+ 1.0≤

NSd

Ncl.Rd

My.Sd2

Mz.Sd2

+

MRd+ 1.0≤

NEyπ

2E⋅ A⋅

k l⋅

i

y

2

NEzπ2

E⋅ A⋅

k l⋅

i

z

2

γRc fc⋅

Fc

γRb

Fb

Cmy fby⋅

1fc

Fey−

2Cmz fbz⋅

1fc

Fez−

+

0.5

⋅+ 1.0≤

γRc fc⋅

Fyc

γRb fby2

fbz2

+⋅

Fb+ 1.0≤

Feyπ

2E⋅

Ky Ly⋅

ry

2

Fezπ

2E⋅

Kz Lz⋅

rz

2

NORSOKISO

Table 8.1 Interaction Formulae for Combined Axial Compression and Bending

19


The differences between the two sets of formulations are illustrated in Figure 8.1 (forthe formulae involving the amplified bending stresses) and Figure 8.2 (for the formulaeinvolving the unamplified bending stresses and the characteristic local bucklingstrength).

As in Subsection 7.2, it has been assumed that the stresses due to forces fromfactored actions are the same in each case. Owing to the differences between Fc andfc (see Subsection 4.5), the ISO characteristic compressive strength has been used forthe compressive stress ratio for both the ISO and NORSOK interaction lines in Figure8.1.

In the case of Figure 8.1, which includes overall buckling effects, there are threeNORSOK interaction lines corresponding with the different values of Fy/E x D/t fromSubsection 4.5 (Table 4.3). As can be seen NORSOK is more conservative than ISO,except for the cases of low Fy/E x D/t ( 0.150) and mainly compression.ñ

For Figure 8.2, which includes local buckling, there are two NORSOK interaction linescorresponding with fy/E x D/t from Subsection 5.2 (Table 5.2). Similar commentsregarding the relative conservatisms from Figure 8.1 apply here also.

20

Figure 8.1 ISO Versus NORSOK Interaction Diagrams for Combined Compressionand Bending - Including Overall Buckling

21

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ISONORSOK <=0.102NORSOK 0.150NORSOK 0.286

Axial Compression plus Bending - Overall

Compressive Stress Ratio

Ben

ding

Str

ess

Rat

io

Figure 8.2 ISO Versus NORSOK for Combined Compression and Bending -Including Local Buckling

22

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ISONORSOK <=0.150NORSOK 0.286

Axial Compression plus Bending - Local

Compressive Stress Ratio

Ben

ding

Str

ess

Rat

io

9. AXIAL TENSION, BENDING AND HYDROSTATIC PRESSURE


The two standards use formulae to compute interaction ratios in the case of combinedaxial tension, bending and hydrostatic loading. The formulae from the two standardsare summarised in Table 9.1.


The basic interaction formulae appear to be identical in form. Differences ininteraction values will result from:

i. partial safety factors on actionsii. partial safety factors / formulaic differences in resistances.

The expression for B, see Table 9.1, depends on Fh/γRh and fh,Rd for ISO and NORSOK,respectively. In the case of the latter, fh,Rd = fh/γM (see Subsection 6.1, Table 6.1,above). The formulae for Fh and fh are identical, hence differences in B between the

two codes stem from the partial safety factors γRh (ISO) and γM (NORSOK), and thesedifferences have been set out in indicative terms in Subsection 6.2, above.

In the resistance denominators for the case of net axial tension, Fth and Fbh (ISO), andfth,Rd and fmh,Rd (NORSOK), the differences between the two codes are due to thedifferences between the partial safety factors set out in Table 9.2.

γM (bending)γRb

γM (tension)*γRt

NORSOKISO

Table 9.2 Potential Sources of Differences

It is not completely clear from the NORSOK code whether the γM for bending is to beused for both fmh,Rd and fth,Rd. Assuming that tension and bending material factorsapply to the resistances, then the comparisons between the partial safety factors areas given in Section 3 (tension) and Subsection 5.2 (bending).

In the resistance denominator for the case of net axial compression, differences stem

from Fyc/γRc (ISO) and fcl/γM (NORSOK). The expressions for Fyc and fcl are virtually

23

identical (see Subsection 4.1), so the differences are due solely to those between γRc

and γM as discussed in Subsection 4.2.

Differences in the remaining interaction formulae in Table 9.1 are due to γRh - γM andγRc - γM differences already discussed.

24

Method A σa.Sd is tensile

σa.Sd σq.Sd≥

σa.Sd σq.Sd−

fth.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤

σa.Sd = design axial stress that excludes effect of capped-end axial compression arising from external hydrostatic pressure

σq.Sd = capped-end design axial compressive stress due to external hydrostatic pressure

σmy.Sd = design bending stress about member y-axis [in-plane]

σmz.Sd = design bending stress about member z-axis [out-of--plane]

fth.RD

fy

γM1 0.09 B

2⋅+ B

2 η⋅− 0.3 B⋅−

⋅=

fmh.Rd

fm

γM1 0.09 B

2⋅+ B

2 η⋅− 0.3 B⋅−

⋅=

Bσp.Sdfh.Rd

= B 1.0≤

η 5 4fh

fy⋅−=

σp.Sd = design hoop stress due to hydrostatic pressure

Method A fa is tensile

fa fq≥

fa fq−

Fth

fby2

fbz2

+

Fbh+ 1.0≤

fa = calculated axial stress due to forces from factored actions that exclude capped-end actions

fq = compressive stress from forces arising from factored capped-end actions due to hydrostatic pressure

Fth

Fy

γRt1 0.09 B

2⋅+ B

2 η⋅− 0.3 B⋅−

⋅=

Fbh

Fb

γRb1 0.09 B

2⋅+ B

2 η⋅− 0.3 B⋅−

⋅=

BγRh fh⋅

Fh= B 1.0≤

η 5 4Fh

Fy⋅−=

fh = hoop stress due to forces from factored hydrostatic pressure

NORSOKISO

Table 9.1 Interaction Formulae for Combined Axial Tension, Bending and Hydrostatic Pressure (1 of 2)

25

σa.Sd σq.Sd<

σa.Sd σq.Sd−

fcl.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤ fcl.Rd

fcl

γM=

when σm.Sd σq.Sd+ σa.Sd− 0.5fcle

γM⋅ and fcle⋅> 0.5 fhe⋅> then additionally

σc.Sd 0.5fhe

γM⋅−

fcle

γM0.5

fhe

γM⋅−

σp.Sd γM⋅

fhe

2

+ 1.0≤

σc.Sd σm.Sd σq.Sd+ σa.Sd−=

σm.Sd

My.Sd2

Mz.Sd2

+

W=

Method B σac.Sd is tensile

σac.Sdfth.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤

σac.Sd = design axial stress that excludes the effect of capped-end axial compression arising from external hydrostatic pressure

fa fq<

γRc fa fq−⋅

Fyc

fby2

fbz2

+

Fbh+ 1.0≤

when fb fq+ fa− 0.5Fhe

γRh⋅ and

Fxe

γRc⋅> 0.5

Fhe

γRh⋅> then additionally

fb fq+ fa− 0.5Fhe

γRh⋅−

Fxe

γRc0.5

Fhe

γRh⋅−

γRh fh⋅

Fhe

2

+ 1.0≤

Method B fac is tensile

fac

Fth

fby2

fbz2

+

Fbh+ 1.0≤

fac = calculated axial stress due to factored actions that include capped-end actions

NORSOKISO

Table 9.1 Interaction Formulae for Combined Axial Tension, Bending and Hydrostatic Pressure (2 of 2)

26

10. AXIAL COMPRESSION, BENDING AND HYDROSTATICPRESSURE


The two standards use formulae to compute interaction ratios in the case of combinedaxial compression, bending and hydrostatic loading. The formulae from the twostandards are summarised in Table 10.1.

The approach taken and general form of the formulae used are identical. Potentialsources of divergence are due to differences between the following. Thesedifferences are discussed in the following subsection.

fcl, RdγRc / Fyc

fmh, RdFbh

fch, RdFch

NORSOKISO

Table 10.2 Potential Sources of Difference in Combined Axial Compression, Bendingand Hydrostatic Pressure Formulations


The formats of the formulations for Fch and fch,Rd are identical, but with potential fordivergence because of the differences between:

fcl = see Table 4.1

γM = 1.15 for λs < 0.5

γM = 0.85 + 0.60 λs for 0.5 λs 1.0ñ ñ

γM = 1.45 for λs > 1.0

ks2 =

fyr j, sd

rc, sd

fcle+

rp, sd

fhe

r j, sd = rc, sd2 - rc, sd rp, sd + rp, sd

2

rc, sd = NsdA +

My, sd2 + Mz, sd

2

W

Fyc = see Table 4.1

γRc = 1.18 (see Subsection 4.2)

NORSOKISO

27

According to Table 4.1, Fyc will for the most part be equal to fcl, so the principal sources

of divergence will be due to γRc (ISO) and γM (NORSOK) as set out in Subsection 4.2.

With reference to Fbh and fmh,Rd, differences between these will be as per Subsection9.2.

Since fcl, Rd = fcl / γM and Fyc = fcl, the third potential source of divergence reduces to thedifferences between γRc and γM discussed above.

28

Method A σa.Sd is compressive

σa.Sdfch.Rd

1fmh.Rd

Cmy σmy.Sd⋅

1σa.Sd

fEy−

2Cmz σmz.Sd⋅

1σa.Sd

fEz−

2

+

0.5

⋅+ 1.0≤

σa.Sd σq.Sd+

fcl.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤

fch.Rd12

fcl

γM⋅ ξ

2 σq.Sd⋅

fcl− ξ

2 1.12 λ2

⋅σq.Sd

fcl⋅++

⋅=

for λ 1.34 12 σq.Sd⋅

fcl−

1−

⋅<

fch.Rd0.9

λ2

fcl

γM⋅= for λ 1.34 1

2 σq.Sd⋅

fcl−

1−

⋅≥

ξ 1 0.28 λ2

⋅−=

when σa.Sd σm.Sd+ σq.Sd+ 0.5fhe

γM⋅ and fcle⋅> 0.5 fhe⋅>

then also treat as in method A for combined tension, bending & hydrostatic pressure

Method A fa is compressive

fa

Fch

1Fbh

Cmy fby⋅

1fa

Fey−

2Cmz fbz⋅

1fa

Fez−

+

0.5

⋅+ 1.0≤

γRc fa fq+( )⋅

Fyc

fby2

fbz2

+

Fbh+ 1.0≤

Fch12

Fyc

γRc⋅ ξ

2 fq⋅

Fyc− ξ

2 1.12 λ2

⋅fq

Fyc⋅++

⋅=

for λ 1.34 12 fq⋅

Fyc−

1−

⋅<

Fch0.9

λ2

Fyc

γRc⋅= for λ 1.34 1

2 fq⋅

Fyc−

1−

⋅≥

ξ 1 0.28 λ2

⋅−=

when fa fb+ fq+ 0.5Fhe

γRh⋅ and

Fxe

γRc⋅> 0.5

Fhe

γRh⋅>


NORSOKISO

Table 10.1 Interaction Formulae for Combined Axial Compression, Bending and Hydrostatic Pressure (1 of 2)

29

Method B σac.Sd is compressive

σac.Sd σq.Sd>

σac.Sd σq.Sd−

fch.Rd

1fmh.Rd

Cmy σmy.Sd⋅

1σac.Sd σq.Sd−

fEy−

2Cmz σmz.Sd⋅

1σac.Sd σq.Sd−

fEz−

2

+

0.5

⋅+ 1.0≤

σac.Sdfcl.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤

when σa.Sd σm.Sd+ 0.5fhe

γM⋅ and fcle⋅> 0.5 fhe⋅>


σac.Sd σq.Sd≤

σac.Sdfcl.Rd

σmy.Sd2

σmz.Sd2

+

fmh.Rd+ 1.0≤

when σa.Sd σm.Sd+ 0.5fhe

γM⋅ and

fcle

γM⋅> 0.5

fhe

γM⋅>


Method B fac is compressive

fac fq>

fac fq−

Fch

1Fbh

Cmy fby⋅

1fac fq−

Fey−

2Cmz fbz⋅

1fac fq−

Fez−

+

0.5

⋅+ 1.0≤

γRc fac⋅

Fyc

fby2

fbz2

+

Fbh+ 1.0≤

when fac fb+ 0.5Fhe

γRh⋅ and

Fxe

γRc⋅> 0.5

Fhe

γRh⋅>


fac fq≤

γRc fac⋅

Fyc

fby2

fbz2

+

Fbh+ 1.0≤

when fac fb+ 0.5Fhe

γRh⋅ and

Fxe

γRc⋅> 0.5

Fhe

γRh⋅>


NORSOKISO

Table 10.1 Interaction Formulae for Combined Axial Compression, Bending and Hydrostatic Pressure (2 of 2)

30

11. DEFINITIONS OF CHARACTERISTIC EQUATIONS

The commentary to the ISO document gives some indications as to the criteria used indeveloping the characteristic equations given. No information is provided inNORSOK.

The screening of test data for use in developing characteristic equations was such thatdata were rejected if any of the following was true:

� absence of yield strength measurements� absence of critical geometrical measurements� initial geometry outside API RP 2A tolerances (with the exception of

specimens subjected to external pressure)� column strengths in excess of the Euler buckling load

� steel thickness ≤ 1.8 mm.

The characteristic equations for local buckling failure under axial compression(according to subsection A.13.2.2.2 of the ISO document) were developed byscreening test data and establishing a curve with 95% survival at the 50% confidenceinterval that satisfied the following conditions:

� the material had a plateau of material characteristic yield strength over therange 0<Fy/Fxe<=0.17

� the general form of the failure equation was as given in Table 4.1� the failure equation converged to the elastic critical buckling curve with

increasing member slenderness ratio� the difference between the mean minus 1.645 standard deviations of test

data and the developed equations was a minimum.

The ISO document also gives biases and coefficients of variation (COVs) for the ratioof experimentally observed resistance to that predicted by the characteristic equationcorresponding to a number of the loading combinations. These statistics have beenre-appraised using an amended database (derived from the original ISO databases) ina study commissioned by HSE [4]. The ISO document and study statistics are givenin Table 11.1, below.

In the main, the differences between the biases and COVs of [3] and [4] are verysmall. The exceptional cases appear to be those for interaction equations involvinghydrostatic pressure. In these cases, the differences are probably due to the way thestatistical calculations were performed; whether on the interaction ratio [3], oriteratively along the individual load axes in failure space [4].

31

0.1121.103340.0981.07534Axial Tension plus HydrostaticPressure

0.1121.252260.0911.19726Axial Compression, Bending,plus Hydrostatic Pressure(Column Buckling)

0.1551.294690.1341.19969Axial Compression, Bending,plus Hydrostatic Pressure (LocalBuckling)

0.0821.029490.0821.02949Axial Compression, plusBending (Column Buckling)

0.0661.251190.0671.24619Axial Compression, plusBending (Local Buckling)

0.1241.142440.1241.142Not

givenHydrostatic Pressure

0.0851.109570.0851.109Not

givenBending

0.0451.063840.0411.05784Axial Compression (ColumnBuckling)

0.0681.068380.0681.06538Axial Compression (LocalBuckling)

COVBiasNumberCOVBiasNumberLoading Type

Study Document [4]ISO Document [3]

Table 11.1 Statistics of Resistance Equations

32

12. CONCLUSIONS

Direct comparisons between the NORSOK [1] and ISO [3] provisions for the strengthof tubular members are possible because they give formulations for tubular membersunder:

� axial tension� bending� compression� hydrostatic pressure� combined axial tension and bending� axial compression combined with bending� combined axial tension, bending and hydrostatic pressure� combined axial compression bending and hydrostatic pressure

The 4th Edition Guidance Notes [2] do not contain specific formulations.

With the exception of the case of combined axial tension and bending for whichadditionally the actual interaction formulae in NORSOK and ISO differ, differencesbetween the two standards in all loading cases are primarily due to partial safety factordifferences. ISO uses constant partial safety factors in resistance formulations;whereas NORSOK uses variable partial safety factors that depend on the slendernessof the component and the severity of the loading. Thus, in the case of NORSOK,partial safety factors for both resistance and loading/actions may occur on theresistance side of the design equation.

A qualitative summary of the relative conservatisms of ISO versus NORSOK is givenin Table 12.1. It should be emphasised that any such comparisons only deal with theresistance side. Any differences identified may be radically altered if there aredifferences between ISO and NORSOK with respect to partial safety factors onloading. Reliability studies, such as [5] may be the most suitable medium to exploresuch overall differences.

33

Difficult to assess because of pressure componentcompression + bending + hydrostatic pressure

Difficult to assess because of pressure componenttension + bending + hydrostatic pressure

NORSOK more conservative, varies < ∼ 15%compression + bending

NORSOK can be more or less conservative, ± 10%tension + bending

NORSOK can be more or less conservative, 16% or8%

hydrostatic pressure

Negligible difference in practical casescompression

NORSOK more conservative, about 10%bending

NORSOK more conservative, about 10%tension

CommentLoad Action / Combination

Table 12.1 Qualitative Comparison of Resistances ISO versus NORSOK

34

13. REFERENCES

1. NORSOK Standard. Design of Steel Structures. N-004. Rev 1, December1998.

2. HSE 4th Edition Guidance Notes. Offshore Installations: Guidance onDesign, Construction and Certification. 1993 Consolidated Edition withAmendment 3.

3. ISO. Petroleum and Natural Gas Industries - Offshore Structures - Part 2:Fixed Steel Structures. ISO/CD 13819-2. Draft 14.05.99.

4. MSL Engineering Limited. Load Factor Calibration for ISO 13819 RegionalAnnex - Component Resistances. Report prepared for HSE. Doc RefC242R001, Rev 0, February 2000.

5. PAFA Consulting Engineers. Implications for Fixed Steel Structures of ISO13819-2 Member Strength Formulations. Report prepared for HSE (draftfinal report). Doc Ref C031-002-R, Rev 0, March 1998.

35

APPENDIX ALISTS OF SYMBOLS

36

design bending capacity/resistance in the presence of external hydrostatic pressure[including partial safety factor]

Fbh

moment reduction factor for the member z-directionCmz

moment reduction factor for the member y-directionCmy

characteristic yield strengthFy

characteristic hoop buckling strengthFh

characteristic axial compressive strengthFc

characteristic bending strengthFb

critical elastic buckling coefficientCx

[elastic hoop buckling strength coefficient]Ch

bending stress about member z-axis (out-of-plane) due to forces from factoredactions

fbz

bending stress about member y-axis (in-plane) due to forces from factored actionsfby

calculated axial stress due to forces from factored actions that include thecapped-end actions

fac

compressive stress from forces arising from factored capped-end actions due tohydrostatic pressure

fq

axial tensile stress due to forces from factored actionsft

hoop stress due to forces from factored hydrostatic pressurefh

axial compressive stress due to forces from factored actionsfc

bending stress due to forces from factored actionsfb

calculated axial stress due to forces from factored actions that exclude capped-endactions

fa

plastic section modulusZ

elastic section modulusS

unbraced length in y or z direction, or length between stiffening rings, diaphragms orend connections

L

effective length factorK

Young’s modulus of elasticityE

outside diameterD

ratio of hoop stress due to forces from factored hydrostatic pressure to factoredcharacteristic hoop buckling strength

B

wall thicknesst

radius of gyrationr

geometric parameterm

ISO NOMENCLATURE

37

partial resistance factor for axial tensile strengthγRt

partial resistance factor for hoop buckling strengthγRh

partial resistance factor for axial compressive strengthγRc

partial resistance factor for bending strengthγRb

factorξ

factorη

column slenderness parameterλ

characteristic local buckling strengthFyc

characteristic elastic local buckling strengthFxe

design axial tensile capacity/resistance in the presence of external hydrostaticpressure [including partial safety factor]

Fth

elastic hoop buckling strengthFhe

Euler buckling strength corresponding to the member z-directionFez

Euler buckling strength corresponding to the member y-directionFey

design axial compression capacity/resistance in the presence of external hydrostaticpressure [including partial safety factor]

Fch

ISO NOMENCLATURE

38

NSddesign axial force

NEzEuler buckling force corresponding to the member z-direction

NEyEuler buckling force corresponding to the member y-direction

Cmzmoment reduction factor for the member z-direction

Cmymoment reduction factor for the member y-direction

Ch[elastic hoop buckling strength coefficient]

Cecritical elastic buckling coefficient

fth,Rddesign axial tensile capacity/resistance in the presence of external hydrostaticpressure [including partial safety factor]

fmh,Rddesign bending capacity/resistance in the presence of external hydrostatic pressure[including partial safety factor]

fcl,Rddesign characteristic local buckling strength [including partial safety factor]

fch,Rddesign axial compression capacity/resistance in the presence of external hydrostaticpressure [including partial safety factor]

fh,Rd[design hoop buckling resistance] [including partial safety factor]

fclecharacteristic elastic local buckling strength

fheelastic hoop buckling strength

fEzEuler buckling strength corresponding to the member z-direction

fEyEuler buckling strength corresponding to the member y-direction

fclcharacteristic local buckling strength

fycharacteristic yield strength

fmcharacteristic bending strength

fhcharacteristic hoop buckling strength

fccharacteristic axial compressive strength

Zplastic section modulus

Welastic section modulus

EYoung’s modulus of elasticity

Doutside diameter

Bratio of hoop stress due to forces from factored hydrostatic pressure to factoredcharacteristic hoop buckling strength

Across-sectional area

twall thickness

lunbraced length in y or z direction, or length between stiffening rings, diaphragms orend connections

keffective length factor

iradius of gyration

NORSOK NOMENCLATURE

39

σmz,Sdbending stress about member z-axis (out-of-plane) due to forces from factoredactions

σmy,Sdbending stress about member y-axis (in-plane) due to forces from factored actions

σac,Sdcalculated axial stress due to forces from factored actions that include thecapped-end actions

σq,Sdcompressive stress from forces arising from factored capped-end actions due tohydrostatic pressure

σp,Sd[design] hoop stress due to forces from factored hydrostatic pressure

σm,Sdbending stress due to forces from factored actions

σa,Sdcalculated axial stress due to forces from factored actions that exclude capped-endactions

λs[slenderness parameter]

γMpartial material factor

ξfactor

ηfactor

µgeometric parameter

λcolumn slenderness parameter

Mz,Sddesign bending moment about member z-axis (out-of-plane)

My,Sddesign bending moment about member y-axis (in-plane)

Nt,Rddesign tensile resistance [including partial safety factor]

Nc,Rddesign compressive resistance [including partial safety factor]

MSddesign bending moment

MRddesign bending resistance [including partial safety factor]

NORSOK NOMENCLATURE

40

fh,Rd[design hoop buckling resistance] [including partial safety factor]

partial resistance factor for hoop buckling strengthγRh

fhcharacteristic hoop buckling strengthFh

σp,Sd[design] hoop stress due to forces from factored hydrostatic pressurefh

Welastic section modulusS

Zplastic section modulusZ

partial resistance factor for bending strengthγRb

MRddesign bending resistance [including partial safety factor]

fmcharacteristic bending strengthFb

MSddesign bending moment

σm,Sdbending stress due to forces from factored actionsfb

twall thicknesst

Doutside diameterD

Cecritical elastic buckling coefficientCx

fclecharacteristic elastic local buckling strengthFxe

EYoung’s modulus of elasticityE

iradius of gyrationr

lunbraced length in y or z direction, or length between stiffening rings,diaphragms or end connections

L

keffective length factorK

fcl,Rddesign characteristic local buckling strength [including partial safetyfactor]

fclcharacteristic local buckling strengthFyc

λcolumn slenderness parameterλ

partial resistance factor for axial compressive strengthγRc

Nc,Rddesign compressive resistance [including partial safety factor]

fccharacteristic axial compressive strengthFc

Across-sectional area

axial compressive stress due to forces from factored actionsfc

γMpartial material factor

partial resistance factor for axial tensile strengthγRt

Nt,Rddesign tensile resistance [including partial safety factor]

fycharacteristic yield strengthFy

NSddesign axial force

axial tensile stress due to forces from factored actionsft

NORSOKEQUIVALENCEISO

41

ξfactorξ

fch,Rddesign axial compression capacity/resistance in the presence ofexternal hydrostatic pressure [including partial safety factor]

Fch

σac,Sdcalculated axial stress due to forces from factored actions that includethe capped-end actions

fac

ηfactorη

Bratio of hoop stress due to forces from factored hydrostatic pressureto factored characteristic hoop buckling strength

B

fmh,Rddesign bending capacity/resistance in the presence of externalhydrostatic pressure [including partial safety factor]

Fbh

fth,Rddesign axial tensile capacity/resistance in the presence of externalhydrostatic pressure [including partial safety factor]

Fth

σq,Sdcompressive stress from forces arising from factored capped-endactions due to hydrostatic pressure

fq

σa,Sdcalculated axial stress due to forces from factored actions thatexclude capped-end actions

fa

NEzEuler buckling force corresponding to the member z-direction

NEyEuler buckling force corresponding to the member y-direction

fEzEuler buckling strength corresponding to the member z-directionFez

fEyEuler buckling strength corresponding to the member y-directionFey

Cmzmoment reduction factor for the member z-directionCmz

Cmymoment reduction factor for the member y-directionCmy

Mz,Sddesign bending moment about member z-axis (out-of-plane)

My,Sddesign bending moment about member y-axis (in-plane)

σmz,Sdbending stress about member z-axis (out-of-plane) due to forces fromfactored actions

fbz

σmy,Sdbending stress about member y-axis (in-plane) due to forces fromfactored actions

fby

µgeometric parameterm

Ch[elastic hoop buckling strength coefficient]Ch

fheelastic hoop buckling strengthFhe

NORSOKEQUIVALENCEISO

42

Printed and published by the Health and Safety ExecutiveC30 1/98

43

Printed and published by the Health and Safety ExecutiveC30 1/98

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