Design Guide Steel Blast Walls

FIRE AND BLAST INFORMATION GROUP

TECHNICAL NOTE AND WORKED EXAMPLES To SUPPLEMENT THE INTERIM GUIDANCE NOTES

STRUCTURES AGAINST EXPLOSION AND FIRE FOR THE DESIGN AND PROTECTION OF TOPSIDE

Design Guide for Stainless

Steel Blast Walls

Technical Note 5

This document is a deliverable of the Fire And Blast Information Group (FABIG). a The Technical Note is based on work carried out by Mr R Brewerton, acting as a Consultant

to The Steel Construction Institute.

This work was funded from FABIG membership income. Additional funding from the Health

FABIG would like to encourage comment and feedback from its membership. If you have

and Safety Executive and Avesta Sheffield is also gratefully acknowledged.

any comments on this Technical Note or any other FABIG activities please address them to the FABIG Project Manager at The Steel Construction Institute.

The information in this document is published with the intent of making it available to members of the Fire And Blast Information Group (FABIG). The information is available for use subject to copyright. The information presented here is expected to contribute to the further improvement in safety. However, The Steel Construction Institute will not accept any liability for loss or damage originating from the use of the information herein.

It The Steel Construction fnstirute, Silwood Park. Ascot, Berkshire. SLS 7QN. United Kingdom.

Tcl: +44 (0) 1344 623345, Fax: +44 (0) 1344 622944

CONTENTS

NOTATION

1

2

3

4

5

6 .--

7

INTRODUCTION 1.1 Stainless steel blast walls 1.2 Scope of this document 1.3 1.4

Typical arrangement of blast wall Guidance for specifiers of blast walls

DESIGN BASIS 2.1 Eurocode 3 2.2 Design criteria and l imirstates 2.3 2 .4 Step-by-step design procedure

Structural behaviour of a profiled sheeting blast wall

CHARACTERISTICS AND PROPERTIES OF STAINLESS STEELS 3.1 Common stainless steels and their composition 3.2 Specifications and designation systems 3.3 Product form 3.4 Properties of stainless steel 3.5 Durability

NATURE OF EXPLOSION LOADING AND STRUCTURAL RESPONSE 4.1 Explosion loading 4.2 4.3

Specified peak explosion pressure, PMAX Structural response to explosion loading

WALL PROFILES 5.1 Choice of profile 5.2 Geometrical proportions 5.3 Section properties

CROSS-SECTION CLASSIFICATION AND EFFECTIVE SECTION PROPERTIES 6.1 General 6.2 Cross-section classification 6.3 6.4

6.5

6.6

Plane elements wi thout stiffeners - effective area Flanges with intermediate stiffeners - cross-section classification and effective area Plane elements with edge stiffeners - cross-section classification and effective area Tension resistance at bolt holes

DESIGN OF CROSS-SECTION TO WITHSTAND OVERALL LONGITUDINAL BENDING 7.1 Overall longitudinal moment resistance 7.2 Effective span

Page No.

... Ill

1 1 1 2 2

3 3 3 3 3

5 5 6 6 7

13

1 6 1 6 16 17

1 9 19 19 19

21 21 21 23

2 6

29 29

30 30 30

~ ~~~ ~

FABIG Technical Note - June 1999 1

Design Guide for Stainless Steel Blast Walls

7.3 Resistance of the wall 7.4 7.5 Shear resistance of wall

DLF and maximum midspan deflection

8 TRANSVERSE LOADING ON THE PROFILE 8.1 8.2 8.3 8.4 8.5

8.6

Loads causing bending of the profile Moments and stresses arising from local loading Verification of adequacy under local loading Buckling resistance under local loading Reduction factor on overall longitudinal moment resistance to account for cross-section flattening Reduction factor on overall longitudinal moment resistance to account for coincident stresses arising from local effects

9 METHODS FOR VERIFYING THE PLASTIC DEFLECTION LIMIT 9.1 9.2 Definition of ductility ratio 9.3 Benefits o f plastic deflection 9.4 9.5 9.6 Designing for rotation capacity 9.7

Definition of plastic deflection limit

Failure modes and energy absorption capacity Cross-section class versus rotation capacity

Determination of the plastic deflection limit

10 CONSTRUCTION DETAILS 10.1 Interfaces with support structures 10.2 10.3 Avoidance of corrosion 10.4 Weld details 10.5 10.6 10.7 Penetration details

Design requirements for the deck structures supporting blast walls

Methods for splicing profiles end-to-end Longitudinal splices and stiffener plates

11 REFERENCES

APPENDIX A

A. 1 A.2 A.3

APPENDIX B

APPENDIX C

APPENDIX D

Checklist of data for inclusion in enquiry documents for blast walls systems General requirements S t ru ctu ra I require ni e n t s Architectural requirements

Strain rate effects

Derivation of elastic critical buckling stress for stiffener in a Type 3 profile

Design examples

31 31 32

34 34 36 36 36

38

39

40 40 40 40 41 4 2 43 43

46 46 48 48 49 49 49 50

52

A- 1 A- 1 A- 1 A- 1

B- 1

c- 1

D- 1

II FABIG Technical Note - June 1999

I INTRODUCTION


1 . 1 Stainless steel blast walls Stainless steel blast walls made from profiled sheeting are commonly used on offshore process platforms where there is a risk of accidental gas explosions. They are usually required to survive the explosion in order to protect personnel and safety critical equipment and to prevent the spread of possible subsequent fire. They can also be used in onshore process plant and in other situations where protection from explosions is a requirement. As well as providing the excellent corrosion resistance required in such environments, stainless steel displays good mechanical properties, energy absorption and ductility characteristics, making it an ideal material for blast wall construction. In particular, the shape of the stress-strain curve in the plastic range ensures higher plastic moment resistance than carbon steel of equivalent strength. The mechanical properties of stainless steel at high temperatures (> 500°C) are superior to those of typical structural carbon steels, thus offering intrinsically greater fire resistance.

It is often beneficial to use high strength materials to resist explosions. In the thichess range commonly used for blast walls (2 - 6 mrn), high- strength carbon steels are not readily available in the widths required. Additionally, local thinning due to corrosion is a risk with thin carbon steel and it is not always possible to ensure painting access to all

surfaces once a walling system is erected. A final but nonetheless important aspect is aesthetics: stainless steel blast walls from profiled sheeting require no additional architectural finishes to produce a pleasing, permanent internal or external appearance. These factors have led to the widespread use of stainless steel for explosion resisting walls offshore.

1.2 Scope of this document This document gives guidance on the design of stainless steel blast walls made from profiled sheeting, including guidance on material behaviour and selection, response to blast loading, design for longitudinal and transverse bending effects, evaluation of plastic deformation capacity and recommendations on construction details. The document specifically addresses walls constructed of panels with simple trapezoidal corrugations with or without longitudinal flange stiffeners (Figure 1 . 1 ) manufactured from the grades of wrought stainless steel which are widely used in offshore structural applications. Longitudinal web stiffeners are not specifically covered, since they rarely prove economic because local effects tend to govern profile design. The guidance is also generally applicable to the more complex proprietary profile shapes.

Explosion pressure

iI\L Type 1 A Type 2 A Type. 3

Unstiffened orofile Stiffened or o f-t l e (bent ) Stiffened orofile (welded)

Figure 1 . l Profile geometries

FABIG Technical Note - June 1999 Page 1


1.3 Typical arrangement of blast wall

Figure 1.2 shows an elevation of a typical blast wall with service penetrations.

The details in this guide refer specifically to vertically spanning walls, however, walls can be installed spanning horizontally between vertical columns. In this case, the attachment details to the columns must be able to accommodate span shortening arising from out of plane deflections in the explosion.

I 5 m - 9 m l I

Note that the design guidance in this document only applies to cross-sections made up of elements complying with the dimensional limits given in Section 5.2.

1.4 Guidance for specifiers of blast walls

Based on the guidance and recommendations in this document, a checklist of information required in enquiry packages for stainless steeI blast wall systems has been drawn up and is given in Appendix A.

Top support girder Top interface

(Figures 10.1,

Lower deck 1 H frame penetrations (Figure 10.6)

Figure 1.2 Typical blast wall with service penetrations

Lower interfaces 1 (Figures 10.3 & 10.4)

A- A

Bracing

Page 2 FABIG Technical Note - June 1999


2 DESIGN BASIS

2.1 Eurocode 3 The design guidance in this publication is based on the provisions in the European design standard for structural stainless steel, Eurocode 3: Part 1.4"'. This standard gives supplementary provisions for design which extend the application of Eurocode 3: Part 1.1''' (the European design standard for carbon steel) and Eurocode 3: Part 1.3") (the European design standard for cold formed thin gauge members and sheeting) to austenitic and duplex stainless steels.

2.2 Design criteria and limit states

The governing limit state for blast wall design is usually the ultimate limit state (ULS), although for lightly-loaded flexible walls the serviceability limit state (SLS) may govern.

Explosions are very rare, accidental events. For this reason, stresses, strains and deflections are permitted to exceed limits normally utilised in conventional elastic design. When considering accidental design situations at the ULS, load and material factors may be taken as unity.

The critical loading to be considered at the SLS is usually due to storm winds; the recommended deflection limits are span/l20, except where more stringent limits are required due to architectural considerations. Permanent deflection of the wall should never occur due to loading at the SLS.

Under explosion loads, typical recommended deflection limits are span/40 to span/25. Maximum absolute values may be dictated by the wall geometry (span and cross-section), or by proximity of vital equipment or other structural members. Larger deflections may be permitted where the end supports can tolerate the applied rotations and in- plane movements, and where the cross-section is such that premature local failure does not occur.

2.3 Structural behaviour of a profiled sheeting blast wall

A typical blast wall spans primarily from top to bottom and its strength depends on the shape and slenderness of the chosen profile. However, in addition, the blast pressure on the sheeting gives rise to transverse forces and moments in the steel

plate. There is some interaction between the two responses, because (a) the large deflections associated with blast loading may generate internal transverse forces that tend to crush the walls of the profile and (b) the response to both sets of transverse forces utilises some of the strength of the steel material, and this may reduce the capacity for longitudinal effects. These will all be discussed in the document.

The local effects limit the capacity to resist overall longitudinal bending. Failure of a corrugated profile is normally in longitudinal bending, where a fold-line typically forms along the middle of the blast wall at the point of maximum bending moment (for example see Figure 4.3). The plastic moment resistance of the fold-line zone is significantly less than the moment resistance of the undeformed wall. Folding results in gross rotations at the support connections and a shortening of the span. Gross rotation and/or span shortening ultimately causes failure of one of the supports. Rotation of the wall then occurs about the other support until the latter fails owing to excessive strain, thereby causing complete collapse of the wall. This is the most common potential ultimate failure mechanism for blast walls.

The allowable ductility ratio (the ratio of the peak deflection predicted to occur during the explosion loading to the deflection at the elastic limit) is normally dictated by the local buckling and crushing resistance of the cross-section at the point of maximum bending moment. This limit is a function of the cross-sectional geometry and the material stress-strain characteristics in the plastic range. The maximum allowable ductility ratio for Class 2, 3 and 4 cross-sections is unity. (The classification of cross-sections according to Eurocode 3: Part 1.4 is explained in Section 6.) For Class 1 cross-sections, the maximum allowable ductility ratio is 1.5 for profiles checked in accordance with Sections 7 and 8 of this document. Higher ductility ratios can be confirmed for profiles verified by one of the methods described in Section 9.

2.4 Step-by-step design procedure

Figure 2.1 shows a basic procedure for designing blast walls in accordance with this document. The steps are explained in the subsequent sections of this document.

FABIG Technical Note - J u n e 1999 Page 3


Calculate new DLF,

Blast loading specification and response

c c

START

Select wall profile and material grade properties

(high strain ra:el

I Calculate section properties C h o o s e G I

I

.~ v

. Choose another profile

Assume initial reduction

I

resistance I

Class 1 section? Determine support conditions and effective

Calculate wall resistance Calculate plastic moment

, stiffness & period

Determine effective span of -1 Calculate DLF, and DLF, r I

Y.*

analysis or choose another Shear

resistance OK?

Y * l

Calculate transverse and axial stresses due to:

1 ) External effects 2) Internal effects

I

> initial?

Figure 2.1 Step-6 y-step design procedure

t-



3 CHARACTERISTICS AND PROPERTIES OF STAINLESS STEELS

Family

3.1 Common stainless steels and their composition

Stainless steels are alloys of iron containing at least 10.5% chromium and usually at least 50% iron. Upon exposure to air or water, a thin, stable, chromium-rich oxide film forms on the surface of these metals. This film provides a high degree of protection that reforms rapidly if damaged by scratching.

BS EN 10088 designation”

The controlled addition of alloying elements results in a wide range of material grades, each offering specific attributes in respect of strength, ability to resist certain atmospheric and chemical environments and to operate at elevated temperatures. Examples from within the major families of stainless steels, their compositions and attributes are shown in Table 3.1.

Austenitic

Duplex

combination of alloying elements results in a different crystal structure of iron from that in ordinary structural carbon steels. Austenitic stainless steels have excellent resistance to general (i. e. uniform) corrosion, different yielding and forming characteristics and significantly better toughness over a wide range of temperatures. Their corrosion performance can be further enhanced by additions of molybdenum. Austenitic stainless steels are also readily weldable.

1.4301

1.4307

1.4401

1.4401

1.4541

1.4362

1.4462

Duplex stainless steels have a mixed austenitic/ferritic microstructure and are based on 22-23 % chromium and 4-5% nickel additions. Grade 1.4462 (2205) has generally better corrosion resistance than the standard austenitic stainless steels, because of the higher content of chromium and presence of molybdenum and nitrogen. Duplex stainless steels are stronger than austenitic steels. They are also readily weldable.

Austenitic stainless steels are the most widely used in the construction industry and are based on 17- 18%’chromium and 8-1 1% nickel additions. This

Table 3.1 Typical content of main alloying elements in the principal grades of stainless steels. (The grades most widely used for offshore blast walls and covered by this guide are shown in bold.)

Popular name” I Cr Ni

304 18 9

304L 18 9

316 17 12

316L 17 12

32 1 18 10

Neil

Mo - -

-It (7c

N -

0.1

0.15 -

Others

L o w c

L o w c

Ti”

Artribures

Good corrosion resisting and fabrication propenies; readily available in a variety of forms. e.g. sheet, tube. fasteners. fixings. efc. 1.4401 (316) has better pirring corrosion resistance than 1.4301 (304).

Low carbon (L) grades should be used where extensive welding of heavy sections is required.

Higher strength and wear resistance than standard austenitic grades with good resistance to stress corrosion cracking. Grade 1.4462 (2205) has berter corrosion resistance than 1.4362 (2304).

Notes: 1) 2) 3)

An explanation of the BS EN 10088 designation system is given in Section 3.2. The popular name originates from the (now panly superseded) BSI and AlSI systems. Titanium is added to stabilise carbon and improve corrosion performance in the hear affected zones of welds. However, except for very heavy section construction, the use of titanium srabilised austenitic steels has been superseded largely by low carbon grades.



3.2 Specifications and

The European material standard for stainless steels, EN 10088, is issued in the UK as BS EN 10088: 1995, Stainless Steels. It consists of three Parts:

designation systems

Part 1, Lisr of stainless steels. This sets out the chemical compositions of particular grades of stainless steel and reference data on physical properties such as density, modulus of elasticity and thermal conductivity . Part 2, Technical delivery conditions for sheet, plate and strip for general purposes. This sets out the chemical compositions and surface finishes for the materials used in flat products, and mechanical properties such as proof strength.

Part 3, Technical delivery conditions for semi- finished products, bars, rock and sections for general purposes. This sets out the chemical compositions and surface finishes for the materials used in long products, and mechanical properties such as proof strength.

Stainless steel producers and suppliers throughout Europe are now following this Standard. The designation systems adopted in the Standard are the European material number and a material name. The material number comprises three components, for example 1.4404, where:

1. 44 04

Steel The group of Individual grade stainless steels identification

The material name system provides some indication of the steel composition, for example X2CrNiMo 17- 1-2-2 indicates:

X 2 CrNiMo 17-12-2

High alloy 0.02% main percentage of steel carbon alloying main alloying

elements elements

Each stainless steel material number has a unique corresponding material name.

In this guide, the designation system adopted is the European material number, followed in brackets by a ‘popular name’ for example 1.4404 (3 16L). The popular name originates from the (now partly superseded) BSI and AISI systems, and is included

here to help those familiar with the older naming convention.

3.3 Product form Most grades of austenitic and duplex stainless steels are available in the following forms:

Plate, sheet, strip, pipe and tube (welded and seamless).

Bar, rod, wire and special wire sections.

Cold formed structural sections (e.g. channels, angles).

Hot rolled sections (e.g. equal and unequal angles).

Extruded sections.

Castings.

Fasteners and fixings.

Sheet, strip and plate are commonly used for structural components, cladding and blast wall systems. Hot rolled sections are available, but structural sections are generally fabricated either by welding together cold formzd plate, sheet and strip or by roll forming. There are casting compositions which offer equivalent corrosion performance to many of the wrought grades.

Stainless steels blast walls are fabricated either from cold rolled strip (for thichesses up to 6 mrn) or from hot rolled strip (for thicknesses greater than 6 mm). Table 3.2 gives a summary of the flat products available, with approximate size ranges.

In general, a basic mill finish will be adequate for a blast wall. BS EN 10088 designates such finishes as 1D or 2D (hot rolled or cold rolled, softened and descaled) and 2B (cold rolled, softened, descaled and lightly flattened by tension levelling or rolling). Generally, cold rolled products have better surface finishes and closer tolerances than hot rolled products of equivalent thickness.

For special architectural requirements, a range of special finishes is also available. These include ground, brushed or polished surfaces. Further guidance on the selection of special finishes is available from steel manufacturers.

Many different companies manufacture stainless steel products, and the size ranges they offer vary. For actual sizes, reference should be made to manufacturers’ information.



Item Process route Surface finish Approximate range of dimens ions

Thickness Width" (m) (m)

Sheet, strip and Hot rolled softened, pickled 2.0 to 8.5 loo0 to 2032 coil (ID)

Cold rolled heat treated, pickled 0.25 to 6.35 Up to 2032 (2D)

D. D

heat treated, 0.25 to 6.35 Up to 2032 pickled, skin passed on bright rolls (2B)

lo00 to 3200 Hot rolled 3 10 140

-9 Plate

lo00 to 2Ooo /-'\ Cold rolled 3 to 8 . Note: Standard widths are 500, lOoo, 1250, 1500 and 2000 mm. Maximum economy can

be achieved by configuring the profile dimensions to suit the standard widths.

Table 3.2 Approximate size range for flat products

3.4 Properties of stainless steel stainless steel typically used for structural applications. These specified strengths relate to

3.4.1 Mechanical properties material in the annealed condition. In . practice,these values will be exceeded i f the material is cold worked (Section 3.4.2). The shape of the stress-strain curve for stainless

steel differs from that of carbon steels. Whereas carbon steel typically exhibits linear elastic behaviour up to the yield strength and a plateau before strain hardening, stainless steel has a more rounded response with no well-defined yield strength (Figure 3.1). This results in a difference in structural behaviour between carbon steel and stainless steel, and consequently different design rules apply in certain cases.

Stainless steel design strengths are generally quoted in terms of a proof strength defined for a particular offset permanent strain, conventionally the 0.2% strain. BS EN 10088 quotes 0.2% proof strengths of around 240 N/mm2 and 420 to 480 N / m 2 respectively for the grades of austenitic and duplex

There is also provision within BS EN 10088 for specifying alternative delivery conditions for certain steels (including austenitic steels 1.4401 (3 16) and 1.4404 (316L)) as cold rolled strip with 0.2% proof strengths up to four times greater than those of the annealed material.

Table 3.3 gives the minimum specified mechanical properties of four grades of stainless steel in BS EN 10088.

Part 1 of BS EN 10088 gives a value of Young's Modulus, E for the grades given in Table 3.3 of 200,000 N/mm*.

FABIG Technical Note -.June 1999 Page 7


- 600 E

E Z 500 1 - v) u)

? 400 v) c.’

300

200

1 00

0

7 I

I - - -

1.4404 (31 6L) / I

E ,I I

I

I’ . . . I . . . * , . . I . . . t . . . I . . . I

0 0.2 0.4 0.6 0.8 1 .o 1.2 1.4

Strain (%)

Figure 3.1 Typical stress-strain curves for stainless steel (not for use in design)

Table 3.3 Minimum specified mechanical properties to BS EN 10088-2

Steel Product Maximum Minimum Minimum Minimum Minimum elongation form“’ thickness 0.2% proof 1.0% proof ultimate after fracmre %

(mm) strase’ stressf2’ tensile R N . 2 RPl.0 strength

(N/mm’)

t <3mm t r3mm ( N h m ’ ) (Nlrnm’) R,

Nota: O1 C=cold rolled smp, H= hot rolled strip, P= hot rolled plate aansversc propertic;



100

3.4.2 Use of manufacturer's strength data

For blast and fire loading cases, strength data may be based on the results of manufacturer's tensile tests, where available. The data should be appropriate to the manufacturing process used by the supplier of the material. The design strength should not be based on the meun strength but rather on a value which has a specific probability of excedance. In the absence of a documented reliability approach, the excedance probability should be taken as 90%. In this case, for a normal distribution of strength variance, the design strength is given by the meaii niirius 1.28 standard deviations.

i , = 2 1 . 3 5 . l -

For other loading cases the minimum specified values given in Table 3.3 should be used.

Low strain rate E y = 14.6 s - ' L E, = 1.38 1 0 ' ~ ~

E, = 2.77 x 10' s .'

I , I I I I I I 8 I I 1

Where the fu l l strain range is used (for example, in non-linear finite element analysis) and the design strength is based on manufacturer's data, the data for the fu l l strain range should be obtained from the same data set, i.e. manufacturer's data should not be used for part of the strain range and generic data for the remainder.

3.4.3 Effect of strain rate on mechanical properties

Stainless steels have a strong strain rate dependency; strengths are increased (particularly in the region of the 0.2% proof strain) and the rupture strain reduced at higher strain rates. Figures 3.2 and 3.3 illustrate this effect by comparing stress- strain curves for 1.4404 (3 16L) and 1 . a 6 2 (2205) at low and high strain rates. The cyclic fluctuations in the 0 to 20% strain range in Figures 3.2 and 3.3 are due to dynamic response of the testing machine.

Figure 3 .2 (3 16LI

1000 r 900

*'" 800 E 700 5

w 600 E 500

v)

4- cn

400

300

200

100

0

Figure 3.3 Effect of strain rate on the stress-strain characteristics of grade 1.4462 (22051

Pane Q FABIG Technical Note - June 1999


Figure 3.4 shows a typical strain versus time curve for a dynamic tensile test using a conventional dynamic testing machine. It illustrates how the strain rate can be idealised as two discrete slopes representing the pre- and post- yield strain rates 1, and h, respectively. The transition between the two slopes occurs in the region of yielding and is seen as a rapidly changing strain rate which is associated with the change in stiffness of the material from elastic to plastic behaviour.

Table 3.4 gives values for the strain rate enhancement factor (KsR)o.l for a range of pre-yield strain rates ky. (KS,& is a factor which can be applied in design to take advantage of the increase in strength at higher strain rates. These values

were derived from a recent test programme investigating high strain rate effects on austenitic and duplex stainless steels(4).

Appendix B gives values of K,, for the 0.1%. 0.2% and 1 % proof strengths ((KS& ,, (KSR)a.z, and (KSR),, respectively) for a range of pre-yield strain rates h,. Values of KSR for the ultimate tensile strength ((KSR),) for a range of post-yield strain rates 6, are also given alongside the rupture strain.

Czujko et al") provides additional data on strain rate enhancement factors and standard deviations on strengths for materials from a particular manufacturing process.

Time Is1

Figure 3.4 Typical strain-time curve for a dynamic tensile test on stainless steel

Table 3.4 Strain rate enhancement factor, (K,,),,


Design Guide 'for Stainless Steel Blast Walls

Class 3 and 4 cross-sections

3.4.4 Determination of than being the minimum specified 0.2% proof

Typical strain rate in extreme fibres (s-')

0.02

enhanced material strengths for design

Class 1 and 2 cross-sections with deflection in the plastic range.

strength R,, given in BS EN 10088. The design strength may be further enhanced when blast loading is being considered tofv' to take advantage

1 .o

The minimum specified values for strength given in BS EN 10088 and strengths measured by the manufacturer are based on static tensile tests carried out in accordance with BS EN 10002-1. The limiting strain rates for these static tensile tests are:

of the improvement in strengih due to the high strain rates where:

r; = f y ( q R I 0 . z (3.1)

where (KSJ0., is given in Table 3.4.

Typical strain rates are given in Table 3.5 and may be used for preliminary desigd6).

by < 2.5 x

b, < 8.0 x

for R,,., , R,,,2 and, where specified, Rp,.O for strengths at strains greater than 1.0% proof strain For assessments of the plastic deflection (see

Section 9) using non-linear finite element analysis (NLFEA), the full enhanced stress-strain curve may be used. Figure 3.5 shows a linearized stress- strain curve which allows for strain rate effects.

For designing structural stainless steel, the design strength& is taken as the 0.2% proof strength. As discussed in Section 3.4.2, for blast walls this value is usually based on manufacturer's data rather

Table 3.5 Recommended strain rates for preliminary design

Class 1 and 2 cross-sections with deflection in the elastic range.

0.2

I

I

I I I I /IE; I

I

I

I

I

YI: I

10.2% 1 % 0.1%

€ 1

Strain

Note: Values for a,,,, ao.z, a,,, a", E , and K,, are given in Table B.l in Appendix B. These strength values are mean strengths for samples of 4 mm thick cold rolled material measured in the longitudinal direction and produced by Avesta Sheffield. Different values will be obtained for material from different suppliers or manufactured by different processes.

Figure 3.5 Linearized stress strain curve allowing for strain rate effects

FABIG Technical Note - June 1999 Paae 1 1


3.4.5 Effect of elevated temperature on mechanical properties

Stainless steels exhibit less strength reduction than carbon steels at temperatures above about 500°C. The degree of reduction at a given temperature depends on the grade and the level of cold working induced during manufacture. Table 3.6 gives material strength (retention) factors derived from anisothermal tests for grade 1.4404 (3 16L)”’. The actual strength at any temperature can be found by multiplying the 0.2% proof strength at room temperature (either the minimum specified value or a value supplied by the manufacturer) by the strength factor. At the time of writing, work is in progress to generate material retention factors for duplex steels (June 1999).

3.4.6 Physical properties

Austenitic stainless steels have thermal expansion coefficients 30-50% greater than those for carbon

Table 3.6

steels, and thermal conductivities of less than 30% of those for carbon steels. This has implications for detailing and in welding, where suitable expansion allowances should be made. I t may also impact on residual stress and buckling behaviour, and this needs to be recognised in the buckling formulae applied in situations where welding is carried out. Duplex stainless steels have similar thermal expansion properties to those of carbon steel and hence considerations in respect of thermal distortion are similar to those for carbon steel.

The density of duplex and ferritic steels is slightly lower than that of carbon steel. Austenitic stainless steels are essentially non-magnetic whereas duplex grades are magnetic.

Table 3.7 gives the room temperature physical properties given in BS EN 10088 for four grades.

Poisson’s ratio v may be taken as 0.3.

Strength factors at elevated temperatures for grade 1.4404 (3 1 6 L ) stainless steel



Steel designation

Table 3.7 Room temperature physical properties to BS EN 10088 (annealed condition)

Density Modulus of Thermal Thermal Heat capacity (kg/m3) elasticity expansion conductivity at 20°C

(kN/mm*) 20 - 100°C at 20°C (J /kg "C) (109°C) (W/m " C)

1.4401 (316)

1.4404 (316L) 8000

I Austenitic I 200 16 15 SO0

1.4362 (2304)

1.4462 (2205) 7 800 200

I Duplex I 13 15 500

3.5 Durability

3.5.1 Corrosion resistance mechanism

Stainless steels have a record of highly satisfactory performance in many different environments. The corrosion resistance of the material arises from the passive, chromium-rich, oxide film that forms on the surface of the steel. Unlike rust that forms on carbon steels, this film is stable, non-porous and adheres tightly to the surface of the steel. I t is usually self-repairing and resistant to chemical attack. If the film is scratched or broken, the exposed surface tends to react with oxygen, thereby renewing the oxide layer (Figure 3.6). The material therefore has intrinsic self-healing properties.

Passive film

Self repair

Figure 3.6 The corrosion protection of stainless steel

The presence of oxygen is essential to the formation of the oxide film. Deposits that fonn on the surface of the steel can reduce the access of oxygen to the surface of the steel and can therefore compromise corrosion resistance.

The stability of the oxide film is dependent upon several factors including the alloying elements present in the material and the corrosive nature of the environment.

To ensure good performance, i t is essential that the correct grade is selected and that appropriate design, fabrication. installation and maintenance practices are followed. The selection of a particular grade of stainless steel is influenced by a number of factors including structural performance, production and manufacturing issues, cost and durability. Further detailed guidance on the corrosion resistance of stainless steels in different environments is given in the Avesra Shefield Corrosion Handbook for Srainless Sreel'8'.

3.5.2 Types of corrosion

The austenitic and duplex stainless steels covered by this guide are resistant to general or uniform corrosion on offshore installations. However, there are areas where an understanding of the ways in which stainless steel can be attacked by corrosion is necessary. These are: weathering and surface discolouration, and the risk of localised attack from chemical microclimates (e.g. salt deposits).

This Section discusses forms of corrosion attack relevant to stainless steels and how such attack can be avoided. Practical design guidance on detailing principles to optimise durability is also presented. Specific details relevant to stainless steel blast walls are given in Section 10.



Table 3.8 Relative corrosion resistance and strength of stainless steel grades

2205

Increasing resistance to pining

and crevice corrosion

316.316L. 2304

Increasing resistance to stress corrosion

The types of corrosion that can affect stainless steel blast walls are:

Pitting corrosion

Crevice corrosion

Galvanic corrosion

Stress corrosion cracking.

Grades 1.4401 (316) and 1.4404 (316L) have been successfully used in offshore blast wall applications for many years. 1.4362 (2304) is 2 more modem grade which has also been used on a number of offshore blast wall projects. To date, grade 1.4462 (2205) has only found application in a limited number of blast walls.

Table 3.8 shows the relative corrosion resistance and strength of these four grades of stainless steel.

Since the alloying elements are expensive, there is a relationship between corrosion resistance and cost. The approximate costs of grades 2304 (1.4362) and 2205 (1.4462) are respectively 10% and 40% greater than grade 316 (1.4401) or 316L (1.4404). The correct grade specification for a given environment is therefore a balance between cost and performance.

Pitting

Pitting is a localised form of corrosion that generally results in small depressions on the surface of the material. It is often associated with exposure to chlorides or salts that penetrate the oxide film where it is weakest, and is a particular consideration in marine environments. Generally, pitting does not significantly reduce the cross-sectional area of components and tends to have little effect upon structural performance. However, the corrosion products from the pits can cause staining on the surface that spreads to an

2205.2304

316,316L

2205

2304 Increasing strength

316. 3161

extent far beyond the pit sites. The staining can usually be removed by cleaning, leaving only minor dulling of the surface by the micropits. However, in regions inaccessible for cleaning, and in severe cases of attack, this can have a serious detrimental effect on the appearance of components such as cladding panels.

Regular washing of the surface can reduce susceptibility to such corrosion. Grades of stainless steel that contain molybdenum are more resistant to pitting.

Crevice corrosion

Corrosion can initiate more easily in narrow crevices than on a freely draining surface because the diffusion of oxidants necessary to maintain the oxide film is restricted and the crevice tends to trap corrosive deposits. In terms of corrosion, a crevice is defined as an opening between 0.025 and 0.1 mm wide, and should not be confused with wider openings that are commonly encountered in engineering structures.

Crevice corrosion is only likely to be a problem if a build-up of chlorides occurs in a stagnant solution within a crevice. Severity of corrosion will then be dependent on the geometry of the crevice; the narrower and deeper it is, the more severe the corrosion tends to become. Crevices may occur at joints, such as under washers or bolt heads, in the threads of bolts, beneath deposits on the surface of stainless steel, beneath absorbent gaskets, or as a result of surface damage such as deep scratches. Every reasonable effort should be made to eliminate details which retain stagnant water.

Galvanic' corrosion

Care should be taken whenever dissimilar metals are in contact. Galvanic (bimetallic) corrosion can

Page 14 FABIG Technical Note - J u n e 1999


occur when different metals are in electrical contact and are both immersed in the same solution (electrolyte). If an electric current flows between the two, the less noble metal (the anode) corrodes at a faster rate than would have occurred if the metals were not in contact.

It is difficult to assess the rate of corrosion between dissimilar metals, and especially the point at which the corrosion risk becomes significant for components only subjected to periodic moisture or modest dampness. Factors such as the relative areas of the different metals, the type of electrolyte and the required service life are all significant. Small carbon steel components in stainless steel assemblies are generally more susceptible to galvanic corrosion than larger carbon steel assemblies used with small stainless steel components.

PD 6484'9' gives guidance on galvanic corrosion based on practical experience in a range of environments.

Stainless steels are the most noble of the common engineering and construction metals and therefore usually form the cathode in a bimetallic couple, and thus rarely suffer from galvanic corrosion. An exception is the couple with copper, which should generally be avoided except under benign conditions. Contact between stainless steel and zinc or aluminium may result in some additional corrosion of the latter two metals. This is unlikely to be significant structurally but the resulting white/grey powder may be deemed unsightly.

from applied loads, but also from residual stresses left after cold working or welding.

3.5.3 Detailing to prevent

In addition to adequate grade selection, attention to detailing plays an important part in reducing the risk of corrosion. The following points summarise recommendations for good detailing to maximise durability:

Avoid arrangements which allow dirt entrapment or chemical concentration.

Provide clear drainage paths.

Avoid gaps, ledges, slits and crevices.

Specify smooth contours and radiused comers to facilitate cleaning.

Avoid sharp changes in section and other stress raisers.

Avoid details which create access problems for welding to achieve the optimum geometry of weld and ease of final finishing.

Aim for conditions allowing full penetration welded joints with smooth contours and weld bead profiles. Insulate connections with other metals.

corrosion

Figure 3.7 illustrates selected good and poor design features. More specific blast wall details are given in Section 10.1.

Galvanic corrosion may be prevented by isolating dissimilar metals, and by excluding water or any other fluid that might act as an electrolyte. When painted carbon steel is joined to stainless steel, it is good practice to paint over the joint and to cover a few centimetres of the stainless steel to prevent the possibility of galvanic corrosion of the carbon steel.

Stress corrosion cracking

Stress corrosion cracking (SCC) is a form of localised attack which can lead to rapid crack growth and loss of load bearing capability. I t occurs under the simultaneous presence of tensile stresses, an aggressive, usually chloride-bearing, environment and metal temperatures above about 60°C. In the presence of high concentrations of some corrosive chemicals, SCC can occur at lower temperatures. Tensile stresses can arise not only

I

Good

A

1 6

Figure 3.7 Design features to prevent corrosion



4 NATURE OF EXPLOSION LOADING AND STRUCTURAL RESPONSE

4.1 Explosion loading Explosion loading is a short-term impulsive load. There are two basic types of impulses: these are illustrated in Figure 4.1.

Impulse Type A is typical of gas or vapour cloud explosions whereas Type B is characteristic of high explosive detonations and impulses from gas or vapour cloud explosions in the far-field. The typical duration of an impulse from a hydrocarbon explosion is significantly larger than that from a TNT explosion.

(typically 10%) of the maximum load/pressure has been achieved. Joining these points to the point of maximum load/pressure produces a triangle which can be used to establish representative rise time (f,) and duration (fa. see Figure 4.2. Careful consideration must be given if multiple load pulses are observed or predicted. if this is so then there is a need to consider the structural response to such peaks in order to guide the definition of the important parameters to characterise these traces. Alternatively, the actual impulse shape may be used as input to a time domain simulation of structural response.

P L Type B (far fieidl

Figure 4.1 Explosion pressure impulses

Load pulse rise time and duration may be calculated by selecting points on a loadpressure-time curve where a certain percentage

4.2 Specified peak explosion pressure, PMAX

The specified peak explosion pressure is, in general, the maximum overpressure (Figure 4.2).

Explosion pressures vary both spatially and temporally over the extent of a blast wall. The design pressure impulse should be the local peak pressure impulse or the impulse averaged over a suitably small area. The design impulse may be varied along the wall according to the results obtained in an explosion pressure analysis.

1000

750

500

250

320 340 360 380 400 420

k 4 k

1, Time from ignition (msl

‘ d 4 Figure 4.2 Derivation of simplified pressure-time profile



4.3 Structural response to explosion loading

4.3.1 General

Pressure loading generated by explosions varies with time, and the resulting response of the structure is therefore also time-dependent. The loading causes the structure to vibrate at its natural period, and large blasts can cause plastic deformation which remains as a permanent set to the structure after the vibration has settled down. The dynamic deflection and stresses will usually be more than those determined by applying the peak load statically.

Stainless steel has considerable ductility. However, the onset of local buckling or local flattening of the cross-section rapidly reduces the moment resistance that can be mobilised. Once the moment resistance starts to fall, all subsequent strain will be concentrated over a small length of section at the point of maximum moment. When this happens, a fold appears in the section at the point of maximum moment. Figure 4.3 shows a finite element model illustrating this failure mode in a Class 4 cross- section.

Figure 4.3 Typical failure mode for Class 4 cross-section

Furthermore, the loss of moment resistance at the critical point in the span results in the virtual instantaneous release of a large proportion of the elastic strain energy in the remainder of the span into the deformation zone. This increases the local deformation causing, in turn, further loss of moment resistance. This explains why the load deflection curve in Figure 9.2 descends sharply beyond the plastic deflection limit. Once the

deflection limit has been reached, the blast wall loses its load carrying resistance.

There are two basic analysis methodologies: the single degree of freedom (SDOF) and the multi degree of freedom (MDOF) methods. A description of these techniques is to be found in the Interim Guidance Notes””; the charts required by the SDOF method are also given in that reference.

4.3.2 Single degree of freedom (SDOF) method

This method avoids complex dynamic structural analysis by converting the time dependent pressure into an equivalent static load. The equivalent static load is given by multiplying the specified peak explosion pressure by a ‘dynamic load factor’ (DLF), where DLF is defined as the ratio of the dynamic reaction to the reaction which would have resulted from the static application of the specified peak explosion pressure.

The following factors affect the dynamic response of the structure:

whether the deflections are elastic or plastic,

the duration of the pressure pulse, td,

the shape of the pressure pulse, i .e. the time to reach the maximum pressure (rise time f,) relative to the duration of the pressure pulse fd,

the natural period of the structure, T.

The method can accommodate walls which deflect in the plastic range and enables the maximum deflection at midspan to be determined. This deflection is usually expressed as the ductility ratio multiplied by the deflection at the elastic limit.

The structure is characterised by a simple spring- mass system subject to an impulsive load. The spring constant is the stiffness of the wall multiplied by a factor dependent upon the end support conditions. The mass is the wall self-weight multiplied by a suitable factor, the value of which varies between 0.5 and 0.78 according to the support conditions and degree of plastic deflection. For simply supported walls with uniform loading the factor is 0.78.

For walls responding elastically to impulse loading characterised by an isosceles triangle, the DLF may be determined using Figure 4.4. FABIG Technical Note 4‘6’, the Interim Guidance Notes“” and



DLF

0.1 0.25 0.5 0.751.0 1.5 2.0 3.0 5.0 10

td

Figure 4.4 Dynamic load factor versus td /T for an isosceles triangle impulse - elastic response

Biggs"') give guidance on the determination of DLF for other cases. In applying the SDOF method care must be taken in the determination of appropriate limits on allowable ductility ratio. Methods for verifying plastic moment resistance are discussed in Section 9.

Figure 4.4 also shows the sensitivity of the DLF to the ratio t,/T for elastic walls. If there is uncertainty about the blast impulse duration td , wall specifications should include a tolerance band on impulse duration to ensure that designs are not carefully tuned to the troughs in the DLF curve.

The required static pressure resistance of the wall is the specified peak explosion pressure multiplied by the DLF. The static pressure resistance may be determined using material strengths enhanced for stLain rate (Sections 3.4.3 and 3.4.4).

With Type B impulses (Figure 4.1) the response is even more dependent upon the natural period. If the natural period is such that the negative pressure phase coincides with the rebound phase of the wall's response, the peak rebound resistance to be mobilised in the wall will be much larger than the first response. In such cases the wall will tend to fail towards the blast rather than inwards. If the wall's natural period is long in relation to the overall impulse duration the wall will respond to the net impulse and much less resistance is required, i.e. the DLF is very small, sometimes less than 0.3.

Time domain SDOF

As an alternative to the use of charts (e.g. Figure 4.4), the peak response may be determined by time domain simulation using a SDOF spring mass model. This is useful where the impulse shape is irregular and therefore not covered by available charts or where the load-deflection characteristic of the SDOF model is neither linear nor bi-linear.

4.3.3 Multi degree of freedom (MDOF) method

In the MDOF method the structure is typically represented by a finite element (FE) model with time-varying loads. The simulation automatically determines local load distribution due to inertia (acceleration) and produces time histories of deflections, stresses etc. The FE model may be linear or non-linear.



5 WALL PROFILES

5.1 Choice of profile

A variety of profile shapes are suitable for blast walls. The most commonly used is the unstiffened profile (Type 1 in Figure 1. I ) . Stiffened profiles (Types 2 and 3 in Figure 1.1) are structurally more efficient than unstiffened profiles, however fabrication costs are higher. Where the overall longitudinal moment resistance of the profile is limited by local buckling of the compression flange, using a stiffened profile may be more economical. Welded flange stiffeners (Type 3) may be added to an existing blast wall to increase its resistance. For smaller profiles, it may be difficult to achieve adequate stiffener depth whilst respecting minimum bending radii.

5.2 Geometrical proportions Members and cross-sections designed in accordance with this guide should satisfy the limits given below, which represent the range for which sufficient experience and verification by testing is already available. These limits are more generous than would normally be used in practice, particularly for blast walls (this is because of the need to resist local effects). They are therefore not in any way prohibitive and, for structural efficiency, lower limits are generally used.

a.

b.

C .

d.

Web slope: 45 5 q5 5 90"

Flat element or intermediately stiffened element connected to a web along one edge with the other edge unsupported:

b/r < 50

Flat element or intermediately stiffened element connected along both edges to webs or flanges:

b/t < 400, s,/t < 400

Flat element or intermediately stiffened element connected to a web along one edge and provided with a small lip along the other edge:

b/t < 60

In order to provide sufficient stiffness and to avoid primary buckling of the stiffener itself, the sizes of stiffeners should be within the following ranges:

0.2 5 c t b 5 0.6 (5 . la)

0.1 5 d t b 5 0.3 (5.lb)

in which the dimensions b, c and d are as indicated in Figure 5.1.

5.3 Section properties Properties should be calculated according to normal practice, taking due account of the sensitivity of the properties of the overall cross-section to any approximations used (Section 5.3.3) and their influence on the predicted resistance of the member. The guidance in this Section is based on the provisions in ENV 1993-1-3'3'. The effects of local buckling should be taken into account by using effective cross-sections, as described in Section 6.

5.3.1 Gross cross-section The properties of the gross cross-section should be determined using the specified nominal dimensions. In calculating gross cross-sectional properties, holes for fasteners need not be deducted, but allowance shall be made for large openings. Plates that are used solely in splices or as battens should not be included.

5.3.2 Net cross-section The net area of a member cross-section, or of an element of a cross-section, should be taken as its gross area minus appropriate deductions for all fasteners holes and other openings. In deducting holes for fasteners, the nominal hole diameter should be used, not the fastener diameter. The area to be deducted for groups of fastener holes may be calculated in accordance with 5.4.2.2 of ENV 1993-1-1O'.

5.3.3 Influence of rounded corners In cross-sections with rounded comers, the notional flat width of the plane elements should be measured from the midpoints of the adjacent elements as indicated in Figure 5.1 and the calculation of section properties should be based upon the actual geometry of the cross section.

The influence of rounded comers with internal radius r I 5t and r 2 0.15bP on section properties may be neglected, and the cross-section may be assumed to consist of plane elements with sharp comers.

FABlG Technical Note - June I999 Page 19


If the internal radius r exceeds these limits the where influence of rounded comers on section properties should be allowed for. This may be done with sufficient accuracy by reducing the properties calculated for an otherwise similar cross-section with sharp comers using the following approximations:

A, , I,, Z, = area, second moment of area and warping constant of the gross cross-sec tion

values of A, , I , and I , for a cross-section with sharp comers

la.,,, I,,,, =

bp,; = notional flat width of plane element i for a cross-section with sharp comers A , = A g , d - 4 (5.2a)

= Zg,sh(1 - 2 4 (5.2b) rn = number of plane elements n = number of curved elements 5

The reductions given by expression 5.2 may also be applied in calculating the effective section properties Acrr Iz.ca and Zw.cll, provided that the notional flat widths of the plane elements are measured to the points of intersection of their midlines.

4 = internal radius of curved element j 1, = L , d l - 46) ( 5 . 2 ~ )

with

6 = 0.43 c r, I bP,; (5.2d) j = l r = l

n m

X is intersection of midlines P is midpoint of corner r,,, = r + K/2 g = r,[tan($ /2) - sin(@ /2)1

a) Midpoint of corner or bend

c) Notional flat width b ,, for a web (b,=slant height s 1

b b, <

k

I I

- _ - - - - _ - -

b) Notional flat width b of plane elements b, c grid d

d) Notional flat width b, of a plane element adjacent to stiffeners

Figure 5.1 Notional flat widths of plane elements 6, allowing for corner radii



6 C R 0 S S -S ECT I0 N C LASS I F I CAT1 0 N AN D EFFECTIVE SECTION PROPERTIES

6.1 General The width-to-thickness ratio of elements that are partly or wholly in compression determine whether they are subject to local buckling with a consequential reduction in the resistance of the cross-section. Elements and cross-sections are classified in most structural design standards depending on their susceptibility to local buckling.

As with carbon steel, the reduced resistance of cross-sections susceptible to local buckling may be allowed for in design by the effective section concept. The effective section should be used throughout the design of the section wherever i t is in compression except where specifically noted otherwise. This reduction need not be made in the design of connections to. that element.

for the effects of local buckling when determining their moment resistance or compression resistance.

As the yield strength of non-linear materials is i l l - defined, so too are the yield and plastic moments. The common definitions that are used are the elastic and plastic section moduli multiplied by a proof stress, usually the 0.2% proof stress. Note that where enhancement due to strain rate effects is taken into account, the design strength is given by fy' (Section 3.4.4) both for section classification and for calculation of the effective width.

Flat elements in a cross-section are either:

internal elements attached on both longitudinal edges to other elements or to longitudinal stiffeners which effectively support the element, or Longitudinal stiffeners also require classification as

well as a check for overall buckling (Section 6.4). outstand elements attached on only one longitudinal edge to an adjacent element, the

The classification of the cross-section as a whole other edge being free. should be taken as that of the highest (least favourable) class of its constituent elements or Elements may be classified as Class 1, 2 or 3 stiffeners that are partially or wholly in depending upon the limits set in Table 6.1 which compression. are based on the provisions in ENV 1993-1-4.

Elements which do not meet the criteria for Class 6.2 Cross-section classification 3 are classified as Class 4.

In principle, stainless steel cross-sections may be classified in the same way as those of carbon steel. Classifications are defined in ENV 1993-1 as follows:

In a Class 4 element, local buckling may become the limiting design criterion and this is accounted for by adopting the effective width concept in accordance with Tables 6.2 and 6.3.

When calculating the effective width of flange and web elements, the value of stress ratio + should be determined iteratively for the effective

Class 1 plastic cross-sections which can form a plastic hinge with the rotation capacity required for plastic analysis.

their plastic moment resistance but have limited rotation capacity.

Class 3 serni-compacr cross-sections are those in which the calculated stress in the extreme compression fibre of the steel member can reach its yield strength, but local buckling is liable to prevent the development of the plastic moment resistance.

Class 4 slender cross-sections are those in which it is necessary to make explicit allowances

Class 2 compact cross-sections which can develop cross-section.

Paae 2 i FABIG Technical Note - June 1999


Table 6.1

(Elements which exceed the limits of Class 3 are to be taken as Class 4)

Limiting width to thickness ratios (ENV 7993- 1-41

Type of section

Class of section

Class 2

(Compact) E - 5 9.4E 1

Type of element Class 1 Class 3

(Semi-compact) (Plastic)

C

1

C

I

- 5 9.oc

- 5 1O.OC

Welded Outstand element of compression flange

c 5 1 1 .O& t

Cold formed

5 s 1 0 . 4 ~ 1

5 I1.9& I

All sections

b, - 5 2 5 . k I

bP - 5 3 0 . 1 ~ Internal element of compression flange

I

5*. - 5 14 .8~ 1

All sections

5 w - s 56.0~ I

Web with neutral axis at mid-depth

generally a>0.5 :

su. 3 2 0 ~ I 13a-1

- 5 -

All sections

a>0.5 : 5”. 308c

I 13a-1 - < -

--s 5u. 1 5 . 3 c K I a s 0.5 :

X I . c - 5 29.1- I a

a 5 0.5 : SU. E - 5 28- I a

5 *. - 5 3 0 . 1 ~ I

All sections

Web where whole element is subject to compression

Notes:

1. Dimensions c, b,, s,, I, are defmed in Figure 5.1.

0.5 235 E

2. wheref,‘ and E are given in Section 3.4.

For Class 3 sections cp is defined as:

3. For Class 1 and 2 section: a is defined as:

4. k, is defined in Tables 6.2 and 6.3



6.3 Plane elements without stiffeners - effective area

In ENV 1993-1-4, the effective widths of compression elements in Class 4 cross-sections are determined from tabulated expressions repeated here as Tables 6.2 and 6.3, using the reduction factor p obtained from the following:

if xp s 0.673, p = 1.0 (6. la)

if xp > 0.673, p = (1.0 - O.22/&)/xp (6.lb)

where

(6. Ic)

is the notional flat width of a plane element (Figure 5.1)

is the modulus of elasticity

is the relevant buckling factor from Table 6.2 or 6 .3

is the largest compressive stress in the relevant element, calculated on the basis of the effective cross-section, when the resistance of the cross-section is reached

The effective area of a slender section in compression, A, is the total of the effective areas of its constituent elements. The effective area of each slender element is the effective breadth b, calculated from Table 6.2 or 6 .3 multiplied by the element thickness.

FABlG Technical Note - June 1999 Paae 23


Table 6.2 Effective width of Class 4 plate elements - doubly supported compression elements (Table 4.1 of ENV 1993-1-31

Stress distribution

7.81 factor k,

Effective width bcK

p = +1: bcrr = Pb,

be, = O.5bc,

+1 > p2 0: be, = Pb,

be, = 0.4bc,

p < -1: bell = Pbc

b,, = 0.46,,

b, = O.6befl

0 > p > -1 I -1 1 - 1 > p > - 3

7.81 - 6.29$ + 9.78q2

Alternatively, for +1 2 p 2 -1: 16 k, =

[(I + $ ) 2 + 0.112(1 - q r y y . 5 + ( 1 + I#)



Effective width of Class 4 plate elements - outstand compression elements (Table Table 6.3 4.2 of ENV 1993-1-3)

0

1.70

Stress distribution [compression positive]

o > p > - 1 -1

1.70 - 5 @ + 17.1f 23.8

I

I + l I p = u,lu,

I Bucuing factor k, 1 0.43

0 1 =2

n I

bP I 0.578 9 + 0.34 1 Buckling I 0.43 1 factor k,,

Effective width b,,

I I



6.4 Flanges with intermediate stiffeners - cross-section classification and effective area

This Section applies to flanges with one intermediate stiffener in the middle of the flange (Type 2 or 3 profiles in Figure 1.1) and the guidance is based on the design provisions in ENV 1993-1-3 (Reference 3).

For Class 1 and 2 cross-sections, there is currently no formal guidance available. Hence the stiffener proportions must be derived from physical tests to demonstrate undiminished resistance over the full strain range required if Class 1 or 2 are to be achieved (see Section 9). Where yielding occurs first in the tension flange, plastic strain in the section is permissible up to the point where the

elastic compression resistance of the stiffened flange is reached. The extent of plastic strain allowed should be consistent with the value for E, assumed and applied in Section 8.1.2.

To be classified as a Class 3 cross-section, the stiffener must be fully effective, i .e. the strength reduction factor for flexural buckling of the stiffener, x = 1.0 (see step (3) below).

A stiffener has a Class 4 cross-section if the strength reduction factor for flexural buckling, x < 1.0 (see step (3) below). The effective thickness of the component parts of a Class 4 stiffener that contribute to overall section resistance have to be factored down by x (see step (4) below).

The procedure for determining the section classification and effective area of a compression flange with an intermediate stiffener is as follows:

Figure 6.1 Trial effective cross-section for a flange with an intermediate stiffener



(1)

The effective cross-section of the flange should be determined in the following way:

Determine trial effective cross-section (Figure 6.1)

Determine a trial value for the effective width of the plate elements b, by calculating a value for b, based on the assumption that 6, is doubly supported (see Table 6.2 and Section 6.3), using o , , , ~ =fy .

Take the effective cross-sectional area of an intermediate stiffener A, as the area of the stiffener itself plus the effective portions of the adjacent plate elements at nominal thickness.

For type 2 stiffened profiles:

AS = t (2 b, + bS)


AS = 2 t (be, + bcJ + tS bs

(6.2a)

(6.2b)

(In general, b / f S should be sufficiently small to ensure that the stiffener element b, is fully effective; where this is not the case the effective width of the stiffener element should be used in the calculations.)

Determine the elastic critical buckling stress of tire intermediate stiffener a,,,

Use the effective area of the stiffener A , to determine the position of the centroidal axis a-a. and hence the effective second moment of area, Z, (see Figure 6.1).

The elastic critical buckling stress of the stiffener (including the adjacent parts of the plate elements b,,,) is primarily a function of the geometry and the effective support provided by the stiffener.


rJ t 3

4bp’ (2bp + 3bJ (6.3a)

This is the same as expression (4.29) in ENV 1993-1-3 with k, set to 1.0 (which ,is applicable when there is no moment restraint provided by the webs which is relevant for blast wall design where the webs are highly utilised).


Calculate the relative slenderness of the stiffener:

(6.3b)

The derivation of this expression is given in Appendix C .

Determine the reduction factor x

FABIG Technical Note - J u n e 1999 Page 27


(6.4a)

(6.4b)

g, is the distance from the midline of the compression flange to the neutral axis of the

g,, is the distance from the midline of the compression flange to the neutral axis of the whole section (positive towards the neutral axis)

area A , (positive towards the neutral axis)

Calculate the reduction factor x for the flexural buckling resistance of the intermediate stiffener as follows:

bur x ? 1.0 I x = cp + (($2 - 2 ) 0 5

where 4 = 0.5 (1 + a (i - Io) + 2) in which:

a = 0.49 and & = 0.40 (no welding on plating in the buckling zone, e.g. Type 2 stiffened profile)

a = 0.76 and I,, = 0.20 (welding on plating in the buckling zone, e.g. Type 3 stiffened profile)

Detennine the effective section of fhe wall cross-section

Calculate the section properties of the whole section (e.g. Wen.e for the compression face and WCtr,, for the tension face) using the effective widths calculated in Step 1, but with the thickness of ail the components within A,, reduced from f lo I , , and from f, to fusd (see Figure 6.2) where:

t , = x r and ts., = x is (6.7a and b)

Optional iterafion

If x is less than 1 .O it may, optionally, be refined iteratively. This is done by returning to Step 1 and calculating a modified value of p using equation (6. lb) with ucomEd equal to xf,' , so that:

- where Ap is the plate slenderness, given by equation (6. Ic).

Iteration should continue until changes in XfY'A, between steps are small.

Defennine the effective section of the wall cross-section ai the SLS

The effective section properties at serviceability limit state may be determined using stress levels appropriate to the serviceability limit state. A* should be replaced in equation (6.4) by the maximum bending stress in the cross-section at serviceability limit state.



- - - - - - - -

Figure 6.2 Effective cross-section for a flange with an intermediate stiffener

6.5 Plane elements with edge stiffeners - cross-section classification and effective area

Blast wall profiles do not usually contain edge stiffeners. In zones of tension the whole stiffener area is effective; in zones of compression, the cross- section should be classified as Class 4 and may be assessed in accordance with Section 4.3.2 of ENV 1993-1-3 (Reference 3).

6.6 Tension resistance at bolt holes

The tension resistance of a cross-section should be taken as the lesser of the plastic resistance of the gross cross-section lVPaRd and the ultimate resistance Nu&, of the net cross-section, in accordance with the provisions in ENV 1993-1-4 (Reference 1).

The plastic resistance of the gross cross-section may be determined using:

(6.9)

The ultimate resistance of the net cross-section

should be determined from:

(6.10)

where

k, = ( 1 + 3 r ( d 0 / u - 0.3)) but k, s 1

r = [number of bolts at the cross-section]/

u = 2e, but u 5 p z

[total number of bolts in the connection]

where

A,,

f,' is the ultimate tensile strength enhanced for

do is the nominal diameter of the bolt hole

e2 is the edge distance from the centre of the bolt hole to the adjacent edge, in the direction perpendicular to the direction of load transfer

p 2 is the spacing centre-to-centre of bolt holes, in the direction perpendicular to the direction of load transfer.

is the net cross-sectional area

strain rate effects

FABlG Technical Note - June 1999 Page 29


7 DESIGN OF CROSS-SECTION TO WITHSTAND OVERALL LONGITUDINAL BENDING

The overall longitudinal moment resistance is given by the modulus of the effective section (see Section 6) multiplied by the enhanced design strength (Section 3.4.4). However, reduction factors may need to be applied to account for local effects.

7.1 Overall longitudinal moment resistance

For Class 1 and 2 cross-sections the whole cross- section is effective and the plastic section modulus Wpl,y may be used to determine the resistance. For Class 3 cross-sections the whole section is effective but the elastic section modulus Wcl.y is used to determine the resistance. For Class 4 cross- sections the elastic modulus of the effective section We,, should be used. Wy is the section modulus for one corrugation.

The overall longitudinal moment resistance per unit width is given by: For Class 1 or 2 cross- sections:

For Class 3 cross-sections:

For Class 4 cross-sections:

where

7.2 Effective span Most blast walls are simply supported at both the top and bottom. The end supports do generate a degree of moment resistance to rotation induced by bending of the wall. These end moments may be taken into account in establishing the resistance of the wall. This may be accomplished by considering the profile wall as simply supported with an effective span LE which is less than the gross height between support levels.

Figure 7.1 shows the bending moment distribution in the wall at the peak response.

c.Rd

Figure 7.1 Longitudinal moment distribution at peak of response

(7.3)

p = pitch of profiled sheeting KF = reduction factor to allow for flattening of

KVM = reduction factor to allow for transverse cross section

stresses

Points of contraflexure will occur at a distance LL above the bottom support and L, below the top support. The effective (simply supported) span LE is (L - L, - 15,).

The effective span LE and lengths L, and LL may be determined from:

Initially the value of the product KF KVM may be taken (usually conservatively) as 0.9; the values used must be confirmed by the methods given i n Sections 8.5 and 8.6.



(7.5b)

For simple support connections comprising a thin strip between support girders and the blast wall (such as those shown in Figures 10.1, 10.2, 10.3 (a) and 10.4) the moment resistances per unit width of wall at the lower support (Mc& and at the upper support (Mc.&, are given as follows:

(7.6a)

(7.6b)

Where f, and t , are ... e critic&support plate thicknesses (see Section 10.1) and fy' is the enhanced design strength of the support material. In the case of stainless steel, fy' is given in Section 3.4.4. For carbon steel, the enhancement on minimum specified yield strength is given in References 6 and 10.

For more complex details, the support moment resistance can be determined by detailed analysis.

7.3 Resistance of the wall The load resistance of the wall per unit width R, is the load distributed over L, that gives rise to Mc,Rd at midspan:

(7.7)

7.4 DLF and maximum midspan deflection

The dynamic response of the wall is dependent upon its stiffness and natural period.

7.4 .1 Stiffness under longitudinal

The stiffness k per unit width for determining the natural period for dynamic response analysis is given by:

bending

k = 384 E I

5 L j P

where

(7.8)

I = second moment of area of the gross cross- section of one corrugation for Class 1, 2 and 3 cross-sections or of the effective cross-section for a Class 4 cross-section

The end support rotations increase the deflection and thus reduce the effective stiffness. The reduced stiffness kR can be shown to be:

k kR = 1.6 (LL + Lu) (7.9)

7.4.2 Natural period The natural period of vibration T is given by:

(7.10)

where

M = mass of one corrugation of the wall profile and any liner and insulation attached

K,, = load-mass factor = 0.78 for simply supported walls and walls with limited end-moment fixity (LJL >0.9) (see Section 7.2). For other cases see Reference 10.

7.4.3 Dynamic response and dynamic load factor

The dynamic response to blast loading may be either elastic or elastic-plastic with plastic deflections. Class 2, 3 or 4 cross-sections cannot sustain plastic deflections without loss of moment resistance and consequently are limited to blast walls which are only required to respond elastically. It is therefore necessary to check whether the dynamic response of the selected wall profile is elastic or plastic.

This is done by determining, for a specified peak explosion pressure, the maximum dynamic load



factor that can be sustained by the wall (DLF), and comparing it with the dynamic load factor mobilised in the wall without deflection i n the plastic deformation range (DLF),, where (DLF), is given by:

(7.11)

PMAx is the specified peak explosion pressure R, is defined in Section 7.3.

For dynamic loading which can be idealised as an isosceles triangular impulse, (DLF), may be determined from Figure 4.4 using f, from Section 4.1 and T from Section 7.4.2. For other impulse shapes see References 6, 10 or 11; alternatively a time-domain SDOF spring-mass model may be used (see Section 4.3.2).

Elastic dynamic response

If (DLF), 2 (DLF), the wall response is elastic and the moment resistance of the selected section is adequate.

The maximum bending stress uMAX mobilised in the wall and the maximum deflection are given by equations 7.12 and 7.13 below:

Plastic dynamic response

(7.13)

If @LF), < (DLF), the wall response is plastic which means that i t deforms plastically. Only Class 1 cross-sections can sustain some degree of plastic deflection. The level of plastic deflection that is mobilised is that which results in a DLF equal to (DLF),.

The maximum deflection of the wall at midspan ym is determined from equations 7.14 and 7.15:

Y" = P Y,I (7.14)

where p is the ductility ratio (given in Figure 9.3 for

isosceles triangular impulses)

y,, i s the midspan deflection of the wall at the elastic limit, given by:

k, is given in Section 7.4.1.

(7.15)

The acceptance criterion for deflection is the most onerous of the acceptance limit defined in Section 2.2 or determined by one of the methods in Section 9.

7.5 Shear resistance of wall Blast walls should have sufficient shear resistance to ensure that the primary failure mode is in bending rather than shear. Whilst adequate shear resistance is usually provided by a typical arrangement of supports (see Figures 10.1 to 10.4), shear resistance at the supports can govern the design of blast walls with Class 4 cross-sections. Intermediate web stiffeners are rarely needed, however.

7.5.1 Shear resistance of profile

The shear load V per unit width may be determined in accordance with Reference 10. In general, the DLF for shear force is slightly lower than that for bending, hence i t is usually conservative to apply the following formula for determining the maximum shear force VMAx:

V,,, = 0.5 PhjAx DLF L, (7.16)

where L, is the distance from the point of zero shear in the wall to the support and the DLF is either (DLF), of (DLF), as determined from Section 7.4.3.

The total shear load VToT = V M x p

where p is the pitch of the corrugations

The shear stress in the web q is given by:

(7.17)

In accordance with ENV 1993-1-4, the shear resistance of a web VW.,,, is the lesser of the shear buckling resistance Vb,Rd and the plastic shear resistance vfl.Rd.



where

For webs with transverse stiffeners at the supports but no intermediate

For webs with transverse stiffeners at the supports and intermediate

For webs with transverse stiffeners at the supports and intermediate

transverse stiffeners (e.g. Figures 10.1 to 10.4)

transverse stiffeners with ah, < 1

transverse stiffeners with a/s, 2 1

The shear buckling resistance vbsRd should be verified when the relative web slenderness 1, > 0.2 or, in the case of an unstiffened web, if s,lt > 1 7 . 3 ~ where E is given in Table 6.1.

Buckling factor for shear buckling, k,

5.34

4 + 5.34 / (ds,)?

5.34 + 4 I (als,)'

The relative web slenderness x, should be obtained from:

Relative web slenderness - 4v

I

Web with transverse stiffeners at the supports only

Web with intermediate trallSVerSe stiffeners as well as transverse stiffeners at the supports

(7.18)

0.2 lw s 0.6

where k, is the buckling factor for shear buckling (Table 7.1).

[ l - 0.63(f - 0 . 2 ) ] ( 4 * / @ ) [ I - O.63(jw - 0.2)](&'/0)

The plastic shear resistance Vp(,Rd and the shear buckling resistance V,.,, (for 2 webs) should be obtained from:

(7.19) I,: Vprm = 2 s,, t - J5

(7.20)

fbv = the shear buckling strength obtained from Table 7.2 for the relevant value of I,.

At the supports, where the web is stiffened by a full depth bearing stiffener (as for example in Figures 10.1 to 10.4), the critical point for shear may be taken as 0.4 s, outboard from the support. Where shear strength criteria are not met, transverse web stiffeners should be provided at a spacing which ensures that the requirements of Table 7.2 are met.

7.5.2 Local support shear and deformation capacity

The support details must be checked for local shear and bending resistance. The bending resistance of the support detail aside from the dedicated hinging zone (at support level) must be sufficient to ensure that a second hinging zone does not develop and that the shear resistance at all levels is greater than the applied shear load. The effects on shear resistance of coincidental axial load should be considered where appropriate.

Table 7.1 Buckling factor for shear buckling, k,

Table 7.2 Shear buckling strength fbv

FABlG Technical Note - June 1999 Page 33


8 TRANSVERSE LOADING ON

8.1 Loads causing bending of the profile

There are two load components: direct pressure and the inertia loads due to acceleration (estermf forces, Figure 8.1) and crushing forces (internal forces, Figure 8.2).

8.1.1 External forces

Direct pressure P

Figure 8.1 Local loading due to the pressure of the explosion

The inertia loads due to acceleration may be accounted for by factoring up the peak pressure by the dynamic load factor (DLF) for overall longitudinal bending, when DLF is greater than 1 .o:

P = Pw DLF 2 PmX

8.1.2 Internal forces

R2 R2

Crushing forces F R

Figure 8.2 Local loading due to crushing forces

Internal crushing forces are due to the out-of-plane (local) component of the overall longitudinal bending stresses, and increase with increasing curvature of the wall. Crushing acts towards the neutral axis and is equal to the overall longitudinal plate stress multiplied by the curvature of the section. At plastic hinges the curvature is steep and this force is large. Even within the elastic

THE PROFILE

range for overall longitudinal bending, the crushing can be significant and needs to be allowed for.

For unstiffened profiles, the effective area of a Class 4 compression flange is concentrated near the webs and therefore distributing the load FRI uniformly produces a higher moment in the flange and is thus conservative. However, for stiffened profiles, the effective area of a Class 4 flange is concentrated towards the centre of the flange and therefore uniformly distributing the load FR, will not be conservative. This factor can be taken into account by using a more realistic distribution of FR, than is shown in Figure 8.2.

When calculating the distribution of FRI along the compression flange of a profile with a Class 4 intermediate flange stiffener, the reduced thickness of the stiffened area t,, and should be used (Section 6.4).

Note that the distribution of FRz is triangular (as shown) for Class 3 and 4 cross-sections whereas i t is rectangular for Class 1 and 2 cross-sections.

The effective area of the compression part of a Class 4 web is concentrated near the compression flanze where the triangular distribution of FRz is maximum. Therefore it is conservative (i.e. the web is subject to a higher moment) if the triangular load is applied over the whole length of the part of the web in the compression zone.

At the location of maximum overall longitudinal moment in the span the crushing forces are as follows:

a) Forces in compression flange FRI and in the compression part of the web FRz are:

i r* \

For Class 3 and 4 cross-sections:

f r' \ (8.3a)

Page 34 FABIG Technical Note -June 1999



(8.3b)

where

K = 1.0 (compression flange yielding at

= uIC lfy (tension flange yielding) the web-flange boundary)

(JIC

EP

gw

is the mean overall longitudinal stress over the area Ac[l,CF is the plastic overall longitudinal strain (minimum 0.2%) is the distance from the midline of the compression flange to the neutral axis of the whole section (positive towards the neutral axis)

Ac[l,cF - is the effective area of compression flange (inclusive of stiffener)

Acrr,cw is the effective area of both webs in the compression zone

b) Forces in the tension part of the web FR3 and tension flange FR4 are:


(8.4a)


(8.4b)

where

K = 1.0 (tension flange yielding)

ulf

h,

= uIT lfy (compression flange yielding) is the mean overall longitudinal stress over the area A , is the height of profile between system lines of flanges (Figure 5.1)

A , A ,

is the area of both webs in the tension zone is the area of the tension flange (inclusive of longitudinal stiffening)

= the compression force in the middle of the web that causes it to buckle

This expression is exact for cross-sections with fully effective webs. There will be a small error in FRz if the web is not fully effective due to the effect of modelling the force distribution as a continuous triangle as opposed to treating it as two discrete blocks either side of an ineffective length.

8.2 Moments and stresses arising from local loading

The moments and stresses arising from the local loads may be determined by a frame analysis of the transverse section or by the moment distribution method (see also the design examples in Appendix D). Typical moment and stress diagrams are shown in Figure 8.3 and 8.4.

M, I

M Ai

, p c M D

D

Figure 8.3 Moments arising from local bending

I I

I

.

B A !

I i %W

!E I ' uE

Figure 8.4 Axial stresses arising froq'J. 1 local bending

-

FABJG Technical Note - June 1999 m9a


4ny additional external asymmetric loads, such as :xplosion wind blowing across the profiled sheeting, ;hould also be taken into account in the calculation of .he moment and stress distribution.

Local effects rarely govern for unstiffened Class 1, ? or 3 sections but they are frequently a limiting ‘actor with stiffened Class 1, 2 and 3 sections and :lass 4 sections in general (see Section 6 for an :xplanation of section classification).

3.3 Verification of adequacy under local loading

3.3.1 Flange

1) At the web / flange boundary

)) At the middle of the flange

(8.7)

) Overall flange resistance check

pf-1 + IM,I 5 1.5 MPR, (8.8)

Jhere M,.,,, = moment resistance of the plate

” 4 ?

- -

is the design strength enhanced for strain rate effects (Section 3.4.4). is the thickness of the plate (for profiles with a Class 4 intermediate flange stiffener, the actual and not the reduced plate thickness should be used).

1.3.2 Web ) At the web I flange boundary

) in the middle third of the web:

(8.10)

Overall web resistance check

where Mp,Rd is defined in 8.3.1

For both web ands flange checks, the moments may be determined assuming a plastic moment distribution.

8.4 Buckling resistance under local loading

There are three primary buckling modes under local loading, as shown in Table 8.1. For the range of geometries typical of stainless steel blast walls, lateral torsional buckling is not a potential failure mode.

8.4.1 Instability check of web and flange

The following is a check against instability of the flange, web and a combination of the flange-web (trough) :

- + - fJ I s 5 1.0 h ’$Rd

(8.12)

Table 8.1 gives values for cr, M and buckling length, I for the three relevant buckling modes.

The buckling strength, fb is given by: f h = x f y (8.13)

(8.14) x = 1 / (4 + (02 - ;iy)

Q = 0.5 (1 + a (A. - ho) + T2) (8.15)

(8.16)

where i = radius of gyration = t 13.464

a = 0.49 and xo = 0.40 (no welding on plating in the buckling zone e.g. Type 2 stiffened pro fi le)

Q = 0.76 and 1, = 0.20 ( w e l d i n g o n plating in the buckling zone e.g. Type 3 stiffened profile)

age 36 FABlG Technical Note - June 1999


Table 8.1 Unity checks for buckling under local loading

(7 M

I (7A M A

(Jcw M c

Root mean Mi3 square stress value over 1

Mode

Flange

I

I

1

bP

Figure 8.5 Transverse trough stiffener arrangement to increase resistance to buckling due to local loading

8.4.2 Acceptance criteria for 8.5 Reduction factor on overall buckling due to local loading longitudinal moment

If any one or more of the unity checks is not satisfied, then the section is not adequate. The section may, however, be adequate for a reduced amount of plastic longitudinal strain ep (i.e. reduced crushing forces, Section 8.1.2). If the unity checks are not even then satisfied when E,, is equal to its minimum value of 0.2%, then the profile is unsuitable for the design pressure.

If the unity check for trough buckling is not satisfied, but the other two unity checks are, the section can be stiffened using transverse trough stiffeners as shown in Figure 8.5. Detailed analysis is required to establish the maximum spacing of these stiffeners.

resistance to account for cross-section flattening

The longitudinal moment resistance given by the expressions in Section 7.1 is reduced using a factor KF to take into account the flattening of the cross- section which occurs due to the local deformations of the flanges (Figure 8.6). These deflections may be determined in a transverse frame analysis. The effect is usually small, but needs to be taken into account.

Compression

Tension

Figure 0.6 Flattening of the cross-section due to local effects

FABIG Technical Note - June 1999 Paae 37


The reduction factor is given by: KFc is a constant based on the section type and

is the deflection at midspan of the midline of the tension flange relative to its edges (positive towards neutral axis), is the deflection at midspan of the midline of the compression flange relative to its edges (positive towards neutral axis), is the overall depth of the undistorted section, is the contribution of the flanges to overall effective section modulus W,,,. For Class 3 sections, Wc,f,y can be replaced by and for Class 1 and 2 sections by WP,.,.

Table 8.2 Reduction factor K,,

class: - For unstiffened Class I , 2 and 3 sections

- For unstiffened Class 4 sections

- For stiffened sections

K,, = 0.5

K,, = 0.5p

K,, = 0.6

and p is given in Sections 6.3 and 6.4.

8.6 Reduction factor on overall longitudinal moment resistance to account for coincident stresses arising from local effects

The longitudinal moment resistance given by the expressions in Section 7.1 is reduced using a factor KVM to take into account the degree the cross- section is utilised in withstanding local effects. Values and expressions for KVb, are given in Table 8.2.

Utilisation of flange to withstand bending due to local effects

1 .o

ihq + 1n.q 2 y 7 . R d

where ' 82 =

and hl, , M , and h4p,Rd are defined in Sections 8.2 and 8.3



9 METHODS FOR VERIFYING THE PLASTIC DEFLECTION LIMIT

9.1 Definition of plastic deflection limit

The plastic limit is the maximum deflection of a wall that can be sustained before the cross-section weakens in the region of maximum moment and consequently loses resistance. At the limit, the wall loses its ductility and fails rapidly. The reference point is normally taken as the point of maximum deflection, which is at mid-height for a vertical spanning simply-supported wall made from profiled sheeting.

Figures 9.1 and 9.2 show the two most common types of load-deflection curve for blast walls from profiled sheeting: Figure 9.1 applies to a Class 1 cross-section and Figure 9.2 to a Class 3 or 4 cross-section. The upper part of Figure 9.2 is curved partly due to material non-linearity and partly due to reducing effective width with increasing stress.

, Elastic deflection

Deflection

Class 1 cross-section

Figure 9.1 Load-deflection curve for Class 1 cross-section

Plastic deflection I , / l imit

Deflection

Class 3 or 4 cross-section

Figure 9.2 Load-deflection curve for Class 3 or 4 cross-section

Normally a wall which is deformed up to its plastic deflection limit in an explosion will have no further reserve of strength, i.e. a small increment in blast pressure compared to the design blast pressure will lead to grossly increased deflection or even detachment of the wall altogether.

9.2 Definition of ductility ratio The ductility ratio is the maximum deflection of the reference point divided by its deflection at the elastic limit. The allowable ductility ratio is the plastic deflection limit divided by the elastic deflection limit. The ductility ratio concept is inherent to the SDOF method of analysis developed in Reference 11, which simplifies the load- deflection relationship to a bi-linear curve (shown dotted in Figure 9.1). In general, the bi-linear line is drawn so that the area under it is the same as the area under the actual loaddeflection curve.

It should be noted that for walls with non-linear load-deflection curves, the elastic limit is hard to define; hence the linearization method should be confirmed by a time-domain analysis (for example, using a SDOF model).

9.3 Benefits of plastic deflection The benefit of the plastic deformation capacity of the wall in terms of increased resistance to blast pressure is dependent upon the parameter tdT where t, is the duration of an equivalent triangular impulse and T is the natural period of the structure.

In the manual SDOF method (see Section 4.3.2), the required resistance of the wall is the maximum applied pressure multiplied by the DLF. Figure 9.3 shows the relationship between DLF and r$T for a range of ductility ratios, ym/ye, where ym is the maximum deflection of the wall at midspan and yc, is the deflection at the elastic limit.

Figure 9.3 is applicable to isosceles triangle shaped impulses; for other triangular shapes DLFs, ductility ratios can be calculated according to References 6, 10 or 11.

In Figure 9.3, the benefit of utilizing a wall with a Class 1 cross-section is illustrated as follows. A wall with a f,lTvalue of 4.0 and a ductility ratio of 3.0 could be designed with a DLF of 0.83, whereas a wall with a Class 2, 3 or 4 cross-section would have to be designed for a DLF of 1.02. This means that the plastic (Class 1) wall would need a moment resistance 19% less than an elastic (Class 2, 3 or 4) wall.



DLF

0.1 0.25 0.5 0.75 1.0 1.5 2.0 3.0 5.0 10

t d /T Figure 9.3 Dynamic load factor versus td /T for an isosceles triangle impulse

Note: Figure 9.3 was developed from Figure 2.26 in Reference 11. It applies to walls with a linear elastic-plastic load-deflection curve.

Over 90% of installed stainless steel blast walls respond elastically to blast loading. They are usually lighter and therefore more economic than walls which respond plastically because it is difficult to obtain an economic section of sufficient depth whilst maintaining low enough blt ratios to ensure a plastic cross-section. Unless specifically requested, suppliers will not usually offer a client a plastic blast wall.

However, sometimes the reduction in DLF arising from allowing plastic deformation can outweigh the economic advantages of an elastic wall and can also lead to the incorporation of strength reserves that would not be available in elastic walls. Furthermore, plastic walls are much easier to upgrade in service than elastic walls because they have large strength reserves for local effects (Section 8). Elastic walls are often governed by their resistance to local effects; when this is the case, upgrades are much more difficult.

9.4 Failure modes and energy absorption capacity

To make a sensible estimate of the plastic deflection limit of a blast wall requires the identification of the primary failure mode.

Figure 4.3 shows a deformation pattern in the midspan zone of a Class 4 cross-section. It is not dissimilar to the deformation pattern of a Class 1 cross-section strained to beyond the plastic deflection limit. Figures 9.1 and 9.2 show typical

load-deflection curves for Class 1 and Class 3/4 cross-sections.

Sections which yield first on the tension side (in longitudinal bending), or which flatten prior to the onset of local buckling exhibit a more gradual loss of moment resistance with increased deflection. This can provide a measure of resistance beyond the plastic defection limit which is useful.

It is misleading to assess the response of blast walls in terms of their energy absorption capacity (area under the load deflection curve). Response should be determined in the time domain or by means of charts created in time domain analysis (References 10 and 11).

9.4.1 Membrane action and other effects of axial loading

Membrane action can occur in panels which have small aspect (width to span) ratios (Figure 9.4). When the boundaries parallel to the spanning direction are restrained against out-of-plane movement and stiffened to provide local axial compression resistance, membrane action develops in the span. This supplements the longitudinal moment resistance and replaces all or part of the resistance lost due to profile flattening or local buckling. Membrane action leads to a build-up of membrane tension which can cause a shift in the position of the neutral axis to the compression face and delay the onset of local buckling of the type shown in Figure 4.3.



Tests have shown that great resistance can be achieved with this form of construction. However, it is not usually practical to ensure the requisite boundary restraint in offshore blast walls.

A .I Main support

Main support \ Membrane tension at midspan Aspect ratio = A/B

Figure 9.4 Membrane action in panels with small aspwt ratios

9 .4 .2 Effect of loading rate on failure mode

High loading rate affects the failure mode in two ways:

If the load is applied for a very short time, some buckling modes may not have the time to form fully before the loading is removed or reduced below the buckling limit, Yield strength is affected by strain rate.

At the loading rates applicable to blast wall design, local buckling is unaffected by loading rate.

For stainless steel blast wall design from profiled sheeting, the most important buckling mode is local buckling. The effect of loading rate on local buckling has been investigated on cold formed stub column^"^). It is found that in the strain rate range lo4 to 1.0 s-*, the effective width and failure strength are not improved by increased speed of loading, other than the effect of strain rate on basic material strength. The cross-section effective widths determined in accordance with Section 6 of this guide are therefore deemed to be applicable to blast walls and no advantage can be taken of loading rate increasing the effective width.

The effect of high strain rates on yield strength should be taken into account (Section 3.4.4).

9.5 Cross-section class versus rotation capacity

The extent of rotation capacity is dependent upon the ratio WP,J Wc,.yr the shape of the material stress- strain curve and the compression strain in the extreme fibre at the point of maximum moment that can be sustained before moment resistance starts to fall.

The fibre strain level at which folding commences is higher than it is in an equivalent strength carbon steel due to the difference in the shape of the material stress-strain curves in the post-elastic region (stainless steel exhibits more strain hardening than carbon steel). The consequence is that, strength for strength, stainless steel corrugated walls are inherently more blast-resistant than carbon steel walls. Stainless steel also exhibits a higher elongation at fracture than carbon steel and therefore is more tolerant to stress-raisers in tension zones and the risk they present in terms of tensile rupture of the wall.

9.5 .1 Class 1 cross-sections

Class 1 cross-sections may be assumed to sustain plastic deflection but if ductility ratios in excess of 1.5 are required, one of the analytical methods outlined in Section 9.7 should be applied.

The basis for the 1.5 limit is as follows: the criterion governing Class 1 dimensions is that a continuously supported (or fixed-ended) beam conforming to Class 1 cross-section dimensions should be able to sustain plastic bending rotation at the supports until the full midspan bending moment resistance is reached. This applies only to materials with similar or better strain-hardeniiy characteristics than normal structural carbon steels and corresponds to a ductility ratio of 1.5. Materials with better strain hardening characteristics will be capable of sustaining higher ductility ratios and materials exhibiting less strain hardening will not sustain a ductility ratio of 1.5.

In practice it will be necessary to reduce b,,/f and s,/f ratios well below the limits given in Section 6 if high ductility ratios (say, > 3) are to be accepted.

9 . 5 . 2 Class 2, 3 and 4 cross- sections

In general, unstiffened and stiffened profiles where the resistance is governed by Class 2, 3 and 4

P = ~ P A 1 FABlG Technical Note - June 1999


elements in compression, do not exhibit any significant moment resistance beyond the elastic deflection limit. Blast walls using such sections should therefore be designed on an elastic basis.

However, Class 2, 3 and 4 cross-sections which yield in tension first are exceptions (this may be achieved by careful selection of dimensions or may occur as a result of coincident membrane tensile stresses). The moment resistance of such sections is then limited by flattening rather than by buckling. I t may be possible to demonstrate by non-linear finite element analysis that there is sufficient rotation capacity for plastic design.

9.6 Designing for rotation capacity

Before commencing analysis for plastic moment resistance, the following measures should be taken to of .

.

improve the inherent- plastic moment resistance the cross-section:

The section shape should be optimised with respect to transverse loading in Section 8, for example by reducing the bp/f ratios. The values of the plastic longitudinal strain E, in Section 8.1.2 should be at least 2% and preferably 4 - 5%.

I f ductility ratios above 1.5 are required, the width-to-thickness ratios of the cross section (bph and sJf) should be reduced beyond the requirements for Class 1 cross-sections by 10 - 20% or more.

9.7 Determination of the plastic deflection limit

This design guide describes three methods that can be used for determining the plastic deflection limit:

non-linear finite element -analysis,

hydraulic or pneumatic load testing of scale models,

explosion testing of scale models.

9.7.1 Non-linear finite element analysis

Non-linear finite element (FE) methods are a powerful way of analysing blast walls from profiled sheeting and can give accurate results when applied properly. Figure 4.3 shows the nature of a buckled zone in a Class 3 or 4 cross-section predicted by a

finite element analysis and the mesh refinement required for accurate prediction.

While non-linear FE analysis can lead to extremely accurate predictions of response and resistance, i t is unfortunate that simplifications made in the analysis, e.g. in meshing, tend to lead to buckling and failure modes being missed and hence there is a tendency towards over-prediction of strength and plastic deformation capacity. The degree of over- prediction can be very large. Proper use of a good program by suitably qualified analysts should eliminate such errors.

Blast walls generally have load-deflection curves that initially rise until the plastic deflection limit is reached; thereafter the load-deflection curve descends steeply (Figures 9.1 and 9.2). Non-linear FE models which involve inversion of a stiffness matrix at each time step cannot cope with falling load-deflection curves or multiple local instabilities and should not be used (these are called implicit non-linear FE analysis models). Whilst algorithms using implicit non-linear FE models to solve these types of problems exist in theory, in practice, they have not been developed to the point that they can be relied upon to produce valid results.

I t is therefore recommended that only expficir forms of non-linear FE analysis programs should be used.

In all cases, the particular version of the analytical model and its method of implementation should be validated against physical tests on similar structural elements with the same inherent failure modes, for example those reported by Malo and Ilstad(I3).

In principle, i t is, necesvry to limit element size to approximately one sixth to one eighth of the local buckling wave length. Where the general deformation pattern of the member does not itself lead to suitable destabilisation, it may be necessary to apply initial imperfections to ensure that buckling is initiated. These should simultaneously account for local buckling, buckling due to local effects, asymmetric and overall buckling modes; typical values should be U500 where )L is the half wave length of the buckle mode.

Initial imperfections do not always affect resistance and plastic deflection and it is furthermore not always clear what sort of imperfections would be critical. It is therefore usually best to study the effect of imperfections in a sensitivity study of the



basic non-linear FE analysis. In principle, symmetrically loaded symmetric structures require initial imperfections where asymmetric failure modes are a possibility.

Where stiffened sections are used, critical buckling modes are often asymmetric or interact with asymmetric ones so that the whole corrugation needs to be modelled. The model boundaries should in general be at the midpoint of the tension flange. Where the tension flange is on the pressure loaded side of the wall (as in continuous span sheeting), the validity of the solution should be confirmed by analysing a wall section comprising two or three corrugations. The number of elements required is typically in the range 4000-8000 for a whole corrugation.

A separate assessment of the deformation capacity of connections and welds should be performed.

Where penetrations are used i t will be necessary to analyse penetrated panels either by separate non- linear FE analysis or by manual methods in accordance with the recommendations in this guide.

The end connections should be modelled together with a sufficient extent of supporting structure to ensure correct representation of end restraint effects. I t is especially important that the modelling should not lead to an overestimate of membrane tension.

It is also important to ensure correct modelling of pressure loading on all horizontal surfaces of end plates as these minor loads can lead to axial compression in the section and overall instability at high deflections.

Where welding is performed on compression flanges and webs, or their boundaries, allowance should be made for residual stresses and the larger imperfections .

Specific guidelines for non-linear FE analysis of stainless steel blast walls from profiled sheeting

Analysis by non-linear FE analysis is usually an iterative process through a series of consecutive analyses in which the analytical model is developed. The series is terminated only when the model has been developed to the point where all potential critical failure modes are satisfactorily

identified and quantified in the analysis. TO achieve this it is usually necessary to evaluate response at loads beyond the design load until the ultimate collapse mode is identified. The final analysis is then carried out with the design loading.

For blast walls from profiled sheeting, the failure modes that specifically need to be checked and therefore identified in the analysis are:

buckling due to overall longitudinal bending (e.g. Figure 4.3)

symmetric web and flange failure modes (e.g. Table 8.1)

asymmetric trough buckling modes (e.g. Table 8.1)

web shear buckling at the supports (e.g. Section 7.5)

support failure modes (e.g. Section 7.5)

tensile rupture at holes and discontinuities in zones of high tensile strains.

The strain levels at which the above failure modes are initiated are highly dependent upon the actual material stress-strain curve in the strain hardening range. It is recommended to use the actual material stress-strain curve i n the analysis or an idealised stress-strain curve (e.8. Figure 3.5).

Mesh geometry simplifications may be made in specific regions of the structure and in respect of specific potential failure modes so long as other calculations and test data show that such specific modes could not apply at the stress and strain levels predicted to occur in those regions and for the material being used.

Membrane stresses can prevent the onset of buckling type failure modes (both in the analysis and in reality). The boundary restraints should be selected so that membrane tensile forces are not overestimated. The calculated boundary restraint forces should be summed and checked to ensure that boundary forces and deflections are representative of the actual structure.

The support structures should be subject to detailed analysis to demonstrate their resistance for the combination of imposed forces and strains. For this analysis it is important not to underestimate membrane forces.

FABIG Technical Note - June 1999 Pane 42


9.7.2 Hydraulic or pneumatic load testing of scale models

Tests can be carried out on a small-scale model, comprising typically three parallel corrugations with strain gauge readings being made 011 the middle corrugation. The long sides of the model must be free from translational restraint to prevent the build-up of membrane tensile stresses. Malo and Ilstad (Reference 13) give an example of a test method and results for a Class 4 profiled steel cross-section.

Such tests can be used to establish the relationship between longitudinal fibre strain and moment resistance up to the collapse load. One of the main parameters of interest to be determined from such a test is the longitudinal fibre strain in the compression flange at which the moment resistance starts to fall and cross-section instability occurs.

It is recommended to use an equal or slightly shorter span than in the prototype so that local effects are not underestimated. The stress-strain curve for the model and the test strain rate should be documented. Where the prototype has different dimensions from the test panel, a suitable calculation procedure should be developed to relate test results to the prototype. Care should be taken to account for both overall longitudinal and local effects.

Strain rates will usually be quite different in the test from those in the prototype. When the incrementing of load in a test is intermittent, the strain rate effects of the material will manifest themselves as periods of creep relaxation between load increments.

The recommendations in this guide should be used for aspects of design not specifically checked in the tests.

9.7.3 Explosion testing of scale

The results of an explosion test on a scale model of a blast wall are only applicable to the geometry and loading profile used in the test. When test results are to be applied to prototypes with different dimensions/loading/material characteristics, the test results should be used to validate a suitable and documented analysis technique so that the latter can be used for prototype design, for example, one based on this guide. To use scaling factors based on other criteria is not reliable.

models

A particular area to be addressed in the testing is the loading, both the peak test pressure and impulse duration. The linearization process should ensure that the actual impulse area for the real-time unfiltered signal is equal to or smaller than that of [he linearized impulse and that the rate of pressure rise is equal.

The effect of the actual material strength and strain rate in the test in relation to the specified strength of the prototype should be considered.

The recommendations in this guide should be used for aspects of design not specifically checked in the tests.

~



\ \ \ \

10 CONSTRUCTION DETAILS

t

10.1 Interfaces with support structures

The interfaces of blast walls with the supporting structure must have sufficient strength to transmit interface loads and plastic rotation capacity to sustain imposed deformations. Imposed deformations arise from:

Insulation and architectural liner where required

shortening of the wall due to midspan deflection,

imposed rotation of the ends of the wall,

relative movement of support structures due to loading applied directly to them.

// f I

I

I I

Where walls are fire-resisting, deformations will occur as a result of thermal expansion in fire, and the end fixing details should be configured to sustain the deformations imposed. Deformations are both axial (due to span shortening) and rotational as the wall may bow out towards the fire.

insulation and architectural liner

Figure 10.1

// f I

I I

.. , Top support girder

, Site weld

architectural liner Insulation and

where required

a)

As small increases in the explosion load can cause large increments in deflection, rotation and shortening, the interfaces should be derailed to ensure large reserves of rotational and displacement capacity.

Figures 10.1 to 10.4 show some typical details. See Figure 1.1 for a typical decking arrangement. The most critical of tul and t,, and tLl and I , should be used for determining (Mc,Rd)U and (Mc.Rd)L respectively in the effective span calculations in Section 7.2.

It is not usually practical to design end support details that can sustain substantial end moment fixity or in-plane membrane tension stresses. High restraint details can be designed but the difficulties during erection would usually outweigh any economic benefits of savings in wall material saved.

C )

Typical upper support details

FABlG Technical Note - June 1999 Paae 45


/ I I I I 1 I I

Insulation and /

/ liner where I

required I

ai chitectural I

I

Outline of brace behind wall

Insulation and architectural liner where reauired

Stainless steel

Figure 10.2 Strengthened upper support detail for high blast (e.g. 2 to 4 bar) applications

Insulation and architectural liner where

e Site weld

(a) (bl

Figure 10.3 Typical lower support details

weld



(nwlation and architectural liner where required

Outline of brace behind wall

A'- I I

I I

1 I 1

JL Figure 10.4 Strengthened lower support detail for high blast le.g. 2 to 4 bar) applications

10.2 Design requirements for the deck structures supporting blast walls

The economy of the overall structure is much enhanced if the deck framing layout is configured to accommodate the blast walls, especially in high blast situations (e.g. 2 - 4 bar). The wall strength is relatively insensitive to the layout of the lower deck but is i t is sensitive to the layout of the upper deck. The horizontal end reactions of the wall are substantial and this needs to be taken into account when configuring the support structure.

10.2.1 Top interface

Wherever possible, the top deck girders should be configured to run perpendicular to the wall (Figure 1.1). Otherwise the top support girder (running parallel to the wall) will be unable to sustain the horizontal top support reaction. In most situations details in Figure 10. I are suitable but in a high blast application, the plate thickness t , becomes exctxcive and a carbon steel fabricated angle and top plate to the wall can be more economic (Figure 10.2).

Where i t is not possible for the top deck girders to run perpendicular to the wall, the bottom flange of the top deck girder will need to be supported at suitably frequent intervals.

10.2.2 Bottom interface

The bottom interface of the wall has to transfer shear and vertical loading to the deck, The vertical loading arises from:

2) the vertical component of the support reaction at the top connection of the wall,

3) secondary loads due to the in-plane shear stiffness of the profiled wall (bulkhead action): these are dependent upon the vertical deflections (if any) of the support structure,

4) any net vertical component of applied blast loading.

--c

The largest of these effects is the reaction of the force element 2) and its value is sensitive to the relative deflection of the decks and the span shortening of the wall due to its midspan deflection.

Where the structural analysis of the interface area is performed by finite element methods, the analysis model should cover a horizontal length of wall greater or equal to the spacing of the deck girders that run perpendicular to the wal! arid should include sec.ondary loads arising from the vertical component of the support reaction at the top connection of the wall.

10.3 Avoidance of corrosion Corrosion at interfaces between carbon steel and stainless steel is a potential hazard. Painting of the carbon steel should be extended 50 mm onto the stainless steel surfaces. For fire-resisting applications, the paint system should not include zinc compounds. This is to avoid the risk of liquid zinc embrittlement of the stainless steel under fire condition^'^^).

In persistently wet situations where chloride ions are present, corrosion of stainless steel can be a risk at

1) the weight of the wall,

~~ ~~~~~~ ~~ ~~



crevice type details, e .g . non-continuous fillet welds, notch details etc.

Paint systems have limited life and can be damaged during installation. I t is necessary to detail interfaces and insulation systems such that dampness or water ponding cannot build up at interfaces and notch type details where crevice corrosion might occur. In offshore platforms, the openness of the structure to the weather, coupled with the occasional use of fire sprinklers, can lead to wetting of insulation and rising damp. The stainless steel/carbon steel interface should be external to the insulation or protected by non-perforated, all-welded liner. Figure 10.3(a) is not preferred where water can penetrate the insulation (e.g. perforated or non- welded liners).

10.4 Weld details Welded connections should be checked in accordance with Section 6.3 of ENV 1993-1-1 and ENV 1993-1-4.

Welds in locations where plastic straining would occur in explosion loading should be carefully detailed to ensure that the plastic straining is not concentrated in the weld itself.

Welds between carbon steel and high strength duplex stainless steel typically have weld metal which is less strong than the parent stainless steel; this factor should be taken into account when configuring the joint and assessing its plastic moment resistance.

Intermittent welds should be avoided in marine or potentially wet environments.

Wciding stainless steel requires use of the inert gas shield process. With butt welds, this must be on both sides for the root pass. It is essential to detail interface welds so that access for the back-gas is possible, otherwise there will be lack of penetration. For example, this can be a problem for the back- weld in Figure 10.1 (a) if the wall is erected with the liner already fitted.

10.5 Methods for splicing profiles end-to-end

End to end splices of profiled sections should be avoided where possible. Where they are unavoidable, they should be located sufficiently away from the point of maximum moment so that the moment transmitted through the joint during

plastic deformation of the wall is less than 85% of the moment resistance of the intact section.

With thin plates, i t is not usually possible to ensure sufficient alignment of butting plates to enable the use of simple butt joints and the sections have to be welded to a transverse plate through the wall as shown in Figure 10.5. The transverse plate should not be thinner than the abutting profiles, nor less than 5 mrn. The transverse plate should be stiff and strong enough to restrain the forces due to misalignment of profiled panels meeting at the plate. The connecting weld detail should be strength tested as part of welding procedure qualification.

6- - Splice plate

Figure 10.5 Method forjoining profiles end- to-end

Strength reduction can arise from a combination of misalignment at splices and from imperfections caused in nearby web and flange plating by the splice welds themselves. The latter cause a local reduction in effective width that can reduce strength and plastic moment resistance.

10.6 Longitudinal splices and stiffener plates

Longitudinal splices cause out-of-plane local deformations in the flange (or web) panel in which they occur. It is preferable to locate such splices in the tension flanges. Where they occur in webs or compression flanges, residual stresses due to welding may reduce the effective width of the element. In compression zones, overlapping plates at a splice contribute to the effective width when the splice is located within the effective width. This may compensate for loss of effective width due to welding residual stresses.



Side beam , Penetration zone , Penetration plate <-

Figure 10.6 Framing of penetrations (H frame)

\ 0 or C member

I Side beam

I Member , Penetration plate

i Figure 10.7 Framing of penetrations (Ring frame)

10.7 Penetration details While it is a general rule that penetrations through blast walls should be avoided where possible, they can be accommodated. In process arees, re-routing pipes beyond the ends of walls causes blockage of explosion venting areas and this can lead to increased explosion pressures; in some instances it is safer overall to accept penetrations through walls.

Penetrations for pipes, cable transits, blast resistant doors and windows should be framed and the framing analysed as a structure for the same loadings as the adjacent wall.

It is always recommended that the explosion load resistance of the penetration frame should be at least equal to the resistance of the unpenetrated wali.

Generally, a pipe sleeve welded into the wall, even when provided with a surrounding doubler plate, will not be sufficient to ensure that the wall is not weakened by the penetration. There exists no economic W q of reliably acalysing such penetrations, and generally they should be avoided by using penetration plates in a rectangular frame.

With a penetration plate arrangement, the momenf continuity in the wall can be assured in two alternative ways as shown in Figure 10.6 and 10.7.

The side beams in Figure 10.6 span the full height of the wall and the penetration plating spans horizontally onto these side beams. All platework and beams are normally stainless steel. The beams are usually cold formed profiles. For the door to maintain its integrity and operability after an explosion, it may be necessary to ensure that the side beams do not deflect plastically in the design explosion.



Figure 10.7 applies to simpler penetrations, generally suitable for walls with lower design pressures (< 0.5 bar). The longitudinal bending moment in the profile sheeting at the interface with the transverse frame members of the penetration frame is taken by torsion along them and then as moment through the longitudinal side members of the frame. The design moment at the profile sheeting interface is the moment that would occur in the profile if the penetration were not there.

This solution usually requires that the transverse frame members comprise box sections, usually made of two L or C sections welded together. The box depth should be equal to the profile depth to avoid weakness at the interface with the profile. In zones of maximum moment, stiffening gussets may be required to compensate for loss of continuity of the profile web through the penetration frame (Figure 10.7).

In walls with high blast loadings or with large numbers of penetrations, for example for whole pipe-racks, i t is preferable that the profiled wall be interrupted in these locations and replaced by a stiffened penetration plate supported by deck to deck side beams designed to withstand the blast loading (Figure 10.6). The penetration plate may be largely unstiffened if it has suitable beams all round its periphery, since it can then react blast loads by membrane action.

It should also be noted that welding of penetrations to profiles causes local out-of-plane distortions and residual stresses that will reduce the flange and web effective widths. This should be allowed for in the design, e.g. by making a 10% reduction in the effective width of compression elements affected by the welding.

Page 50 FABlG Technical Note - June 1999


I 1

1.

2.

3.

4.

5.

6.

7 .

8.

9.

10.

11.

12.

REFERENCES

ENV 1993-1-4 Eurocode 3 : Design of steel structures, Part 1.4: General rules and supplementary rules for stainless steels BSI, 1996

ENV 1993-1-1 Eurocode 3: Design of steel structures, Part 1.1 : General Rules and Rules for buildings BSI, 1993

ENV 1993-1-3 Eurocode 3: Design of steel structures, Part 1.3: General Rules, Supplementary rules for cold-formed thin-gauge members and sheeting BSI, 1996

JONES, N and BIRCH, R S Dynamic and static tensile tests on stainless steel University of Liverpool Impact Research Centre Confidential Repon to the Steel Construction Institute, March 1998.

CZUJKO, JOHANNESSEN & GROTH Material Characteristic & Strain Rate Effect in Duplex Stainless Steel World Duplex 97, Maastricht, October 1997

FIRE AND BLAST INFORMATION GROUP Explosion resistant design of offshore structures - Technical Note 4 The Steel Construction Institute, 1996

Elevated temperature properties of grade 3 16L stainless steel Confidential Contract Technical Note for The Steel Construction Institute from British Steel plc, Swinden Technology Centre, SL/PDE/CTN/S 12587/1/98/D, March 1998

Avesta Sheffield corrosion handbook for stainless steels Avesta Sheffield ABI 1994

PD 6484 Commentary on corrosion at bimetallic contacts and its alleviation British Standards Institution, 1979

Interim Guidance Notes for the Design and Protection of Topsides Structures against explosion and fire SCI-P-122, The Steel Construction Institute, 1991,

BIGGS, J, M Introduction to Structural Dynamics McGraw-Hill, 1964

CHI-LING PAN and WEI-WEN YU Mechanical properties of sheet steels and structural strength of cold formed stub columns affected by strain rate Fourth Pacific Structural Steel Conference, Vol 1 , Steel Structures, Pergamon Press, Singapore, October 1995



13. MALO, K A and ILSTAD, H Quasi-static response of corrugated thin-walled panel. Fourth international conference on computational plasticity fundamentals and applications, Barcelona, Spain, 1995.

14. SEDRIKS, A.J. Corrosion of Stainless Steels John Wiley and sons, Chichester

Page 52 FABlG Technical Note - June 1999


NOTATI 0 N

The notation adopted in this guide is in accordance with the Eurocodes and therefore in some cases differs from that adopted in previous SCI publications such as the Interim Guidance Notes and FABIG's Technical Notes.

Clear spacing between stiffeners (Section 7.5.1) Area Effective area Area of intermediate stiffener (Section 6.4) Width Width of plate in compression (Tables 6.2 and 6.3) Effective width of a Class 4 element Notional flat width of plane element (Figure 5.1) Width of stiffener Width of plate in tension (Tables 6.2 and 6.3) Width of outstand Width of outstand Dynamic Load Factor Young's modulus Buckling strength (Section 8.4.1) Shear buckling strength (Section 7.5.1) Nominal design strength Enhanced design strength for strain rate effects (Section 3.4.4) Crushing force (Section 8.1.2) distance from the midline of the compression flange to the neutral axis of the whole section (positive towards the neutral axis) distance from the midline of the compression flange to the neutral axis of the stiffener area A, (positive towards the neutral axis) Shear modulus Overall height Web height, measured between system lines of flanges Radius of gyration Section inertia Moment of inertia of intermediate stiffener Overall stiffness Reduced stiffness to account for end support rotation (Section 7.4.1)

Buckling factor for local buckling (Section 6) Buckling factor for shear buckling (Section 7.5.1) Factor (Section 8) Reduction factor on longitudinal moment resistance to account for flattening (Section 8.5) Load-mass factor (Section 7.4.2) Strain rate enhancement factor (Section 3.4.3) Reduction factor on longitudinal moment resistance to account for coincident stresses arising from local loads (Section 8.6) Buckling length (Section 8.4) Total span length Effective span length (Section 7.2j Design moment resistance Lower support moment resistance Upper support moment resistance Peak moment induced in wall Moment resistance of the plate (Section 8.3) Mass of wall profile Pitch of profiles PM,, DLF (Section 8.1.1) Specified peak explosion pressure Minimum specified 0.2% proof strength Minimum specified 1 .O% proof strength Minimum specified tensile strength, load resistance of wall Shear stress Internal bend radius Slant height of a web, measured parallel to the slope between midpoints of comers Plate thickness, time Duration of an equivalent triangular impulse Lower support plate thickness Explosion pressure rise time Thickness of welded stiffener Upper support plate thickness Natural period of the structure (Section 7.4.2) Shear force Shear buckling resistance (Section 7.5.1)

~~~ ~ ~~~~

... FABIG Technical Note - June 1999 I l l


Plastic shear resistance (Section 7.5.1) Shear resistance of a web (Section 7.5.1) Effective section modulus (Class 4 cross- sections) Elastic section modulus (Class 3 cross- sections) Plastic section modulus (Class 1 and 2 cross-sections) Midspan deflection of the wall at the elastic limit Peak midspan dynamic deflection (total elastic plus plastic deflection under explosion load) Ductility ratio, also denoted as p

deflection of flange arising from flattening of cross-section (Section 8.5)

0.5 235 E (Section 6)

Notation

Strain ‘Plastic longitudinal strain Post-yield strain rate Pre-yield strain rate Slenderness Plate slenderness Relative web slenderness (Section 7.5) Ductility ratio Poisson’s ratio Reduction factor Stress Maximum bending stress mobilised in the wall (Section 7.4.3)

ucom.Ed

OC,,

0 I C

0 0 . I

00.2

01.0

; X ‘p

Largest compressive stress in an element, calculated on the basis of the effective cross-section, when the resistance of the cross-section is reached Elastic critical buckling stress of an intermediate stiffener (Section 6.4) Mean longitudinal stress (Section 8) Measured 0.1 % proof strength Measured 0.2% proof strength Measured 1 .O% proof strength Measured tensile strength Web angle Reduction factor (for bucklins) Stress ratio

In accordance with Eurocode notation, the following convention for member axes has been adopted:

y-y axis parallel to the plane of the sheeting 2-2 axis perpendicular to the plane of the

sheeting a-a local axis of the cross-section of an

intermediate flange stiffener (parallel to the plane of the sheeting)

Note: Cross-section dimensions

Overall dimensions, including overall height A , internal bend radius r and other external dimensions denoted by symbols without subscripts are measured to the face of the material, unless stated otherwise.

Cross-sectional dimensions denoted by symbols with subscripts, such as hw or s,, are measured either to the midline of the material, the system line of the element or the midpoint of the corner, unless stated otherwise.

iV FABlG Technical Note - June 1999

Design Guide for Stainless Steel Blast Wall:

APPENDIX A Checklist of data for inclusion in enquiry documents for blast walls systems

The following information needs to be included in enquiry packages for stainless steel blast walls.

A. 1 General requirements 1. Plan drawings showing location of proposed blast walls and main structural elements of the decks

between which the walls are to span.

2. Space allocation for the wall, inclusive of any liner and insulation.

3. Sectional views showing main structure at top and bottom of blast walls.

4. Elevation drawings showing height of walls, locations and dimensions of door openings, pipe and cable penetrations (where known at the time of issue of enquiry documents).

5. Schedule of penetrations.

6. Any special requirements, e.g. panel widths.

A. 2 Structural requirements 1. Choice of structural materials.

2. Blast rating (from each side), including specified peak explosion pressure. impulse duration and rise time to peak or, where impulse is not triangular, the details of the impulse shape. Tolerance band on impulse duration (not less than +20%).

3. Allowable peak deflection in the design explosion.

4. Limits on deflection due to serviceability/meteorological wind loading.

5. Design wind gust speed.

6. Any other special structural requirements.

A.3 Architectural requirements 1.

2.

3.

4.

5.

6.

Fire rating (from each side) and any supplementary requirements on surface temperature rise (e.g. Norwegian HO (400) rating).

Atmospheric exposure (for each face), e.g. sea spray, weather and rain or internal.

Any special requirements on architectural finish, e.g. sound absorbent perforated liners.

Door types and blast rating.

Surface finish, where critical.

Deflection limitations at any specific service penetrations (if more stringent than items 3 or 4 in Section A.2)

FABIG Technical Note - June 1999 A- 1

Design Guide for Stainless Steel Blast Wall

APPENDIX B Strain rate effects

Table B.1 summarises the results of a programme of tensile tests at high strain rates on grade 1.4404 (316L), 1.4362 (2304) and 1.4462 (2205) (Reference 4).

The strength values in the table are mean strengths for samples of 4 mm thick cold rolled material measured in the longitudinal direction and produced by Avesta Sheffield.

Different strength values will be obtained for material from different suppliers or manufactured by differen processes.

FABIG Technical Note - June 1999 B- 1

Table B. I Strain rate enhancement on 0. 7, 0.2, 7.0 proof strengths and the ultimate tensile strength - Grade

- 1.4404 (316L)

0" (N/mm')

Er GL= 60mm (%)

(KSR)"

0.97

1 .oo

1.01

1.02

1.03

1.05

1.07

0.98

1 .oo

1.01

1.02

1.02

1.03

1.05

0.97

1 .oo

1.01

1.03

1.03

1.05

1.08

(JI.0 (NlKMl')

316

332

335

346

352

366

404

00.1 ( N / l l d )

269

287

29 1

304

31 1

327

372

1.38e-04

1.69e-03

2.50e-03

8.63e-03

1.78e-02

8.80e-02

7.42e + 00

0.93

0.99

1 .00

1.04

1.07

1.12

1.28

276

296

300

313

32 1

338

385

0.92

0.99

1 .00

1.04

1.07

1.13

1.28

0.94

0.99

1 .OO

1.03

1.05

1.09

1.21

597

615

619

628

632

644

658

58.7 2.770e-04

8.000e-03

1 S90e-02

9.630e-02

1.790e-01

1.700e+00

2.120e+01

2.77e-04

8.00e-03

1.66e-02

9.54e-02

1.82e-01

1.77e+00

1.67e + 01

49.3

50.3

50.0

51.0

52.7

1.38-04

9.90e-04

2 SOe-03

5.50e-03

1 . 1 1 e-02

1 .OOe-0 1

5.39e +00

525

536

543

549

555

572

604

0.97

0.99

1.00

1.01

1.02

1.05

1.11

548

562

572

58 1

588

613

656

0.96

0.98

1 .oo

1.02

1.03

1.07

1.15

615

626

634

64 1

647

666

700

0.97

0.99

1 .oo 1.01

1.02

1.05

1.10

739

754

758

766

769

779

790

36.0

28.0

26.0

29.7

29.0

30.7

1.4362 (2304)

~ ~~ ~

0.95

1 .oo

1 .oo

1.02

1.03

1.08

1.16

596

627

627

638

648

682

737

0.95

1 .oo

1 .oo

1.02

1.03

1.09

1.18

680

705

705

715

723

75 1

797

0.96

1 .oo

1 .oo

1.01

1.03

1.07

1.13

2.77e-04

8.00e-03

1.62e-02

9.49e-02

1.81e-01

1.76e+00

1.56e+01

813

84 1

847

862

867

887

905

34.3

29.0

29.3

30.0

30.0

28.3

1.4462 (2205)

-

1.38e-04

2.40e-03

2.50e-03

5.53e-03

1.12e-02

1.23e-01

6.48e+00

565

59 1

592

60 1

610

639

688

Design Guide for Stainless Steel Blast Wa

M2 = hi,

APPENDIX C Derivation of elastic critical buckling stress for stiffener in a Type 3 profile

i3 - E 12(1 - v2) $2

= 0.5 U bpi E

The critical buckling stress uCres for a stiffener is given in Section 4.3.1 of ENV 1993-1-3:

where

K = spring stiffness per unit length, as defined below I, = effective second moment of area of the stiffener (see Figure 6.1)

ENV 1993-1-3 gives:

U 6

K = -

where 6 is the deflection due to the unit load U (per unit length of stiffener)

For a Type 3 stiffened profile:

4 Moment diagragm

From the above moment diagram:

3 EI 2 EI

By inverting expression (2.4:

(C.2

FABlG Technical Note - June 1999 c- 1


U 6

K = - = 6 E I 1

$, +

M2 $2 $1

U

By substituting for M, from expression C.3 into C.5:

U 6

K = - = 6 E I

, 3 1

By substituting I = into expression C.6: 12 (1 - v2)

From expression C.l and setting v = 0.3:

This is expression 6.3b in Section 6.4.

c-2 FABIG Technical Note - June 1999

Design Guide for Stainless Steel Blast Wal

APPENDIX D Design examples

Example 1 is a Class 4 unstiffened profile.

Example 2 is a Class 4 stiffened profile (type 2).

FABIG Technical Note - June 1999 D- 1

Job No: OSH 348 The Steel Page 1 of 28 Rev A

Construction B\ Institute

Example 1 - Unstiffened Blast Wall

Job Title

Subject Example I - Unstiffened

Stainless Steel Blast Walls

Contents: Page

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 3441 623345 Fax: (01 3441 622944

CALCULATION SHEET

1. 2. 3.

4. 5. 6. 7. 8.

Client FABIG Made by AAC

Checked by RWB

Geometrical Properh'es 2/28 Material Properties 3/28 Cross-Section Classif cahon and Effective Section Properties 4/28 Overall Longitudinal Moment Resistance 10/28 Shear Resistance 15/28 Local Support Shear and D e f o m d o n Capacio 16/28 Local Effects 18/28 Reduction Factor on Longitudinal Moment Resistance 27/28

>. P. I. <.

centre line of flanges

: t t - 5

k P - 1200mm

f Deck plate = 8 mm

Material ProiJerties

Wall Grade = 1.4362 (AVESTA SAF2304) Mean measured u-.~ = 540 N / m d Standard Deviation on uo.t Cfrom the supplier) = 22.8 N l m d E = 200,000 N / m d

D-2

)ate Jun I999


Upper support Stainless Steel, grade 1.4362 (SAF 2304)

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01344) 623345 Fax: (01 344) 622944

CALCULATION SHEET

Lower support Carbon Steel, grade 355


Checked by RWB

Loading

Specific peak explosion pressure PMM = 50 kN/m2

Shape = isosceles triangle

Impulse duration t i Minimum = 0.064 s Maximum = 0.106 s

Proximity of adjacent equipment dictates a maximum midspan deflection of span/40 = 125mm

1. GEOMETRICAL. PROPER TIES

1.1 Influence of Rounded Comers

Comers can be assumed to be sharp if r s- 5t and r s 0.15bp

t = 5mm bp = 400mm

.: r 5 5 x 5 = 25mm and r 5 0.15 x 400 = 6Omm

.: assume all comers are sharp since r = 3t = 15mm

1.2 Dimensional Limit Check

Web slope: 45 O 5 4 5 90 O

4 = 56.31 O .: OK

Flat element connected dong both edges: bp lt < 400, s, lt < 400

5p = #Omm s, = 300/sin 56.31 O = 360.6mm

bp /t = 80 < 400 s, /t = 72 < 400 .: OK

late Jun 1999

Section 5.3.3

Section 5.2

D-3

Job No: OSH 348 The Steel

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01 344) 622944

CALCULATION SHEET

Page 3 of 28 Rev A

Unstiffened blast wall cross-section complies with dimensional limits

.-. design recommendations apply

2. MATERIAL PROPERTIES

Please note these strengths are provided by the manufacturer specifically for this example. For actual design based on manufacturers ' data, data on mean strength and standard deviation should be obtained from the supplier.

Stainless steel grade 1.4362 (A VESTA SAF 2304)

Mean q2 = 540 N/mm2 standard deviation = 22.8 N/mm2

For an exceedance probability of 90%:

f u ' mean q2 - (1.28 x standard deviation)

= 540 - (1.28 x 22.8) = 510.8 N/mm2

Assume this is a Class 3 or 4 cross-section

.: strain rate 4 = 0.02s"

Interpolate value for strain rate enhancement factor (KsR)o.2

(K,R)O.Z = 1.04

Enhanced design strength due to high strain rates

A= = f r (KsIJo.2

= 510.8 x 1.04 = 531.2N/md

D-4

)ate Jun 1999

~~~

Section 5.2

Section 3.4

Section 3.4.2

Table 3.5

Table 3.4

S :rion3.4.4

Equ. 3.1



Page 4 of 28 Rev A

CALCULATION SHEET

3 CROSS-SECTION CLASSIFICATION AND EFFECTIVE SECTION PROPER TIES

Internal elements of compression _flange

For Class 3, b i t 5 3 0 . 7 ~

0.5 235 E = [T 210,000]

= 0.649 235 531.2 21 0,000

b i t s -30 .7~ = 19.9

For this example b$t = 80 .: exceeds h i t of Class 3

.: Cross-section is Class 4

3.1 Effective Width of the Compression Flange

Internal compression element

+

bp

- - 531.2 N/mm2 0, = 0 2 = 4’

.I k, = 4.0

a,,,, - - 531.2 N / m d

Section 6.2

Table 6.1

Table 6.1

Table 6.2

Equ. 6.Ic

D-5



CALCULATION SHEET

Page 5 of 28 Rev A

= 2.169 531.2 X, = 1.052 400 J 5 200,000 x 4

[ 0.22) 1.0 - T

0.41 4

be8 = ~ b p = 0.414 x 400 = 165.6 min

531 .2N/mm2

+

3.2 Effective Width of the Web

Assume the trapezoidal section is an I-beam to calculate the effective widrh of the web.

3.2.1 1st iteradion

Internal compression element

Assume the web to be fully effective

I-beam web represents 2 inclined webs

thickness of I-beam web = 2thin0 = 12mm

)ate Jun 1999

Equ. 6.lb

Table 6.2

0-6

The Steel Construction Institute

Job No: OSH 348

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: 101 3441 622944

Page 6 of 28

CALCULATION SHEET

Subject Example 1 - Unstiffened

A , = 165.6 x 5 = 8 2 8 m d

A , = (200 4- 200 + 25) x 5

A, = 300 x 12 = 3600mm2

A = 828 -k 2125 + 3600 = 6 5 5 3 m d

take moments around the tension flange:

(828 x 300) + (3600 X ' 150) =

y = 120mm

Z = (828 x 180') + (2125 X 120')

= 2125 m d

6553

-

l2 30d + (3600 x 3 d ) + [ 12 i

= 26,830,000 -k 30,600,000 + 27,000,000 + 3,240,000

= 87,670,000 mm4

Effective section modulus:

Z 180.0

- wcrr.cF -

- - at top of web, a,

at bottom of web, a, =

= 487,000md

- - 731,000 mm3

= 531.2 N / m d A' 120

-0,x - 180

- 354.1 N / m d

L @ = - - - - 0.667 o > $42-1

0-1

0-7

Jun 1999

Table 6.2

Job No: OSH 348 The Steel ?age 7 of 28 Rev A

k, = 7.81 - 6.29 + 9.78 #

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01 3441 622944

CALCULATION SHEET

= 16.36


Checked by RWB

X, = 1.052 t

531.2 J 200,000 x 16.36 360.6 = 1.052 x -

5

= 0.968 > 0.673

p = 0.80

Effective widths of web:

- - b, = Pb, be, = 0.4 b, -

b, = 0.6 b, -

-

-

[ 1.0 - y] -

- .: p - h

P

- 0.80 x 180.0 -

57.6 mm

86.4 mm

144.0 mm

~~ 120

531 .2Nlmm1

354.1 Nlrnrn’

3.2.2 Td Iteration

Calculate new effective widths of web, based on position of N.A. given by the IH iteration.

0-8

late Jun 1999

Equ. 6.lc

Equ. 6 . lb

Table 6.2

Job No: OSH 348 Page 8 of 28

Job Title


Stainless Steel Blast Wdls The Steel Construction Institute


CALCULATION SHEET

Using the same procedure as for the I" iterQtion, the following values are re-calculated.

Y - - = 113.0 mm I -

Wefl/.cF = 442,000 mm3 WefJTF =

a, = 531.2 N/mm2 0 2

= - 0.604 kcl

= 1.004 > 0.673 .: p

Vew effective widths of web:

b, = 145.9 mm

: be, = 58.3 mm be,

Hence revised effective section of web is:

113.0 'i .2 Nlrnrn'

82,610,000 mm4

731,000 mm3

- 321.0 N/mm2

15.2

0.78

87.6 mm

j was 12Omm in I" iter.

Table 6.2

D-9

Job No: OSH 348 The Steel -

?age 9 of 28 Rev A

I I I


I CALCULATION SHEET I I Checked by RWB


3.2.3 3& Iterason

Calculade a further revised effective section of web based on pos&ion of N.A. from 2& iteration.

/ 21 25 mm'

Using the same procedure as for the I" iteration, the following values are re-caiculated.

Y = 112 mm I = 82,180,000 mm4

Wc/r.c- = 437,000 m d Wc//.TF = 733,000 mm3

0 1 = 531.2 N / m d 0 2 - - - 316.9 N / m d

@ = - 0.596 k o = 14.9

x, = 1.013 > 0.673

.: p = 0.77 compare with 2"d iteration, negligible difference

.:

-

Effective section is as follows:

82.8 234.4 02.8

/

212.5 1 3 4 . 6 1 b L 2 12.5

was I13mm in 2"6 iter.

D-10

Job No: OSH 348 Page 10 of 28 Rev A

Job litle

Subject Example 1 - Unstiffened Stainless .%eel Blast walk SE 1



CALCULATION SHEET

4. OVERALL LONGITUDINAL MOMENT RESISTANCE

P

W@, = W e J p = 437,000md

p = I200mm

Assume for this example, KF = KvM = 0.98

- 437,000 x 531.2 x 0.98 x 0.98 1200 *' Mr.Rd -

= 185,700 Nmm/mm width

4.1 Effective Span

4.1.1 Lower support (11 mm thick plate)

Carbon steel grade 355 4 = 355 N/mm2

From example I in FABIG Technical Note 4, for grade 355, in view of the imposed out-of-plane deformation of the plaie under blast loading, the ductility ratio of the lower support plate will exceed 2.0 and so an enhancement factor of 1.17 can be assumed.

.: Enhancement factor = 1.17

6' = 1.17 x f u = 415.4N/mrd

t, = I1 mm

= 12,600 Nmm/mm width

Date Jun 1999

Date Jun 1999

Section 7.1

Equ. 7.3

FABIG Technical

Note 4, Ex.1

Equ. 7.6a

D-1 1

Job No: OSH 348 Page 11 of 28 The Steel

Silwood Park, Ascot, Berks SL5 7QN Telephone: I01 344) 623345 Fax: I01 344) 622944

CALCULATION SHEET

Rev A

4.1.2 Upper support (8 mm thick plate)

Stainless steel grade 1.4362 (SAF 2304)

Refer to Page 3/28 (for 5 mm thick material)

Thickness of plaie is 8mm .: reduce& for 5mm thickness by 5%

& = 510.8 x 0.95 = 485.3 N / m d

Plastic section modulus and plastic deflection

.:

Adopt 0.2 % proof strength

Interpolate value for (KsR)o.2

(KSR)O.t = 1.084

f,' = 485.3 x 1.084 = 526.1 N/mm2

Strain rate = 1.0 s-'

= 8418 Nmm/mrn width

4.2 Effective Length

185,700 185,700 + (0.5 x 12,600) + (0.5 x 8418)

= 5000 4 = 4864mm

Page 3/28

Table 3.5

Table 3.4

Equ. 7.6b

Equ. 7.4

0-1 2

IJobNo: o s H 3 4 8 I Page 12 of 28 I Rev A 1 The Steel Construction ~ o b Title Stainless Steel Blast Walls Institute

Subject Example I - Unstiffened Silwood Park, Ascot, Berks SL5 70N I Telephone: (01344) 623345 Fax: (01344) 622944

CALCULATION SHEET Checked by RWB I I

- 1 4864

2 [{T 1 85, 700

L, [J- Mc. Rd - 2

4864

2 ' [ I

- - 185,700

I +

Resistance of the W d l

54.5 mm

81.2 mm

384 EI k = 5 LE P

- 384 x 200,000 x 82,180,000 5 x (4864y x 1200

-

= 9.141 N / m d

Reduced stinness (allowing for support bending)

Equ. 7.5a

Equ. 7.5b

Section 7.3

Equ. 7.7

Section 7.4.1

Equ. 7.8

Equ. 7.9

D-13


Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01344) 622944 Client FABZG

CALCULATION SHEET

Page 13 of 28 Rev A

- 9.141 - 1.6 (81.2 + 54.5)

4864 I +

= 8.750 N / m d

4.5 Natural Period

Made by AAC

Checked by RWB

Mass, M = wall -k liner and insulation

Assume liner and insulaiion = 20 k g / d

.: Mass of liner and insulation = 20 x A = = 117kg

20 x 1200 x 4864 X 1p6

Wall = Volume x Density

Volume

Density

Mass, it

= (25 + 400 + 360.6 + 400 + 360.6) t x LE x l@9 = 1546.2 x 5 x 4864 X lQ9 = 0.0376 m3

= 7800 kg/m3

= (0.0376 x 7800) + 117 = 410 kg

- L E > 0.9 .: KLM = 0.78 L

= 0.035 s T = 2 x 4 410 x 0.78

1.2 x 8.750 x 106

0-14

late Jun 1999

Section 7.4.2

Equ. 7.10

Table 3.7

Section 7.4.2

Equ. 7.10


Silwood Park, Ascot, Berks SL5 70N Telephone: (01 344) 623345 Fax: (01 344) 622944

CALCULATION SHEET

Page 14 of 28 Rev A

4.6 Dynamic Load Factor

R m = 305.4 N/mm width

P- = 50kN/m2

305.4 x Id 50 x Id x 4.864

( D L F ) R =

tdk,, = 0.064s td- = 0.106s

Assuming the response is elastic

= 1.8 td min - 0.064 T 0.035

- - -

LE

= 1.26

= 4.864m

.: worst case ( D W E = 1.20

( D W R ’ ( D w E .: wall response is elastic and the moment resistance of section is adequate.

Date Jun 1999

Date Jun 1999 ~ ~ ~~

Section 7.4.3

Equ. 7.11

Equ. 7-11

Fig 4.2

Fig 4.4

Section 7.4.3

D-15


1.2 = 531.2 x - = 505.9 N/mm2

1.26 c -

%Ax -

Silwood Park, Ascot, Berks SL5 7QN Telephone: 101 344) 623345 Fax: (01 344) 622944

CALCULATION SHEET

= 33mm - - ‘MAX ( D L F ) ~ L~ - - 0.05 x 1.2 x 4864 8.750 Y,

kR


Checked by RWB

The limit on deflection is 125mm .: OK

5. SHEAR RESISTANCE

V M u = 0.5 P M A x DLF Ls

PMu = 0.05 N/mm2 (DLF), = 1.2

Upper support is more critical than the lower

L E 4864 - + L , -50 = - + 54.5 - 5 0 = 2437 mm 2 2

.: L, =

V,, = 0.5 X 0.05 x 1.2 x 2437

= 73.1 N/mm

V M A X p q . = 2 sw sin4 t

- 73.1 x 1200 - 2 x 360.6 x sin56.31 x 5 4

= 29.2N/md

17.3 E = 17.3 X 0.649 = 11.2

- - - 360.6 = 72.1 d 17.3 E sw

t 5 -

.: necessary to verify Vb,Rd

Equ. 7.12

Equ. 7.13

Section 7.5

Equ. 7.16

Page 14/28

Page 12/28

Equ. 7.17

Page 4/28

Section 7.5.1

D-16


No intenned&e transverse stiffeners

Silwood Park, Ascot, Berks SL5 70N Telephone: (01 344) 623345 Fax: (01 344) 622944

CALCULATION SHEET

531.2 J--- 5.34 x 200,000 - 0.8 x 360.6 -

5 X W

Client FABIG Made by AAC Checked by RWB

X U = 1.29 > 0.6

*’ f b r = [l - 0.42 > w J [ 5) = [l - (0.42 x 1.29)J - - E2) -

‘b,Rd = s w t f b ~ = 506,600 N

.: k, = 5.34

- - I .29

140.5 N/mm2

= 507 kN

Total shear load (shared between 2 webs)

6.

6.1 Lower Support Detail Check (Figure I0.3a)

LOCAL. SUPPORT SHEAR AND DEFORMATION CAPACITY

1

~ ~~~

Equ. 7.18

Table 7.1

Table 7.2

Equ. 7.20

Section 7.5.2

D-17


Silwood Park, Ascot, Berks SL5 7 Q N Telephone: (01 344) 623345 Fax: (01 344) 6 2 2 9 4 4

CALCULATION SHEET

Page 17 of 28 Rev A

Check Point 1

Plastic hinge location

(Mc.R,JL = 12,600 Nmm/mm

Check Point 2

Deck plate t = 8 mm

t 2 s2 - x 4' 4 4

= - x 355 x 1.17 Mc.Rd = = 6646 Nrnm/mm

(Mc.RdL Moment at Check Point 2 = 2

= 6300 Nmm/mm < Mc.Rd .: OK

Check Point 3

t 2 s2 - x 4' = - x 415.4 = 6646 Nmm/mm 4 4 Mc.Rd =

33.8 33 8 = (Mc-RJL x - = 12,600 X -

LL 81.2 Moment at Check Point 3

= 5245 Nmm/mm < Mc.Rd .-. OK

6.2 Upper Support Detail Check (Figure lO.la)

0-1 8

late Jun 1999 ____

l a t e Jun 1999

Page 10/28


Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01344) 622944

Page 18 of 28 Rev A

CALCULATION SHEET

Client FABIG

Check Point 1

Plustic hinge location

Check Point 2

Made by AAC

Checked by RWB

.: OK

- 62 4

Mc.Rd - - x 531.2 = 4781 Nmm/mrn

7. LOCAL. EFFECTS

7.1 External Forces

- - @ W E = 1.2 PMAX -

P = 1.2 x 0.05 = O.O6N/mrd

7.2 Internal Forces

h FR1 h

0.05 N / m d

Page 11/28

Section 8.1.1

Page 14/28

Section 8.1.2

D-19


Compression members

I

Compression flange yielding .-. K = I

EP = 0.2%

A,CF - -


CALCULATION SHEET

g, = 188mm

.: FR, = 1.0 X 531.2

._

AAC Client FABIG Made by

Checked by RWB

533.2 0.2 200,000 I00

+ -

I88 828

828 m d

= 10.89 N/mm length

Unstiffened profile .: FRI is distributed uniformly over the whole length of the compression flange, 400mm, to produce the muximum moment distribution.

A,, = ((70.07 x 5) + (106.48 x 5)) x 2 = I 7 6 6 m d

I766 .: FR2 = 4

= 5.8I N/mm

Class 4 cross-section .-. distribution of FR2 is triangular over the whole !ength of the compression part of the web, 225.95mm, to produce the lnarimum moment dstrlbution.

Equ. 8.2

Page 9/28

Section 8. I.2

Equ. 8.3a

Page 9128

Page 9/28

Section 8.1.2 Page 9/28

0-20


Job Title

Subject Example I - Unstiffened Skuhless Steel Blast Walk


Fax: (01344) 622944 mi FABIG

CALCULATION SHEET I

AAC Made by

Checked by RWB

Tension members

4 \hw -gw

OIT = a, = - 316.9 N/mm2

A , = 134.61 x 5 x 2 = 1346mm2

0.2 + - 531.2 (-0.597)' x 531.2 200,000 100

300 - 188 . :Fm =

4

= 2.65 N/mm length

I346

Cross-section is Class 4 .: Distribution of FR1 is triangular over the tension part of the web, 134.6mm

\ h w - g w

A , = 425 x 5 =

ATF

2125 mm2

-: FKd = (- 0.597) x (- 316.9)

= 16.71 N/mm length

0.2 200,000 100

300 - 188

f- 531.2

2125

FR4 is distributed over the whole lL.:gth of the tension flange, 400mm

Equ. 8 . k

Page 9/28

Page 9/28

Equ. 8.5

Page 9/28

0-2 1



C ALC U LATlO N SHEET

Page 21 of 28 Rev A

Internal Forces (N/mm length)

10.89 Nlmm - 5.81 Nlmm *

;t r' -+.

2.65 Nlmm

16.71 Nlmm 2

k 200 200 4

Check - These forces should balance

+ F m =- 10'89 + 5.81 = 11.26 FRI - 2 2

+ F R 3 =- 16.71 + 2.65 = 11.01 FR4 - 2 2

FR4 2 + F m = - 2 + FR3

FRI - .: OK

7.3 Calculation of Moments and Stresses arising from Local Loading (external (7.1) and internal forces (7.2))

For this example, the package QSE was used to carry out the frame znalysis. The i n p u and ouout details are m c h e d at the end of this m p l e . The following model was analysed:

D-22

late Jun I999

late Jun I999

Section 8.1.2

JO~I NO: OSH 348 lPage 22 of 28 lRev A

J o b m e Stainless Steel Blast Walls



Silwood Park, Ascot, Berks SL5 7QN Telephone: 101 344) 623345 Fax: I01 344) 622944 Client FABIG

CALCULATION SHEET

Made by AAC Checked by RWB

A strip of wall was modelled with the support conditions shown above.

The external loading applied to the frame model is transmitted to the remainder of the wall via web shear, .: the vertical component of this web shear should equal the vertical component of the external load.

Note: The web load is adjusted to include any imbalance in the intenial loads.

Y-comp of web shear = vertical comp. of external + internal load

= (0.06 X 600) + (11.26 - 11.01)

= 36.25 N/mm

Web shear load 36.25 = 43.57 N/mm - - sin56. 31 O

The results from the frame analysis are as follows:

D-23

Job No: OSf? 348 The Steel

Silwood Park, Ascot, Berks SL5 7QN Telephone: (013441 623345 Fax: (01344) 622944

CALCULATION SHEET

Page 23 of 28 Rev A

Moment diagram (Nmm/mm length)

674

28

Axiul Stress Diagram (Nlmm2)

6.740 /

Displacement Diagram (mm)

.t. 0.355

7.4 F h g e Checks

t 2 * s2 4 y 4

Mp.Rd = - f = - x 531.2 = 3320 N/mm/mm

D-24

Figure 8.3

Figure 8.4

Section 8.3.1


Job No: OSH 348 Page 24 of 28


Rev A

CALCU LATl ON SHEET

- + - la,' 5 1.0 l M B l

Mp.Rd f Y *

1070 5.980 3320 531.2

i - = 0.33 < 1.0

- + - 1% I Mp.Rd 4' 674 5.980 - f - = 0.21 < 1.0

3320 531.2

5 1.0 I MBI I uBWl - f -

Mp. Rd 4' 1070 6.219 3320 531.2

+ - = 0.33 < 1.0

.: OK

.: OK

.-. OK

.: OK

i; 1.0 lMcl I <JmI

Mp.Rd fY'

- + -

.-. OK 369 7.180 3320 531.2

+ - = 0.12 < I.0

IMB fMol + IMC I Mp.Rd 2

Io70 + 340 + 369 = 1074 < 1.5 MpSRd .: OK 2

.D-25

~ ~~

late Jun 1999

late Jun 1999

Equ. 8.6

Equ. 8.7

Equ. 8.8

Section 8.3.2

Equ. 8.9

Equ. 8.10

Equ. 8.11



CALCULATION SHEET

~

Page 25 of 28 Rev A

7.6 Insrcrbility Check of Web and Flange

7.6.1 Flange check

400 mm - I = bp -

u = 0, = 5.980 N / m d

M = M * - - 674 Nmm/mm

No welding in bucWing zone

..

i

x

V

x

4

X

a = 0.49

t 3.464

- - -

- I 1 - - - i rq

= 0.3

lo = 0.40

= 1.443mm 5 3.464

- - -

- - - 400 1 J ( I 0 . 3 ’ )

1.443 r 200,000

= 4.34

= 0.5 (1 + 0.49 (4.34 - 0.4) + 4 . 3 4 10.88 - -

)ate JUIZ 1999

late Jun 1999

Section 8.4.1

Equ. 8.12

Table 8.1

Equ. 8.16

Equ. 8.15

Equ. 8.14

0-26

SF The Steel Construction Institute


Job Title

Subject Example 1 - Unstiffened StaideSS Steel Blast walk 1

I t


CALCULATION SHEET I IChecked by RWB


= 0.048 < 1.0 1 10.88 + (10.882 - 4.342)0.5

- -

fb = Xf,' = 0.048 x 531.2 = 25.5 N . m d

5.980 1.5 x 674 = o.54 ~

25.5 3320 - +

7.6.2 Web check

- - 360.6 mm I = s w

o = ocw - - 7.180 N/mm2

M = M C - - 369 Nmmlmm

531.2 (1 - 0.3') - - 1.443 x 200,000

4 = 0.5 (1 + 0.49 (3.91 - 0.4) + 3.912)

3.91

9.00 - -

0.058 < 1.0 - - 1 9 + (92 - 3.912)0.5

fb = 0.058 X 531.2 = 30.8 N / m d

x =

7.180 1.5 x 369 = o.40 ~

30.8 3320 - +

7.6.3 Trough check

400 1 = 5 + 0.85 sw = - + (0.85 x 360.6) = 506.5 mm 2 2

.: OK

2 2 2 = 4 uA %W -+ OCW

3

0-27

Equ. 8.13

Equ. 8.12

Table 8.1

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8.13

Equ. 8.12

Table 8.1

Job No: OsH 348 The Steel Page 27 of 28 Rev A

5.98d + 6.2192 + 7.18d = 6.48 N , , m 2 = J 3


C ALCU LATl ON SHEET

M = MB = 1070 Nmm/mm length


Checked by RWB

506.5 1 531.2 (1 - 0.32) - 1.443 n 200 000

x = - - J -

4 = 0.5 (1 + 0.49 (5.49 - 0.4) + 5.49')

- - 1 16.82 + (16.822 - 5.49')'-'

x =

f b = 0.031 x 531.2 = 16.47N/mm2

6.48 1.5 x 1070 = o.88 < - + 16.47 3320

5.49

- - 16.82

0.031 < 1.0

8. REDUCTION FACTOR ON LONGITUDINAL MOMENT RESISTANCE

8.1 KF

Using displacement results obtained from the frame analysis, the deflections of the jlanges at midspan relative to their edges are as follows:

0.338

4 = 0.338 mm 6, = 3.835 mm

h = 305mm t = 5 m m

.: OK

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8.13

Equ. 8.12

Section 8.5

Figure 8.8

Page 23/28

Job No: OSH 348 Page 28 of 28 The Steel Rev A

Wefly = 437,000 mm'

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01344) 62294.4

CALCULATION SHEET

- - 53) +(a28 x 18g2) + (425 53) +(2125 x 112) 12 12 Ifl


Checked by RWB

= 1725 + 29,264,832 -k 4427 + 26,656,000

= 55,930,000 mm4

KFC = * 0.5-p for unstiffened Class 4 sections

= 0.5 X 0.77 = 0.385

1 (0.5 x 0.338) + (0.385 x 3.835) 305 - 5

= 1 - 437,000

= 0.996

8.2 KvM

MA = 674Nrnrn/mrn MB = 1070 Nmm/mm

MPqRd = 3320 Nmm/mm

IMA I + IMB I = 674 + 1070 = I744

0.8 MPeM = 0.8 x 3320 = 2656 Nmm/mm

IMA 1 -k IMB I < o*8Mp.Rd

On page 10/28, assumed KF = K , = 0.98

.: KvM = 1.0

KF = 0.996 > 0.98 and KvM = 1.0 > 0.98 -: OK

late Jun 1999

Page 9/28

Page 9/28

Equ. 8.17

Section 8.6

Page 23/28

Table 8.2

Job No

osh3485

iClh FABlG

Sheel No ReV

2

I File UNSTIFF.PSA

1 2

I Datflme 07-Mav-199914

(kN/mrn2) (kN/rnm') (kg/m3 (xlOd/'C) Steel 200.000 7.aE 3 12.000 Concrete 1 o.Oo0 2.4E 3 1O.OOO

Materials

(kNlmm) (kN/mm) (kNlmm) (kNdrad) (kNmlrad) 1 Fixed Fixed Fixed

I Mat I Name I E I G I V I Density I a I

(kNrnlrad)

Type Basic Name

I I 4

4 1 Fixed 1 i I I Fixed I I

I I

Dead I DL1 lextemal I I Dead I DL2 I internal I I Dead I DL3 lweb I

Combination Load Cases

Rinl T o e : 66107/1999 1590 QSE Space for Windows Version 2.20

Sdhvae kansed lo STEEL CONSTRVCTlON INSTlTLCTE

M T l t l e Stainless Steel Blast W a l l s

c'leni FABlG

Loadings For Moment loads Wa = Moment kNm, for Settlements Wa = Distance (mm) or Rotation (rad). Temperature loads

Job No shes No Rev

osh3485 3 P M

Re' E x a m p i e 1 - Unstrffened Profile

By AAC Oa*May 99 cM RWB

File UNSTIFF PSA I Daiefrlme 07-Mav-1999 14 03

Wa = T (C). Lack of Fit

Node Displacements

Element End Forces

W R u n 3 d 3 Rin( Tmna'DaIe: 06107/1999 1520 QSE Space for Windom Version 2.20

IJob No: OSH348 IPage 1 of 27 [Rev A The Steel Construction JobTitle Stainless Steel Blast walk Institute

Subject Example 2 - Stiffened Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (01 344) 622944

CALCU LATlO N SHEET


Checked by RWB

Example 2 - Stiffened Blast Wall

Contents:

I . Geometrical Propetties 2. Material Properties 3.

4. Overall Longitudinal Moment Resistance 5. Shear Resistance 6. 7. Local Effects 8.

Cross-Section Classification and Effective Section Properties

Local Support Shear and Deformation Capacity

Reduction Factor on Longitudinal Moment Resistance

Page

2/2 7 3/2 7

3/27 9/27

I4/2 7 I5/2 7 17/27 26/2 7

215 I 135 350 135 215 ./ \ / <. c F-+f = I = 1 - 9

entre line 130 x 130 x 5 - - - - -L - x 900 stiffener

I

! P = 1050rnrn Overlap = 25 m r n 4

IAX

Material ProDetties

Wall Grade = 1.4362 (AVESTA SAF2304) Mean measured u-.~ = 540 N / m d Standard Deviation on uOq2 Cfrom the supplier) = 22.8 N / m d E = 200,000 N / m d

)ate Jun I999

late Jun I999

0-33

Job No: OSH 348 The S t e e l

I Construction \\\ lJob Title Stainless Steel Blast walls Page 2 of 27 Rev A

Institute // Subject Example 2 - Stiffened


CALCULATION SHEET

Client FABIG Made by AAC Checked by RWB

Upper support Stainless Steel, grade 1.4362 (SAF 2304)

Lower support Carbon Steel, grade 355

Loading

Specijtc peak explosion pressure PAux = 80 k N / d

Shape = isosceles triangle

Impulse duration td = 0.06 s

ProximiQ of adjacent equipment dictates a maximum midspan deflection of span/40 = 105mm

1. GEOMETRICAL PROPERTIES

1.1 Influence of Rounded Comers

t = 5 m m

.: r s 5t

.: assume all sharp comers

r = 3t = 15mm

r s 0.15 bp = 52.5 mm

bp = 350 mm

1.2 Dimensional Limit Check

Web slope Q = 56 O .: 4 5 " s Q 1~90"

Flat element connected along both edges

bp = 350 mm s, = 2OO/sin 56.0 O = 241.3 mm

b i t = 70 < 400 5 = 48 < 400 t

Cross-section complies with dimensional limz&

.: design recommenciarions apply

.: OK

.: OK

Section 5.3.3

Section 5.2

Section 5.2

0-34


Job No: OSH 348

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: (013441 622944

Page 3 of 27 Rev A

CALCULATION SHEET

Client FABIG Made by AAC Date Jun 1999

Checked by RWB Date Jun 1999

Subject Example 2 - Stiffened

2. MATERlAL PROPERTIES

Please note these strengths are provided by the manufacturer specifically for this example. For actual design based on manufacturers' data, data on mean strength and standard deviation should be obtained from the supplier.

Stainless steel grade 1.4362 (AVESTA SAF 2304)

Mean o--.~ = 540 N / m d standard deviation = 22.8 N/mm2

For an exceedance probability of 90%:

fy = mean 00.2 - (1.28 x standard deviation)

= 540 - (1.28 x 22.8) = 510.8 N/mm2

Assume this is a Class 3 or 4 cross-section

.: strain rate 5 = O.02s-I

Interpolate value for strain rate enhancement factor (KsR)o.2

(KsJ0.2 = 1.04

Enhanced design strength due to high strain rates

A' = fy (KsJ0.2

= 510.8 x 1.04 = 531.2 N / m d

3 CROSS-SECTION CLASSIFICATION AND EFFECTIVE SECTION PROPERTIES

Internal element of compression flange

E = 0.649

bp = 350mm t = 5 m m

For Class 3, b/t s 3 0 . 7 ~ = 19.9

Section 3.4

Section 3.4.2

Table 3.5

Table 3.4

Section 3.4.4

Equ. 3.1

Section 6.2

Table 6.1

Ex. I

0-35



CALCULATION SHEET

Page 4 of 27 Rev A

For this example bdt = 70 .: exceeds limit of Class 3

.: Cross-section is Class 4

3.1 Effective Width of the Compression Flange

350 BJ

83.1 183.8 83.1 / -. .I/

- 1 -

260

3.2 Compression Flange

3.2. I Determine trial effective cross-section

bPI = 83.1 mm

0 1 = A' = 531.2 N / m d = a,

a,,,, = 531.2 N l m d

.: k, = 4.0

= 0.451 531.2 2, = 1.052 X - 5 200,000 x 4

0-36

~~

Section 6.4

Section 6.4 Step (la)

Figure 6.1b

Equ. 6 . l c


Client FABIG

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 3441 623345 Fax: (01 344) 622944 Made by AAC

Checked by RWB CALCULATION SHEET

L T i t l e Stainless Steel B h t Walls

Subject Example 2 - Stiffened r- 2, < 0.673 .: p = 1.0

ben = ~ b p 1 = 1.0 x 83.1 mm =

- be, = 0.5 b, -

41.55 I 41.55 ./ I r , .

+

183.8 mm

41.55 mm

I 531.2 1.052 x - 18:.8 11 200,000 x 4

[ 1.0 - -=) = 0.782

0.996

0.782 x 183.8 = 143.7 mm

O.Sb, = 71.85 mm

83.1 rnm

= 0.996 > 0.673

41.5S1.55 71.85 40.1 71.85 41.531.55

5 W

260

For Type 3 profle A, = 2 t (beI + be j + t, b,

A, = 2 x 5 (41.55 + 71.85) + (5 x 260) = 2434 m d

0-37

Date Jun I999 I

Equ. 6.Ia

Table 6.2

Equ. 6.lb

Step (lb) Figure 6.lb

Equ. 6.2b


‘ J O ~ NO: OSH 348

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01344) 623345 Fax: (013441 622944

Page 6 of 27 Rev A

CALCULATION SHEET



Stiffener Check

bp = 130mrn t = 5 m m

lp = 1.052 x - = 0.705

(1.0 - -=) P =

0.705 = 0.976 < 1.0

Note: The mean stress in the vee-stiffener is significantly less than A*, hence the vee-stiffener will be fully effective.

3.2.2 Determine elastic critical buckling stress

First calculate position of centroidal axis and hence I,

183.8

Eccentricity of stiffener only from centre of compression flange =

94.4 - = 47.2mm 2

Asgw.9 - - (130 x 5 x2) x 47.2

= 25.2 mm 1300 x 47.2 - - 2434 gws

Assume the stineener to be a T-section to calculate its geometrical properties

0-38



Page 7 of 27 Rev A

CALCULATION SHEET I t 1

,226.8 X 5

( l4 Is = (226.8 x 5 x 25.2) +

+ (14 x 94.4 x (47.2 - 25.2f)

720,000 + 981,000 + 640,000 =

= 2,341,000 mm4

Type 3 profile

0.5 1.5 2.1 E I - t 3 -

%,r - AS

1, = 2,341,000 mm4

bp2 = 183.8 rnm

bPI = 83.1 mm

b, = 260 mm

0.5

- 2434 %r,s -

= 1604Nlmmf

-0.5

3.2.3 Determine reduction factor x

Mean axial stress f , in the stiffener depends on the position of the reutrd axis of the stiffened profie.

For g, = IIOmm (estimate)

2nd g, = 25.2 mrn

0-39

Equ. 6.3b

step (3)


Job Title


Stainless Steel Blast Walls The Steel Construction Institute

Silwood Park, Ascot, Berks SL5 7 Q N Telephone: (01 344) 623345 Fax: (01 344) 622944 Client FABIG Made by AAC Date Jun 1999

f, = 4' [ g w iwgws) = 531.2 ( 1101~F2] = 409.5 N/mm2

The calculated value of g, is shown to be 106.lmm in Section 3.4. The x value determined below is conservcrt've.

Welding on plating in buckling zone

.: a = 0.76

4 =

2, = 0.20

0.5 (1 + a (2 - 23 + J2)

= 0.5 (1 + 0.76 (0.505 - 0.20) . I O.S0S2) = 0.743

= 0.776 1

0.743 + (0.7432 - 0.5052)0.5 - -

3.3 Determine the effective section of the wall cross-section

f - 'nd - fs,red = x t, = 0.776 x 5 = 3.88 mm

(assume the web is fully effective)

(226.8 x 3.88) + (83.1 x 5 ) / = 1295.5 mm'

2275 mm'

Equ. 6.4

Equ. 6.6

Equ. 6.5

0-40



CALCULATION SHEET

-

Job Title

Subject Example 2 - Stiffened Stainless Steel Blast W d s

It can be shown that:

- - - 93.9 mm I = 47,173,000 mm4 Y

at top of web oI = f,' = 531.2 N / m d

Check whether the web is fully effective (as assumed above)

- - - 0.885 o > p s - - 1 02 p = - 0 1

k, = 7.81 - 6.29 @ + 9.78 4 = 21

15.3&p0 = 15.3 X 0.649 X @ = 45.5 2 48

.: Web is Class 4

531.2 200,000 x 21

241.3 J p = 1.052 x - 5

= 0.571 < 0.673

.: p = 1.0 -: Web is fully effective

4. OVERALL LONGITUDINAL MOMENT RESISTANCE

Weay = WefJcF = #S,OOO mm3 p = 105Omm

Assume for this example, KF = KyM = 0.95

Table 6.2

Page 3/27

Equ. 6.lc

Equ. 6.1a

Section 7.1

Equ. 7.3

0-4 1


445,000 x 531.2 x 0.95 x 0.95 1050

- K R d -


CALCULATION SHEET

- - 203,000 Nmm/mm


Checked by RWB

4.1 Effective Span

4.1.1 Lower support (16mm thick plate)

Carbon steel grade 355 fJ = 355N/mm2

From example 1 in FABIG Technical Note 4, for grade 355, in view of the imposed out-of-plane deformation of ihe plate under blast loading, the ductility ratio of the lower support plate will exceed 2.0 and so an enhancement factor of 1.1 7 can be assumed.

2. Enhancement factor = 1.17

A8 = 355 x 1.17 = 415.4N/md

tL = 16mm

t; - "4' - 4 *: (Mc.RdL -

- - - 162 x 415.4 = 26,60ONmm/mm 4

4.1.2 Upper support (1 Omm thick plate)

Stainless steel grade 1.4362 (SAF 2304)

Refer to Page 3/27 uor 5 mm thick material)

Thickness of plute is IOmm .: reduce6 for 5mm thickness by 5%

fJ = 510.8 X 0.95 = 485.3 N / m d

Plastic section modulus and plastic deflection

= 510.8 N / m d

Section 7.2

FA BIG Technical

Note 4, Ex. I

Page 3/27

Table 2.5

D-42



CALCULATION SHEET

Job Title Stainless Steel B h t Walls

.:

Adopt 0.2% proof strength

Interpolate value for (KsJOv2

(Ksdo.2 = 1.084

4' = 485.3 x 1.084 = 526.1 N / m d

Strain rate = 1.0 s-'

2

- x f r ' -

-: (Mc.Rd)" - 4

- - - I d x 526.1 = 13,200 Nmm/mm 4

4.2 Effective Length

203,000 203,000 + (0.5 x 26,600) + (0.5 X 13,200)

4200 .I] 4008 mm

2

= 64.Imm

Table 3.4

Equ. 7.6b

Equ. 7.4

Equ. 7.5a

Equ. 7.5b

0-43



CALCULATION SHEET

/Job Title Stainless Steel B h t walk -


- - - 4008 [JF - I ] = 127.3 rnm 2 203,000

4.3 Resistance of the Wall

4.4 Stiffness under Longitudinal Bending

- 384 x 200,000 x 47,173,000 5 x (4008y x 1050

- 384 E I

5 L: P k =

= 10.72 N/mm2

Reduced stifiness (allowing for support bending)

= 9.96 N/mm2 10.72 kR = 1.6 (64.1 127.3)

4008 I +

4.5 Natural Period

wall i- liner and insulation - Mass, M -

Assume liner and insulation = 20 k g / d

-: Mass of liner and insulation = 20 x I050 x 4008 x lo6 = 84.2 kg

Wid = Volume x Density

Section 7.3

Equ. 7.7

Section 7.4.1

Page 9/27 Equ. 7.8

Equ. 7.9

Section 7.4.2

Equ. 7.10

D-44


Job Title

Subject Example 2 - Stiiffened

Stainless steel Blast walls The Steel Construction Institute


CALCULATJON SHEET

Volume = (25 + 430 + 241.3 + 350 +260 + 241.3) t LE X 109 = 1547.6 x 5 X 4008 X 1Q9 = 0.0310 m’

Density = 7800kg/m’

Mass, M = (0.0310 x 7800) i- 84.2 = 326 kg

.: KLM = 0.78 LE - > 0.9 L

= 0.0310 s 326 x 0.78 T = 2~ 1.05 x 9.96 x 106

4.6 Dynamic Load Factor

- Rtn = 405.2 N/mm PMM -

= 1.26 405.2 x Id 80 x Id x 4.008

(DLF)R =

t, = 0.06 s

bsurning the response is elastic

= 1.94 - 0.06 - - - T 0.031 0

80 kN/m2

.: ( D W , = 1.00

: wall response is elastic and the moment resistance of section is zdequate.

1.00 = 531.2 x - = 421.6 N/mm2

1.26 -

%Ax -

Table 3.7

Section 7.4.2

Equ. 7.10

Section 7.4.3

Equ. 7.11

Equ. 7.11

Fig 4.4

Section 7.4.3

Equ. 7.12

D-45

Job No: OSH 348 Page 14 of 27 The Steel

= 32.2 mm - p~~ ( D L f l ~ LE - - 0.08 x 1.00 x 4008 - 9.96 Ylll

kR

Rev A

The limit on deflection is 105mm .: OK

Construction Institute

Silwood Park, Ascot, Berks SL5 7QN Telephone: 101 344) 623345 Fax: (01344) 622944

CALCU LATl ON SHEET

5. SHEAR RESISTANCE

V,, = 0.5P,,DLFLs

P,, = 0.08 N/mrn2 (DLF), = 1.00

Upper support is more ctiticai than the lower

Job Title




StaideSS Steel B h t walls

LE 4008 - + L , - 50 = - + 64.1 - 50 = 2018 mm 2 2

.: L, =

V,, = 0.5 x 0.08 x 1.00 x 2018 = 80.7 N/mm

- - 'MAX p 2 sw sin 4 t 4

- 80.7 x 1050 - 2 x 241.3 x sin 56" x 5 4

17.3 E = 17.3 X 0.649 = 11.2

- sw - - - 241.3 = 48.26 r' 17.3 E t 5

.: necessary to ven& Vb,Rd

No intermediate transverse stiffeners

= 42.4 N / m d

.: k, = 5.34

0-46

Equ. 7.13

Section 7.5

Equ. 7.16

Page 13/27

Page 11/27

Equ. 7.17

Page 3/27

Section 7.5.1

Equ. 7.18

Table 7.1


~~~ ~~

0.86 - - 531.2 5.34 x 200,000

- 0.8 x 241.3 - 5 2 W


CALCULATION SHEET

2, = 0.86 > 0.6


Checked by RWB

- -: f b v = [ . - 0.42 A,,,] 195.9 N / m d

vb,Rd = sw l f b v = 473,000 N

Total shear load (shared between 2 webs)

V T O , = V,, x p = 84,700 N < V,.,, .: OK

6. LOCAL SUPPORT SHEAR AND DEFORMATION CAPACITY

6.1 Lower Support D e f d Check (Figure 1 0 . 3 ~ )

Check point 3 , T4vT 10

Carbon steel Grade 355

16

Check point 1

** 11 Check point 2

L = 127.3 I Check Point 1

Plastic hinge localion (MCeRJL = 26,600 Nmm/mm

Check Point 2

Deck plate t = 12 mm

t 2 122 - x fy* = - x 355 x 1.17 = 15,000 Nmmlrnrn 4 4 Mc.Rd =

D-47

71 Jun 1999

Table 7.3

Equ. 7.20

Section 7.5.2


(McXJL Moment at Check Point 2 = -- 2

Page 16 of 27 Rev A

= 13,300 Nmm/mm < Mc.Rd .: OK

Check Point 3

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: 101 3441 622944

C ALCU LATl ON SHEET

Id x 355 x 1.17 = I0,400 Nmm/mm - t 2 Mc.Rd - 7 fy' = - 4


Client FABIG Made by AAC Date Jun I999


[ L, - (;; - 10) Moment at Check Point 3 = (Mc.RJL x

= 26,600 x 0.293 = 7794 Nmm/mm < Mc.Rd

6.2 Upper Support Detail Check (Figure lO.1a)

.. OK

II %.Rd u

Check Point I

Plastic hinge localion (Mc.Rd)U = 13,200 Nmm/mm

Check Point 2

- S2 Mc-Rd - - x 531.2 = 8500 Nmm/mm 4

(64.1 - (SO - 10)) Moment = 13,200 x 64. I

= 4963 Nmm/mm < Mc.Rd .: OK

0-48


Client FABIG

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01344) 623345 Fax: (01 344) 622944 Made by AAC Date Jun I999

Checked by RWB Date Jun 1999 CALCU LATlO N SHEET

7. LOCAL EFFECTS

7. I External Forces

M(DL1;3E = 1.0 PMAX

P = 1.0 x 0.08 = O.OSN/md

= 0.08 N/mm2

7.2 Internal Forces

F" I

106. lmm

F U 2 -

Compression members

( c + & P FR, = K a,, E

Compression flange yielding .: K = 1.0

= 0.2% g, = 106.1 mm 5

A,, = (2 x 5 x 41.55) + (2 x 3.88 X (41.55 + 71.85))

+ (260 x 3.88)

= 415.5 + 880.0 + 1008.8 = 2 3 0 4 m d

Section 8. I . I

Page 14/27

Section 8.1.2

Equ. 8.2



CALCULATION SHEET


(531.2 x 415.5) + (412.9 x (880.0 + 1008.8)) - - = 434 N/mm2

2304

531-2 f 0.002 .: FR1 = 1.0 X 434 2OO,OOO [ 106.1 ] 2304

= 43.88 N/mm width

Note: The distribution of FRI along the compression flange is proportional to the effective thicknesses

@ = 5 6 "

- I A _ _

- 106. i Aefl.cw - -

= 7.47 N/mm

Class 4 cross-section .: distribution of FRz is triangular over the whole length of the compression part of the web, 106.1 /sin 56.0 O = 128.Omm

01 T .: K = 7 Compression f h g e yielriing

fr

a,, = a, = - 470.1 N / m d

Equ. 8.3a

Section 8.1.2

Equ. 8.4a

0-50


= - 0.885 - - 470. I K - 531.2

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01344) 623345 Fax: (01344) 622944

CALCULATION SHEET

531.2 .t 0.002 Fm = ( -0.885)2 X 531.2 200,000 [ ) I130

4 200 - 106.1


Checked by RWB

= 5.83 N/mm

Cross-section is Class 4 .-. Distribution of FR3 is triangular over the tension part of the web, 93.9/sin 56.0 * = 113.Omm

A , = (215 + 215 + 25) x 5 = 2275md

531-2 + 0.002 FR4 = (- 0.885) x (- 470.1) [ 2OO,OOO ] x 2275

200 - 106.1

= 46.93 N/mm

FR4 is distributed over the whole length of the tension flange, 430mm

Internal Forces (N/mm length)

43.88 7.47 - 7.47

Equ. 8.5

0-5 1


Note: The distribution of FR, is proportional to the effective thicknesses

Page 20 of 27 Rev A

FR4 FRl - + 'R3 Check balance of internal forces - + FR2 - 7 2

Construction Institute

Silwood Park, Ascot, Berks SL5 7QN Telephone: 101 344) 623345 Fax: (013441 622944

CALCU LATlON SHEET

+ 7.47 = 29.41 43.88 + FRz = - 5

2 2

Job Title

Subject Example 2 - Stiflened


Checked by RWB Date Jun I999

Stainless Steel Blast walls

-

+ 5.83 = 29.30 46.93 + FR3 = - 5

2 2

7.3 Calculation of Moments and Stresses arising from Local Loading (external (7.1) and internal forces (7.2))

For this example, the package QSE was used to carry out the frame analysis. The input and output details are attached at the end of this example. The following model was analysed:

OK

A strip of waU was modelled with the supporC conditions shown above.

The external loading applied to the frame model is transmitted to the remainder of the wall via web shear, .: the vertical component of this web shear should equal the vertical component of the external load.

Note: The web load is adjusted to include any imbalance in the internal loads.

Section 8.1.2

D-52


Job No: OSH 348


Page 21 of 27 Rev A

CALCULATION SHEET

Job Title Stainless Steel B h t Walls Subject Example 2 - Stiffened

Y-comp of web shear = vertical comp. of external -+ internal load

== (0.08 x 525) + (29.41 - 29.30)

= 42.11 Nlmm

Web shear load - - 42* ' I = 50.79 Nlmm sin 56"

Moment diagram (Nmm/mm length)

265

306

Axial Stress Diagram (N/mm2)

13.394

Figure 8.3

Figure 8.4

0-53



Page 22 of 27 Rev A

CALCULATION SHEET

Displacement Diagram (mrn)

5.830

--+ 2.154

7.4 Flange Checks

t 2 s2 - f = - x 531.2 4 y 4

- M c . R d -

Mp.Rd f Y =

= 3320 Nmm/mm length

.: OK

.: OK

1.5 x 3320 = 4980

Date Jun 1999

Section 8.3.1

Equ. 8.6

Equ. 8.7

Equ. 8.8

0-54

Job No: OSH 348

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01 344) 623345 Fax: I01 344) 622944

Page 23 of 27 Rev A

CALCULATION SHEET

7.5 Web Checks

Mp.Rd 4'

I


= 0.4 < 1.0 .. 1290 11.143 3320 531.2 - +

s 1.0 lMcl I ucwl Mp.Rd 4' - + -

1.5 x 3320 = 4980

OK

.: OK

.: OK

7.6 Instability Check

- i- fb Mp.Rd

7.6.1 Overall flange check

350 mm - 1 = b,, -

u = 0, = 9.417 N / m d

0-55

Section 8.3.2

Equ. 8.9

Equ. 8.10

Equ. 8.11

Equ. 8.12

Table 8.1

Job No: OSH 348

Job Title


stainless Steel B h t W a h Construction Institute

Page 24 of 27 Rev A


CALCULATION SHEET

Welding on plate in buckling zone


Checked by RWB

a = 0.76 2, = 0.20

9.4I7 31.9

= I.443 mm 5 - t 3.464 3.464

531.2 ( I - 0.32) - - 1.443 ;rr 200,000

0.5 (1 + a (2 - XJ + 2') 0.5 ( I + 0.76 (3.80 - 0.2) + 3.802)

I

3.80

- - 9.09

= 0.058 < I.0 .: OK I 9.09 +- (9.09 - 3.802)'.'

xf,' = 0.06 X 531.2 = 31.9 Nlmrn'

i l S = 0.30 + 0.48 = 0.78 < I.0 .: OK 3320

7.6.2 Flunge check - stiffener strut

I = 183.8mm

o = 13.394N/md

M = 742 Nmm/mm

No welding on placing in buckling zone.

0-56

)ate Jun 1999 I

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8. I3

Equ. 8.I2



I I I

Job No: OsH 348 Page 25 of 27 Rev A

Job Title

Subject Example 2 - Sriffened

Client FABIG Made by AAC loate Jun 1999

StahkSS Steel Blust wds

.: a = 0.49 x,, = 0.40

= 1.443mm I - 5 i = - - - 3.464 3.464

531.2 (1 - 0.32) = 1.993 1.443 x 200,000

4 = 0.5 (1 + 0.49 (1.993 - 0.4) + 1.993') = 2.876

= 0.202 1 2.876 + (2.8762 - 1.9932)0.5

x =

fb = 0.202 x 531.2 = 107.3 N/mm2

13.394 1.5 x 742 = o.46 < -i

107.3 3320

.-. stiffener strut is less critical than overall flange check.

7.6.3 Web check

1

0

M

2

4

X

fb

241.24 mm - - s w

gcw - - 11.143 N/mm2

325 Nmm/mm - Mc -

(1 - 0.32) = 2.62 1.443 n 200,000

- - 0.5 (1 + 0.49 (2.62 - 0.4) 4- 2.62)

= 0.123 < 1.0 1 4.48 + (4.4g2 - 2.622)0.5

xf,' = 0.123 x 531.2 = 65.3N/mm2

.: OK

4.48

-: OK

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8.13

Equ. 8.12

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8.13

0-57

~ TheSteel Construction Institute


C ALC U LATlO N SHEET

- + 325 = 0.17 + 0.15 = 0.32 < 1.0 65.3 3320

5.6.4 Trough check

I

U

M

2

4

X

f b

10.69 26.6

.: OK

5 + 0.85 sw = - 350 + (0.85 x 241.24) = 380.05 mm 2 2

9.4172 + 11.1432 + 11.4152 = N,mm2

3

1290 Nmm/mm - M B -

380.05 I 531.2 (I - 0.32) = 4.12 - 1.443 - n 4 200,000

- - 0.5 (I + 0.76 (4.12 - 0.2) + 4.12’)

= 0.050 < 2.0 1 10.48 + (10.482 - 4.122)0.5

xf,* = 0.050 x 531.2 = 26.6 N / m d

+ 1290 = 0.40 + 0.58 = 0.98 < 1.0 3320

10.48

8. REDUCTION FACTOR ON LONGITUDINAL MOMENT RESISTANCE

8.1 KF

5.830 - 2.178 = 3.652 f

.: OK

0-58

Equ. 8.12

Equ. 8.16

Equ. 8.15

Equ. 8.14

Equ. 8.13

Equ. 8-12

Section 8.5

Page 22/27


Client FABIG

Silwood Park, Ascot, Berks SL5 7QN Telephone: (01344) 623345 Fax: (01344) 622944 Made by AAC

Checked by RWB CALCU LATlO N SHEET

~

Job Title


Stainless Steel Blast walls

2.154 4 = 3.652

205 mm t = 5 m m

445,000 mm3

( (226.8 x 3.88) + (83.1 x 5) ) 106.12

+ (455 x 5 x 93.9)

14,584,000 -k 20,059,000 = 34,643,000 mm4

0.6 For stiffened sections

1 h - t I - WJz4f.Y

w4JY

I = 0.5 x 2.154 + 0.6 x 3.652 205 - 5

I - 445,000

0.988

1068 Nmm/mm

3320 Nmm/mm

1290 Nmm/mm

IMA I + I MB I = 1068 + I290 = 2358 Nmm/mm

0.8 x Mc.Rd = 0.8 x 3320 = 2656 Nmmlmm

IMA I IMB I < o.8Mc.Rd .: KvM = 1.0

On Page I0/27, assumed KF = K , = 0.95

K F = 0.989 > 0.95 and KvM = 1.0 > 0.95 .: OK

D-59

l a t e Jun 1999

Equ. 8.17

Section 8.6

Table 8.2

Software lensed lo STEEL CONSTRUCTION INSTITUTE

Job Title Stainless Steel Blast Walls

Cllcnt FABIG

JobNo Sheet No Rev

1 osh3485

Pad

Example 2 - Stiffened Profile

RWB By AAC OateMay 99

F'ic STIFF PSA I Datflm 07-May- 1999 15 54

I Structure T V D ~ I PLANE FRAME 1

Name: Date:

Engineer Checked Approved

AAC RWB May 99 May 99

Number of Basic Load Cases- Number of Combination Load Cases Number of Envelope Load Cases

Included in this printout are data for: I All 1 The Whole Structure I

3 2 0

TY Pe

I I

Comb I c2 I total 2 1 uc Name 1

Nodes

5 1 0.560 1

0.035

4 0.468 0.200 0.200

Emt

1 2

NodeA NodeB Length PropA Prop6 p (m) degrees

1 2 0.215 1 0 2 3 0.241 1 0

- Prop Section A 1, 1, J Material

(an') (an4) (an3 (m4) 1 steel plate 50.00 1 .o 1 .o 1

P d runell)ale: 06/0711999 1520 QSE Space for Windows Version 2.20 PrintRmldJ

sdhvan, llcsnsed lo STEEL CONSTRUCTION INSTrrUTE

W T W ~ Stainless Steel Blast Walls

By PAC Oate May 99 RWB

Job No Sheel No Rev

osh3485 2 Pat

Rd Example 2 - Stiffened Profile

Iclien( FABIG

9 TimberSC7 13.600 960.000

10 TimberSC8 15.600 1.OBE 3

1 1 TirnberSC9 18.000 1.2E 3

I STIFF PSA

0.000 0.000 0.000

Dead Dead

supports

Fixed Fixed Fixed Fwed Fixed Fixed Fixed

DL1 external DL2 internal

Basic Load Cases

Comb. Combination U C Name Basic Basic UC Name

Name

Factor

C1 total 1

C2 total 2

I Dead I DL3 !web

DLl external 1 .oo DL? internal 1 .oo DL1 external 1 .oo

Combination Load Cases

1 I 1 1 . 0 0 I DL3 I web I 1.00 I DL? I internal

QSE Space for Windows Version 2.20 RintRUnZd3

Job No

0s h3485 Sheel No Rev

3

Loadings

Sdhvare licensed lo STEEL CONSTRUCTION INSTITUTE

Title Stainless Steel Blast Walls

clied FABIG

Wa = T (C). Lack of Fit

I I Pad

Ref Example 2 - Stiffened Profile

By AAC May 99 RWB

STIFF.PSA I Datd-me 07-May-1999 1 5 : s

Node Displacements

Element End Forces

4 4 c 2 66.969 21.766 -0.186

5 c2 -66.969 -0.000 -0.743

5 4 c2 -1 3.872 -14.249 1.254

6 c2 13.872 14.249 0.623

QSE Space for Windows Version 2.20 p r M R u n 3 d 3

Design Guide Steel Blast Walls

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