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Design Manual for Roads and Bridges
Highway Structures & BridgesInspection & Assessment
CS 456The assessment of steel highway bridges andstructures(formerly BD 56/10)
Revision 0
SummaryThis document gives requirements for the assessment of existing steel structures and structuralelement on motorways and other trunk roads. This document was developed to assessstructures designed using British Standards BS 5400-3 , BS 5400-10 and older Standards. Therequirements for assessment are presented as additions and amendments to the design clausesand annexes of BS 5400-3 for static strength, and BS 5400-10 for fatigue strength.
Application by Overseeing OrganisationsAny specific requirements for Overseeing Organisations alternative or supplementary to those given in this documentare given in National Application Annexes to this document.
Feedback and EnquiriesUsers of this document are encouraged to raise any enquiries and/or provide feedback on the content and usageof this document to the dedicated Highways England team. The email address for all enquiries and feedback is:[email protected]
This is a controlled document.
CS 456 Revision 0 Contents
Contents
Release notes 2
Foreword 3Publishing information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Contractual and legal considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Introduction 4Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Assumptions made in the preparation of the document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Abbreviations and symbols 5
Terms and definitions 6
1. Scope 7Aspects covered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2. Assessment processes and basis for assessment for static strength 8Assessment processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Basis of assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Assessment Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Assessment process and basis of assessment for fatigue 9General guidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Corrections to BS 5400: Part 10: 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Assessment: near ends of spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Assessment: mid span regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4. Normative references 14
5. Informative references 15
Appendix A. Amendments to BS5400-3 for assessment 16
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CS 456 Revision 0 Release notes
Release notesVersion Date Details of amendments0 Mar 2020
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CS 456 Revision 0 Foreword
Foreword
Publishing informationThis document is published by Highways England .
This document supersedes BD 56, BD 13, BA 9 and BD 9, which are withdrawn.
Contractual and legal considerationsThis document forms part of the works specification. It does not purport to include all the necessaryprovisions of a contract. Users are responsible for applying all appropriate documents applicable totheir contract.
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CS 456 Revision 0 Introduction
Introduction
BackgroundThis document gives requirements for the assessment of existing steel structures and structuralelements on motorways and other trunk roads.
This document was developed to assess structures designed using BS 5400-3 [Ref 5.N], BS 5400-10[Ref 4.N] and older Standards.
The requirements for assessment are presented as additions and amendments to the design clausesand annexes of BS 5400-3 [Ref 5.N] for static strength, and BS 5400-10 [Ref 4.N] for fatigue strength.
These additions and amendments have been specifically developed to suit assessment conditions.
The objectives of this document include:
1) To cater for structural forms that are not permitted by BS 5400-3 [Ref 5.N] and BS 5400-10 [Ref 4.N]or by BS EN 1993-2 [Ref 2.N].
2) To produce a more realistic assessment of the strength of steel elements than is possible using thedesign codes. This is achieved in part by taking advantage of the information available duringassessment in respect of the material strength, geometric properties and imperfections, and actualbridge usage which can only be predicted at design stage.
3) To amend some parts of BS 5400-3 [Ref 5.N] and BS 5400-10 [Ref 4.N] which have been eitherconservatively interpreted for use in design, or updated by later evidence allowing a less conservativeinterpretation.
This document also includes updates to BS 5400-3 [Ref 5.N] that were previously published in BD 13.
Assumptions made in the preparation of the documentThe assumptions made in GG 101 [Ref 3.N] apply to this document.
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CS 456 Revision 0 Abbreviations and symbols
Abbreviations and symbols
AbbreviationsAbbreviations Definition
HSFG High strength friction grip (bolts)
MT Magnetic testing - also Magnetic particle inspection (MPI)
NDT or n.d.t. Non-destructive testing
PAUT Phased array ultrasonic testing
PT Penetrant testing
SLS Serviceability limit state
u.d.l. Uniformly distributed load
ULS Ultimate limit state
UT Ultrasonic testing
UTS Ultimate tensile strength
VT Visual testing
Symbols
Symbol Meaning
n The actual annual flow of particular vehicle type in traffic lane
NThe maximum allowable annual flow of particular vehicle type/lane if the trafficconsisted of only this vehicle type
t Plate thickness
γf3 Partial factor for load effects
Note: In addition to the symbols listed above there are many symbols used in BS 5400-3 [Ref 5.N] andAppendix A of this document, some of which are only used in specific equations. The meanings ofthese symbols are given in Appendix A and BS 5400-3 [Ref 5.N], including lists below equations inwhich they are used.
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CS 456 Revision 0 Terms and definitions
Terms and definitions
TermsTerm Definition
The assessment rulesCS 454 [Ref 1.N], BS 5400-3 [Ref 5.N] and BS 5400-10 [Ref 3.N]as amended by this document.
ClassThe classification of the structural detail, as defined in BS 5400-10[Ref 4.N].
Condensed traffic loadspectrum
A version of the load spectrum that is modified for convenience, togive equivalent results by using fewer vehicle types.
Effective stress rangeThe range of stress due to the effects of fatigue loading, after takinginto account any reduction of the compressive part of the stressrange for non-welded details. Definition from BS 5400-10 [Ref 4.N].
FatigueThe damage, by gradual cracking of a structural part, caused byrepeated applications of a stress which is insufficient to inducefailure by a single application.
Fatigue life
Period of time for which the probability of fatigue cracking remainsbelow a level that would be acceptable throughout the design life ofa normal bridge structure, which is based on the 2.3% probability offailure criterion.
HA LoadingA traffic load model developed to represent the effects of normaltraffic on longitudinally spanning bridge decks, As defined in CS454 [Ref 1.N]
HB loading A traffic load model to represent the effects of abnormal trafficloads, as defined in CS 454 [Ref 1.N]
Load spectrum A tabulation showing the relative frequencies of loading events ofdifferent intensities experienced by the structure.
Miner's summationA method to determine the cumulative impact on fatigue insituations where multiple stress ranges occur of varyingamplitudes. Definition from BS 5400-10 [Ref 4.N].
Standard load spectrumThe load spectrum that has been adopted based on the analysis ofactual traffic on typical roads.Definition from BS 5400-10 [Ref 4.N].
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CS 456 Revision 0 1. Scope
1. Scope
Aspects covered1.1 This document shall be used for the assessment of existing steel highway bridges and structures on
motorways and other trunk roads.
1.2 This document shall not be used for assessment of steel castings, wires, cables, anchorages andsaddles for suspension and cable stayed bridges and the assessment of orthotropic steel decks.
1.2.1 For assessment of steel castings, wires, cables, anchorages, saddles, suspension and cable stayedbridges and orthotropic steel decks assessors should seek guidance from specialist literature.
1.3 This document shall not be employed for assessment of structures designed using BS EN 1993-2 [Ref2.N].
1.4 This document shall not be used for new structures or design.
NOTE Aspects of this document can be useful for the assessment of the retained parts of existing structuresthat are being modified or upgraded.
Implementation1.5 This document shall be implemented forthwith on all schemes involving assessment of existing steel
highway bridges and structures and their structural elements on the Overseeing Organisations'motorway and all-purpose trunk roads according to the implementation requirements of GG 101 [Ref3.N].
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CS 456 Revision 0 2. Assessment processes and basis for assessment...
2. Assessment processes and basis for assessment for staticstrength
Assessment processes2.1 The assessment processes described in CS 454 [Ref 1.N] shall be applied to static strength
assessment.
Basis of assessment2.2 The provisions of BS 5400-3 [Ref 5.N] as amended by Appendix A and BS 5400-10 [Ref 4.N] as
amended by this document shall be applied for assessment of existing steel structures and structuralelements.
NOTE 1 Appendix A is presented in the form of additions to BS 5400-3 [Ref 5.N] for assessment. The additionsin Appendix A have been specifically developed to suit assessment conditions.
NOTE 2 Clause references in Appendix A refer to BS 5400-3 [Ref 5.N] as amended by Appendix A.
2.3 Where a clause in BS 5400-3 [Ref 5.N] is not replaced or modified in Appendix A, the clause from BS5400-3 [Ref 5.N] shall be applied for assessment without modification.
2.4 Annexes in Appendix A and in BS 5400-3 [Ref 5.N] that are termed Normative shall be applied forassessment.
2.5 Annexes in Appendix A and in BS 5400-3 [Ref 5.N] termed Informative shall be applied for assessmentunless an alternative method is agreed with the Overseeing Organisation and documented in theassessment basis.
Assessment Objectives
2.6 The assessment objectives shall be according to Section 4 of BS 5400-3 [Ref 5.N] as amended byAppendix A.
NOTE 1 The assessment objectives include requirements for loads, partial factors and limit states forassessment, and typically refer to CS 454 [Ref 1.N].
NOTE 2 The assessment objectives include assessment of the SLS limit state according to BS 5400-3 [Ref 5.N]as amended by Appendix A.
NOTE 3 The partial factor γf3 in BS 5400-3 [Ref 5.N] and the assessment additions is included as a reduction tothe resistance. This approach differs from the usage in CS 454 [Ref 1.N]. The additional application ofthis factor on the load side results in double counting.
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CS 456 Revision 0 3. Assessment process and basis of assessment fo...
3. Assessment process and basis of assessment for fatigue
General guidance3.1 Fatigue assessment shall be undertaken for one or more of the following reasons:
1) where damage tolerance is poor and fatigue failure can cause premature loss of strength orserviceability;
2) where fatigue life predictions are required in order to plan future maintenance.
NOTE Fatigue analysis is not normally necessary for bridge assessment because it is not usually necessary torepair or strengthen a structure at the present day just because it might theoretically need to berepaired or strengthened at some time in the future.
3.2 Fatigue assessment shall be carried out in accordance with the procedures set out in BS 5400-10 [Ref4.N] and this document.
3.3 Fatigue assessment of shear connectors shall also take account of the provisions of CS 456 [Ref 7.N].
3.4 Highway bridges shall be assessed for fatigue for the standard design life of 120 years using thestandard traffic loading model and the annual flow of commercial vehicles given in Table 1 of BS5400-10 [Ref 4.N] unless special circumstances apply (see Cl. 3.4.1 below).
3.4.1 Where special circumstances apply, a non-standard design life, a non-standard load spectrum ornon-standard vehicle flows may be used. Special circumstances can include:
1) temporary structures, which may employ a non-standard design life;
2) structures subject to weight restrictions, and accommodation bridges where the vehicle weightsdepend upon a particular usage (such as access to a farm or factory), which may employ anon-standard load spectrum;
3) structures that carry traffic flows substantially different from standard flows, which may employnon-standard vehicle flow rates.
NOTE Any special circumstances that currently apply to a particular structure can change during its design life.
3.5 Where a fatigue life prediction is required, the theoretical remaining fatigue life shall be determined inaccordance with the damage calculation procedures described in BS 5400-10 [Ref 4.N].
NOTE A prediction of remaining life depends upon the actual past and predicted future traffic using the bridge.It will therefore require realistic or conservative past and future traffic models to be defined.
3.6 The effective stress range for a welded detail shall include compression stresses.
NOTE Compression stresses are considered to be just as damaging for fatigue assessment as tensilestresses.
3.7 The fatigue life of any detail shall be based on the 2.3% probability of failure criterion as used to obtainthe design curves in Figure 14 of BS 5400-10 [Ref 4.N].
NOTE This criterion is also implicit in the damage charts in Figure 10 and the limiting stress ranges in Figure 8of BS 5400-10 [Ref 4.N].
3.8 The modifications to fatigue assessment criteria provided by this document have been specificallydeveloped to suit assessment conditions and shall not be used in design or construction.
Corrections to BS 5400: Part 10: 19803.9 The following corrections shall be made to the text of BS 5400-10 [Ref 4.N], as shown in Table 3.9 for
the purposes of this document.
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CS 456 Revision 0 3. Assessment process and basis of assessment fo...
Table 3.9 Corrections to BS 5400: Part 10: 1980
PageNumber
Clause
4 5.1.2.2 Paragraph 1, lines 6, 7 and 8: Delete statement within brackets.
5 6.2.1 Figure 1: Delete "M1" and "P1", insert "M1" and "P1".
6 6.3 Figure 2: Delete "σN" and "σt" on axes, insert "σn" and "σt".
8 7.2.5 Paragraph 1, Line 9: Delete "127r", insert "127r".
17 8.3.2 Figure 11: Insert bold line on graph for KF=2.2 from L=1 to L=2.5.
20 9.2.4 Paragraph 1, Line 8: Delete "at"", insert "of".
21 11.2 Figure 14: Insert "of" after "summary" in title.
22 11.2 Paragraph 1, Line 4: Delete "16", insert "14".
25 B1 Paragraph 1, Line 6: Delete "of the graph".
25 AppendixC
Title, Line 1: Delete ";".
30 D.2.2 Paragraph 1, Line 1: Delete "These", insert "To".
32 D.3.3 Paragraph 1, Line 3: Delete "(see also figure 1)".
36 E.1 Figure 19, NOTE Line 2: Delete "F,", insert ",F".
45 H.4.1Figure 26, NOTE: The note does not refer specifically to Figure 26 butshould be included as part of the general text of H.4.1.
45 H.4.3 Sub-clause 1, Type 3.1, Line 6: Delete "5.1.2.5", insert "5.1.2.4"
46 H.4.3Sub-clause 9, Types 3.7 and 3.8, Paragraph 2, Line 7: Delete"lameller", insert "lamellar"
49,51,53 H.1.1Table 17(a), 17(b) and 17(c): Delete "†" Important features that changesignificantly from one type of another.". Delete "†" where it occursattached to class letters in the tables.
Loading3.10 Miner's summation of fatigue damage shall be carried out using either of the following two traffic load
models:
1) the traffic load spectrum specified in Table 11 of BS 5400-10 [Ref 4.N];
2) the condensed traffic load spectra of vehicle weights and axle weights provided in Table 3.10a andTable 3.10b respectively.
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CS 456 Revision 0 3. Assessment process and basis of assessment fo...
Table 3.10a Condensed commercial vehicle axle weight spectrum
Total axle weight (kN) Total number of axles for 106 vehicles256 360
169 700
144 940
99 649000
77 300000
59 517000
47 268000
36 700000
18 420000
Total: 2,856,000
Table 3.10b Condensed commercial gross weight spectrum
Proportion of standard fatigue vehicle gross weight Proportion of total vehicles
6.75 0.00001
5.03 0.00002
4.09 0.00003
2.14 0.00044
1.06 0.10450
0.82 0.105
0.72 0.090
0.43 0.320
0.20 0.380
Total: 1.0
3.11 Where it is not possible to determine stresses accurately by theoretical analysis, fatigue assessmentshall be based on actual stress measurements.
3.12 When the standard axle or standard wheel ( BS 5400-10 [Ref 4.N] 7.2.2.2) is used in conjunction withthe commercial vehicle axle weight spectrum in Table 14 of BS 5400-10 [Ref 4.N] or in Table 3.10 (forexample, when doing an explicit Miner's summation) the wheel contact area shall be varied on thebasis of a constant pressure of 0.5 N/mm2 for each particular axle or wheel weight.
Assessment: near ends of spans3.13 Where standard types of shear connectors that meet the requirements of BS 5400-5 [Ref 6.N] are
employed in simply supported longitudinal girders, Tables 3.13a or 3.13b shall be used to assesswhether or not they need to be checked for fatigue.
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CS 456 Revision 0 3. Assessment process and basis of assessment fo...
Table 3.13a Fatigue check table for shear stud connecttors
Type of carriageway Dual 3-lane motorway 3-lane all purpose
Dual 2-lane motorway 2-lane all purpose
Dual 3-lane all purpose 2-lane slip road
Dual 2-lane all purpose Single lane slip road
HB design criteria 25 - 45 units HB
Location of stud shear connectors Support ends of a simple span
Type of girder Up to 100 m long, simply supported longitudinal girders
Type of construction Propped Unpropped
Main girder spacing 1.5m - 4m 2m - 4m
Table 3.13b Fatigue assessment table for standard stud shear connectors in accommodationbridges
Maximum allowable annual flow/lane (N) if traffic consisted ofonly one vehicle typeVehicle
typeTotal weight
(kN)Span <= 20m 20 <span <= 100m
5A-L 250 20 90
4A-H 335 2 10
4A-M 260 15 70
4A-L 145 1700 7100
4R-H 280 10 30
4R-M 240 30 120
4R-L 120 6700 27600
3A-H 215 70 300
3A-M 140 2000 8500
3A-L 90 90000 443000
3R-H 240 30 120
3R-M 195 150 630
3R-L 120 6700 27600
2R-H 135 3000 12400
2R-M 65 Unlimited Unlimited
2R-L 30 Unlimited Unlimited
3.14 Table 3.13a shall be used to assess whether fatigue shear checks at the end of the span are required.If all the conditions noted in Table 3.13a are satisfied, no fatigue checks at the end of the span areneeded.
NOTE 1 Table 3.13b covers the design of normal highway bridges which are subjected to both HA and HB typesof loading as described in BS 5400-2 [Ref 1.I].
NOTE 2 The stud connectors are assumed to have a design life of 120 years and be subjected to the standardload spectra and traffic flows given in BS 5400-10 [Ref 4.N].
3.15 Table 3.13b shall be used to define the traffic model for accommodation bridges that have limited usageand that are designed for HA loading only.
3.16 Fatigue life shall be deemed to be satisfactory if the sum of all values 'n/N' is less than unity, where:
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CS 456 Revision 0 3. Assessment process and basis of assessment fo...
1) n = actual annual flow of particular vehicle type in traffic lane;
2) N = maximum allowable annual flow of particular vehicle type/lane if the traffic consisted of only thisvehicle type;
3) the stud shear connectors can be anywhere in the span and are assumed to be designed to theminimum static strength requirements of BS 5400-5 [Ref 6.N]; and,
4) the bridges are assumed to be simply supported, single carriageway with one or two lanes.
NOTE Some conservative assumptions have been made in deriving these tables. Thus even though a tableindicates that the fatigue strength or life is inadequate the connector can be found to be satisfactorywhen detailed calculations are carried out.
Assessment: mid span regions3.17 Stud connectors at mid-span regions shall be checked for fatigue even when Tables 3.13a and 3.13b
illustrate that the design of stud connectors is not governed by static considerations at the ends of aspan.
3.18 For plates less than 40 mm and greater than 12 mm, the effective life shall be taken as:[calculated design life] · [1− 0.02[t− 12]] , where t = plate thickness in mm .
3.19 For plates less than 100 mm and greater tor equal to 40 mm, the effective life shall be taken as:[calculated design life] · [0.44− 0.004[t− 40]] where t = plate thickness in mm .
3.20 Where structures have no specified fatigue loading criteria, welded connections with classificationinferior to Class F shall be assumed to be at risk of premature cracking.
NOTE Some structures (including footbridges), have no specified fatigue load model. Some non-load-carryingwelded joints can attract uncertain stresses due to displacements. Inspection can be the only rationalapproach to assessing such details.
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CS 456 Revision 0 4. Normative references
4. Normative referencesThe following documents, in whole or in part, are normative references for this document and areindispensable for its application. For dated references, only the edition cited applies. For undatedreferences, the latest edition of the referenced document (including any amendments) applies.
Ref 1.N Highways England. CS 454, 'Assessment of highway bridges and structures'
Ref 2.N BSI. BS EN 1993-2, 'Eurocode 3. Design of steel structures Part 2: Steel bridges'
Ref 3.N Highways England. GG 101, 'Introduction to the Design Manual for Roads andBridges'
Ref 4.N BSI. BS 5400-10, 'Steel, concrete and composite bridges. Part 10: Code of practicefor fatigue'
Ref 5.N BSI. BS 5400-3, 'Steel, concrete and composite bridges. Part 3: Code of practice fordesign of steel bridges'
Ref 6.N BSI. BS 5400-5, 'Steel, concrete and composite bridges. Part 5: Code of practice fordesign of composite bridges'
Ref 7.N Highways England. CS 456, 'The assessment of steel highway bridges andstructures'
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CS 456 Revision 0 5. Informative references
5. Informative referencesThe following documents are informative references for this document and provide supportinginformation.
Ref 1.I BSI. BS 5400-2, 'Steel, concrete and composite bridges. Specification for loads'
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CS 456 Revision 0 Appendix A. Amendments to BS5400-3 for assessment
Appendix A. Amendments to BS5400-3 for assessment
16
17
Contents
1. Scope .......................................................................................................................................... 18
2. Normative references ................................................................................................................... 18
4. Assessment objectives ................................................................................................................ 19
5 Construction and workmanship .................................................................................................... 25
6 Properties of materials ................................................................................................................. 27
7 Global analysis for load effects .................................................................................................... 31
8 Stress analysis ............................................................................................................................. 33
9 Assessment of beams .................................................................................................................. 36
10 Assessment of compression members ..................................................................................... 75
11 Assessment of tension members .............................................................................................. 82
12 Assessment of trusses ............................................................................................................. 85
14 Assessment of connections ...................................................................................................... 87
15 Outmoded forms of construction ............................................................................................. 100
16 Bearings and bearing areas ................................................................................................... 104
Annex G - Equations used for production of curves in Figures .......................................................... 106
Annex H - Derivation of nominal yield stress for assessment ............................................................ 107
Annex I - Inspections for assessment................................................................................................ 111
Annex J - Determination of effective stiffener imperfection for stiffened compression flanges ........... 119
Annex K – Assessment of crossbeams in compression flanges ........................................................ 121
Annex L – Assessment of stiffened diaphragms not complying with limitations ................................. 125
Annex M – Critical buckling loads for battened members .................................................................. 137
Annex N – Modified critical buckling stress of stiffened panels utilising orthotropic actions ............... 139
Annex P – Effective width coefficients for plates unrestrained in plane along their longitudinal edges ......................................................................................................................................................... 153
Annex S – Shape limitations for assessment .................................................................................... 155
Annex T – Derivation of buckling coefficients for web panels ............................................................ 161
Annex Z – Bibliography to Appendix A .............................................................................................. 169
18
Appendix A – Amendments to BS5400-3 for assessment
[BS5400-3, Delete existing clause 1 and replace with the following] 1. Scope
This document shall be used for the assessment of steel highway bridges and their structural components.
NOTE 1 Assessment additions in this document extend BS 5400-3 to cater for the majority of existing steel highway bridges.
2. Normative references [BS5400-3, Add at end of clause 2]
BS 4360 BS 15 BS 153 BS 968 BS 4232 BS 5400-9 BS 5950 BS 5135: 1974 & 1984 BS 7910 BS 548 BS 2762
BS EN 1090-2 BS EN 1337 BS EN 1993-1-5 BS EN 1993-1-8 BS EN ISO 17635 BS EN ISO 17637 BS EN ISO 17640 BS EN ISO 13588 BS EN ISO 3542-1 BS EN ISO 10863
CS 454 CS 455 CS 457 CD 361
NOTE 1 Additional documents are listed in Annex Z. These relate to specific documents called up in the added text, as well as listing other background reading useful for the general interpretation of BS 5400-3 in the context of assessment.
19
4. Assessment objectives
[BS5400, Replace clause 4.1.1 with] 4.1.1 Assessment Basis
The basis of assessment shall align with the requirements of CS 454.
NOTE 1 This includes general requirements for verification that were covered by BS 5400-1.
The compliance criteria for assessment of structural steelwork in existing bridges shall be in accordance with the design requirements, except as amended for assessment.
Where other documents are used for derivation of load effects, analysis or other objectives, the principles and requirements of this document shall still be applied unless specifically stated otherwise.
The information used for assessment shall be established or verified as required by Annex I and the inspection requirements of CS 454.
NOTE 2 An initial (preliminary) assessment will usually be carried out prior to full assessment to determine the criticality of components and thus avoid undue detailed assessment, inspections and analyses on non-critical elements. See further comments in 8.5.1 and Annex I in relation to imperfections and inspection.
Assessment resistance shall be based on the requirements of this document.
For purposes of assessment, alternative methods of calculating strength or resistance of elements may be used provided that the results of an adequate number of representative laboratory tests are performed to enable the statistical relationships between the strength or resistance by the alternative methods and the observed results to be obtained.
The tests should be appropriate for the element being assessed with respect to:
1) Loading and support conditions;2) The effects of imperfections or eccentricities;3) Material properties;4) Dimensional parameters (such as slenderness);5) For elements where the strength is influenced by residual rolling or welding stresses, the
size and fabrication procedures of the specimens to be similar to those of the elementsbeing assessed.
NOTE 3 To provide significant benefit at least five relevant test results are generally needed, excluding any “outliers”.
The relevant material properties (such as yield stress) should be obtained for the components of the specimens and allowed for in the theoretical or empirical predictions.
Where geometric imperfections are important for models of failure, all relevant geometric imperfections in the specimen should be recorded and allowed for in the prediction method used, together with the actual cross sectional dimensions.
[BS5400-3, Replace clause 4.1.2 with] 4.1.2 Assessment loads and combinations
The loading for assessment of existing bridges shall be in accordance with CS 454.
20
The assessment should determine, in terms of vehicle loading, the carrying capacity of the structure as limited by the critical sections or elements.
4.2.2 Serviceability limit state [BS5400-3, Add at end of clause 4.2.2, under Table 1]
Where serviceability criteria in this standard cannot be met, the following information shall be determined and submitted to the Overseeing Organisation for approval before the assessment is undertaken:
1) the level of the serviceability criteria at which there would be a loss of utility or public concern or excessive permanent deflection
2) the proposed alternative criteria for assessment.
NOTE 1 The serviceability limit states for steel bridges are defined in 3.3 of BS 5400-1 and 4.2.2 of BS 5400-3 in general terms.
NOTE 2 The particular requirements of individual assessments can demonstrate the need for more specific serviceability checks or the possibility of accepting some levels of unserviceability depending on user requirements and individual circumstances.
NOTE 3 Where additional serviceability checks are required in further cases than Table 1 according to individual assessment circumstances, the requirements are set out in the relevant clauses.
NOTE 4 The following NOTES 5 to 10 are given in relation to Table 1 and the assessment notes where serviceability checks are required:
NOTE 5 For Clause 9.2.3.1(a), the value of the ratio between maximum and mean stress in particular will generally not be applicable and serviceability checks could be required for significantly lower ratios, (see 9.2.3 and use of ΨR). The intention of the check is to ensure that outer parts of wide flanges do not yield under SLS conditions with consequent loss of stiffness. For stiffened compression flanges this also serves as a control of premature buckling of the outermost stiffeners which have been designed elastically. The redistribution capacity of stiffened flanges cannot be simply determined even for compact sections. With possible lower ratios between 𝛾𝑓𝑙𝛾𝑓3 at ULS and that at SLS the serviceability check is ever more necessary (see further guidance in 9.2.3.1).
NOTE 6 Clauses 9.2.3.1(b) & 9.5.5 are intended as a control on permanent deformation under SLS conditions. Clearly the amount of permanent deformation depends on the proportions of a beam. 9.5.5 limits the strain allowed in the tension flange at ULS to twice the yield strain. With ratios between 𝛾𝑓𝑙𝛾𝑓3 for the two limit states (ie ULS/SLS) greater than 1.3 no yielding is expected at the SLS in a particular beam. Even in extreme cases the limitation on flange strain at the ULS serves to restrict permanent deformation at the SLS to a fraction of the elastic deflection.
NOTE 7 For Clauses 9.2.3.1(c) & 9.10.3.3, in assessment of the adequacy of existing beams, these clauses are necessary to limit permanent deflections under SLS loading. The limit to deformation of a deck plate is commonly set by criteria related to the performance of the surfacing. Permanent rutting could necessitate resurfacing. 9.10.3.3.1 deals with a loading condition not treated at ULS and in consequence the serviceability check of 9.10.3.3 is required.
NOTE 8 For Clauses 9.9.8 & 9.2.3.1(d), if the shape factor, S, is less than the ratio between 𝛾𝑓𝑙𝛾𝑓3 for the ULS and SLS respectively there can be no need for a SLS check for steel beams. However the check is included for assessment because it is increasingly likely for SLS to be critical due to the smaller partial factors which can used.
NOTE 9 For Clause 12.2.3, permanent strains due to secondary stresses are unlikely to cause permanent deflections of a bridge but they could cause buckling of non-compact sections. The check serves to avoid this (see further guidance in 12).
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NOTE 10 For Clauses 14.2.3 & 14.5.4.1.2, when deflections resulting from bolt slip are shown to have no adverse effects, the criteria are waived (see further guidance in 14).
4.3.2 Safety factor format [BS5400-3, Add at end of clause 4.3.2]
Where deterioration or damage has occurred to the structure which cannot be included in the resistance calculation using measured dimensions or imperfections, a condition factor shall be estimated to represent the resistance remaining.
Where a condition factor is required to be applied, the safety format to be used in applying the assessment requirements of this document shall be according to Equation 4.3.2:
(𝑒𝑓𝑓𝑒𝑐𝑡𝑠 𝑜𝑓 𝛾𝑓𝐿 , 𝑄𝑘) ≤𝐹𝑐(𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝜎𝑦 𝑎𝑛𝑑 𝑜𝑡ℎ𝑒𝑟 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠)
𝛾𝑓3𝛾𝑚 Equation 4.3.2
where
Fc is the condition factor.
𝑄𝑘, 𝛾𝑓𝐿 are the Actions and load factors according to [BD21].
NOTE 1 Condition factors are not intended to cover deficiencies of the materials in a structure that are separately allowed for in the calculation of resistance, for example in cases where the strength of deficient material is calculated from testing.
Loads used with the clauses in this document should not include 𝛾𝑓3 as a partial factor.
NOTE 2 The partial factor 𝛾𝑓3 in this document and in BS 5400-3 is already included as a reduction to the resistance and use on the load side would result in double counting.
[BS5400-3, Replace existing clause 4.3.3 with] 4.3.3 Values of partial factors
The partial factor 𝛾𝑓3 shall be taken from CS 454.
NOTE 2 The partial factor 𝛾𝑓3 is applied throughout this document as a reduction to the resistance in accordance with 4.3.2, which is different to the approach in CS 454.
Where measurements have been taken to verify the dimensional accuracy, the measured stresses closely resemble the load effects and approval from the Overseeing Organisation is obtained, the partial factor 𝛾𝑓3 may be reduced to 1.05 at the ultimate limit state.
The partial factor 𝛾𝑓𝐿 shall be taken from CS 454.
NOTE 3 Where permanent locked in effects occur due to the weight of formwork added and removed at different stages, the same partial factor 𝛾𝑓𝐿 applies for both addition and removal.
The partial safety factor 𝛾𝑚 shall be taken from Table 2, except where alternative methods of calculating strength and resistance are used.
22
Table 2 – Partial factors, 𝜸𝒎 = 𝜸𝒎𝟏𝜸𝒎𝟐
a) Ultimate limit state
The value of 𝛾𝑚 for the ultimate limit state should be taken as 1.05, except in the following clauses for which the appropriate value of 𝛾𝑚 is given.
Structural component and behaviour
Clauses 𝛾𝑚
Strength of longitudinal stiffeners
9.10.2.3a) and b), 9.11.5.2
1.20 (fibre in compression) 1.05 (fibre in tension)
Buckling resistance of stiffeners
9.13.5.3, 9.13.6, 9.14.4.3, 9.17.6.7, 9.17.7.3.2, 9.17.8
1.20
Fasteners in tension 14.5.3.2, 14.5.3.3, 14.5.3.5
1.20
Fasteners in shear 14.5.3.4 1.10
Friction capacity of HSFG bolts
14.5.4.2 1.30
Welds 14.6.3.11.1, 14.6.3.11.2, 14.6.2.11.3
1.20
Compression members 10.6.1.1, 10.6.3 0.95 +1.8
(𝐿
𝑟+5)
but not greater than 1.05
b) Serviceability limit state
The value of 𝛾𝑚 for the serviceability limit state should be taken as 1.00, except in the following clauses for which the appropriate value of 𝛾𝑚 is given.
Structural component and behaviour
Clauses 𝛾𝑚
Friction capacity of HSFG bolts
14.5.4.2 1.20
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Where alternative methods of calculating strength or resistance are used as permitted by 4.1.1, the value of resistance shall be taken as:
𝑅∗ =𝑅𝑘
𝛾𝑚𝛾𝑓3 Equation 4.3.3
where
𝑅𝑘 is the characteristic predicted resistance
𝛾𝑚 is calculated using the following equation instead of from Table 2:
𝛾𝑚 = (1.05 + 26.5 𝑚𝑐𝑣2)𝑚𝑚𝑒𝑎𝑛
𝑚𝑚𝑒𝑎𝑛 = 𝑚𝑡𝑒𝑠𝑡𝑠 + 𝑘𝑚𝑠𝑡
𝑚𝑐𝑣 = 𝑚𝑠𝑡/𝑚𝑡𝑒𝑠𝑡𝑠
𝑚𝑡𝑒𝑠𝑡𝑠 is the mean value of the ratios for each test between the resistance predicted using the proposed method and the measured resistance.
𝑚𝑠𝑡 is the standard deviation of the ratios for each test between the resistance predicted using the proposed method and the measured resistance.
𝑘 is a correction factor obtained from Table 4.3 in which n is the number of tests.
Table 4.3 – Sample standard deviation correction factor, k, for number of tests, n
n 2* 3* 4* 5 6 7 8 9 10 11 k 4.47 1.69 1.18 0.95 0.82 0.73 0.67 0.62 0.58 0.55
n 12 13 14 15 16 17 18 19 20 21 k 0.52 0.49 0.47 0.45 0.44 0.42 0.41 0.40 0.39 0.38
n 22 23 24 25 31 41 61 121 Ꚙ k 0.37 0.36 0.35 0.34 0.31 0.26 0.21 0.15 0.00
Note * The use of less than five tests is usually insufficient to give benefit. NOTE 4 This assessment addition provides the derivation of the partial factor 𝛾𝑚 for cases where
methods of prediction of strengths of elements differ from the methods in this document. Such alternative methods and their associated equations might offer advantages in instances in which more recent research may lead to improvement in prediction.
4.5.1 General [BS5400-3, Add at end of clause 4.5.1]
For existing bridges, any inaccessible surface that does not comply with 4.5.5.1 or 4.5.5.2 as appropriate shall be surveyed for corrosion losses in accordance with 8.7 and Annex I.
The thickness for assessment shall be in accordance with 8.7.
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4.5.2 Provision of drainage [BS5400-3, Add at end of clause 4.5.2]
Existing sealed box members and other hollow sections shall be inspected to determine whether water has collected in them.
Water shall not be permitted to remain or continue to collect.
NOTE 1 Water can collect in nominally sealed members, possibly due to condensation from air passing through small welding pores. This can cause bursting due to freezing and internal corrosion.
4.5.3 Sealing [BS 5400-3, Amend Clause 4.5.3]
The first two paragraphs shall be deleted for assessment.
[BS 5400-3, Replace existing clause 4.5.4 with] 4.5.4 Narrow gaps and spaces
NOTE 1 Not applicable for assessment.
[BS5400-3, Replace existing clause 4.5.6 with] 4.5.6 Thickness of weathering steel
The thickness of material for assessment shall be taken as the specified thickness at construction reduced by a corrosion allowance but not exceeding the current measured thickness.
The corrosion allowance should be taken in accordance with CD 340.
NOTE 2 The corrosion allowance for weathering steel is a reduction in thickness considered to cater for the loss of structurally effective material due to the developing rust patina during the remaining life of the structure.
NOTE 3 The loss of thickness is typically very small, but in some circumstances the material does not perform as intended and the corrosion is significant (e.g. with poor detailing or adverse environmental conditions).
Where weathering steel surfaces receive corrosion protective treatment, the corrosion allowance may be taken as zero.
For parts of a structure where the measured loss of thickness since the time of construction meets or exceeds the corrosion allowance, these parts shall be assessed based on the measured thickness and the parts protected by a corrosion protection system.
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5 Construction and workmanship 5.1 Workmanship [BS5400-3, Add at end of clause 5.1]
In the assessment of existing structures allowance shall be made for geometric and other imperfections in accordance with 8.5.
[BS5400-3, Replace existing clause 5.2 with] 5.2 Robustness
The load rating for the structure shall be determined without any reductions due to robustness.
Additionally, the robustness of the structure should be considered during the preliminary assessment.
Any areas of the structure having insufficient robustness such as to risk a loss of integrity in one or more critical structural components shall be considered for special assessment.
Details of the areas with insufficient robustness and proposals for special assessment (if any) shall be submitted for approval to the Overseeing Organisation before the assessment is undertaken.
[BS5400-3, Replace existing clause 5.4 with] 5.4 Composite steel/concrete construction
Where the strength of the shear connection between the materials in composite construction does not comply with the relevant ultimate limit state provisions of CS 457 and the strength of the concrete parts using CS 455, composite action shall not be assumed.
5.5 Built-up members [BS5400-3, Add at end of clause 5.5]
In assessment of built up members which do not comply with the design requirements, the connection of their elements shall comply with 14.
5.6 Diaphragms and fixings required during construction [BS5400-3, Add at end of clause 5.6]
Where permanent changes or residual effects arise from temporary attachments, the consequences shall be taken into account in assessment.
NOTE 1 Construction diaphragms and fixings can cause stress raisers and welding residual stress with the consequent potential risk of brittle fracture and fatigue. Where they have been removed it is possible that they can still cause adverse effects.
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[BS5400-3, Replace existing Clause 5.7 with] 5.7 Camber
NOTE 1 Not applicable to assessment.
5.9 Support cross beams [BS5400-3, Add at end of clause 5.9]
Where an existing bridge deck is supported on cross beams and also directly on one or more supports at a pier or abutment, the analysis shall represent the total support system and any restraints that it provides.
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6 Properties of materials [BS5400-3, Replace existing clause 6.1.1 with] 6.1.1 Performance
NOTE 1 Not applicable to assessment.
[BS5400-3, Replace existing clause 6.2 with] 6.2 Nominal yield stress
The nominal yield stress for assessment shall be derived in accordance with Annex H.
For assessment of critical components in existing structures, nominal measured material thicknesses should be used where possible.
For assessment of critical components in existing structures, the yield stress should be taken as either:
1) the specified minimum yield stress, or 2) the yield stress determined by test results without reduction to allow for thickness
variability.
NOTE 1 The values of nominal yield stress given in 6.2 of BS5400-3 allow for the tolerances in thickness for rolled materials and provide consistent characteristic values of the ratio of the product of yield stress and thickness to that of nominal thickness and specified minimum yield stress. This is not always the case for assessment because yield strength can be derived from testing, and therefore does not include an allowance for thickness tolerance, however this remains valid because the assessment is based on measured thickness (see 8.7) for critical components.
Where beams of hybrid construction using steel with different grades are assessed, each
part shall be assessed with the yield stress appropriate to that part.
6.3 Ultimate tensile stress [BS5400-3, Add at end of clause 6.3]
The ultimate tensile stress of tension elements and their connections of steel not complying with BS EN 10025, BS 4360, BS 15, BS 968 or BS5400-6 shall be established from mill test certificates or by tests on samples of the materials of the elements.
Where test data is used to derive the values of the ultimate tensile stress, the method shall be applied as for yield stress according to Annex H.
Where a plastic method of analysis is used in assessment in accordance with clause 7.5, the steel in the parts assumed to have plastic capacity shall comply with 1 or 2 below:
1) BS EN 10025, BS 4360, BS 15 or BS 968 2) have ultimate tensile stress not less than 1.1 𝜎𝑦
where
𝜎𝑦 is the nominal yield stress derived in accordance with Annex H.
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NOTE 1 The available data shows that, for particular samples of BS 4360 structural steels, the coefficients of variation of yield stress and of ultimate stress are similar. Thus, the assumptions made regarding the variability of yield stress are a reasonable basis for determining ultimate stresses.
The ultimate tensile stress may alternatively be assessed approximately by means of hardness test.
6.4 Ductility [BS5400-3, Add at end of clause 6.4]
Where one or more of the following methods are used for assessment:
1) plastic method of analysis is used in accordance with 7.5, or 2) the plastic moment capacity of a compact section is utilised, or 3) redistribution of tensile stress is assumed,
the ductility of the steel shall be not less than equivalent to an elongation of 15% on a gauge length 5.65(𝑆𝑜
0.5).
where
𝑆𝑜 is the original cross-sectional area of the test piece.
Where a plastic method of analysis is used, the strain capacity of the material at the ultimate tensile stress shall be at least 20 times the strain corresponding to the yield stress.
NOTE 2 In addition where plastic methods of global analysis are used, an adequate yield plateau is required. This is deemed to be satisfied if the stress-strain diagram for the steel shows that the ultimate strain corresponding to the ultimate tensile stress is at least 20 times the yield strain corresponding to the material yield stress.
6.5 Notch toughness 6.5.1 General [BS5400-3, Add at end of clause 6.5.1]
Existing structures shall meet the requirements of 6.5.4 or 6.5.5. Where structures do not comply with 6.5.4 or 6.5.5, the processes in 6.5.6 shall be applied.
NOTE 1 Earlier bridge design codes had lesser requirements for notch toughness, and sometimes none at all. The majority of bridges built before about 1970 therefore have, by today’s standards, either inadequate or unknown and probably inadequate notch toughness. These bridges have experienced low temperatures during service, with or without live load, depending on circumstances, yet there are very few recorded examples of failure due to brittle fracture.
6.5.2 Design minimum temperature [BS5400-3, Amend clause 6.5.2]
The definition of 𝑈𝑒 shall be replaced with:
𝑈𝑒 is the minimum effective bridge temperature given in CS 454, in degrees Celsius.
29
6.5.3.5 Rate of loading [BS5400-3, Add at end of clause 6.5.3.5]
Where the impact loading from over height vehicles is assessed and at least 5.3 m headroom is available, the value of 𝑘𝑠 should be taken as 1.0.
6.5.4 Maximum permitted thickness [BS5400-3, Add at end of clause 6.5.4]
The fracture toughness of the welds in tensile areas shall satisfy the minimum fracture toughness of the parent material or where permitted by BS5400-6 the relaxed limits for welds with overmatching strength.
[BS5400-3, Add new clause 6.5.5] 6.5.5 Energy Absorption
Where the requirements of 6.5.4 are not met, the energy absorption measured in joules, 𝐶𝑣, of the material used to resist the applied tensile stress shall satisfy the inequality in Equation 6.5.5.
𝐶𝑣 ≥𝜎𝑦
355(𝑡
2) , for type 1
≥𝜎𝑦
355(𝑡
4) , for type 2 Equation 6.5.5
where
type 1 is any part which is subjected to applied principal tensile stress at the ultimate limit state (ignoring geometric stress concentrations) greater than 100 N/mm2 and which in addition has either
1. any welded connection or attachment, or
2. welded repair of surface defects and has not been subsequently inspectedby crack detection of at least a 10% random sample, or
3. punched holes which have not been subsequently reamed.
type 2 is all parts subjected to applied tensile stress and which are not type 1.
𝐶𝑣 is the energy absorption in Charpy V-notch tests defined in BS EN 10025 and carried out at the design minimum temperature U (in joules).
𝜎𝑦 is the nominal yield stress.
𝑡 is the thickness of the plate or section in mm.
Where in the assessment of the adequacy of the bridge either the tensile components do not satisfy the provisions of 6.5.4 or the impact energy absorption values are unknown, the energy absorption of the material, 𝐶𝑣, may be determined by testing samples taken from non-critical areas of the components.
NOTE Recommendations and advice for test samples are given in Annex I.
30
The fracture toughness of the welds in tensile areas shall satisfy the minimum fracture toughness of the parent material or where permitted by BS5400-6 the relaxed limits for welds with overmatching strength.
[BS5400-3, Add new clause 6.5.6] 6.5.6 Assessment of risk for non-compliant structures
Where a structure does not comply with 6.5.4 nor 6.5.5, the risk level category shall be determined using the flow chart in Figure X.1 of Annex X.
Structures in the risk level 1 category may be deemed satisfactory with no further assessment. Structures in the risk level 2 category shall be deemed non-compliant unless they are demonstrated to be satisfactory by alternative criteria or information. Any alternative criteria and information shall be submitted to the Overseeing Organisation for approval.
NOTE 1 The flow chart Figure X.2 gives guidance on the action to be taken if Risk Level 2 has been identified.
NOTE 2 Where non-compliance with the requirements of 6.5.5 is shown and the structure cannot be shown to comply with risk level 1, it can still be possible to deem a bridge satisfactory based on its form of construction, the then current design codes and steel specifications, and the service history of the bridge. For example, bridges which have been in service for a long period might have sufficient notch toughness to withstand normal traffic.
The following information is important to provide in these circumstances:
1) details of investigations carried out including test results; and2) the load history e.g. actual abnormal load movements; and3) the service history e.g. operation at low or very low temperatures; and4) the details of any non-compliant joints; and5) any evidence of cracking at non-compliant joints.
Where the fracture toughness of the welds in tensile areas does not satisfy the minimum fracture toughness of the parent material for risk level 1 given on Figure X.1, the structure shall be treated as risk level 2.
6.7 Modular ratio [BS5400-3, Delete the first sentence of clause 6.7 and substitute the following]
For global analysis of composite bridges the modular ratios for stiffness according to CS 457 shall be used.
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7 Global analysis for load effects 7.1 Analysis general [BS5400-3, Add at end of clause 7.1]
Alternatively, a plastic method of analysis according to 7.5 may be used.
7.2 Sectional Properties [BS5400-3, Add at end of clause 7.2]
The sectional properties to be used for global analysis shall be calculated assuming one of:
1) the specified sizes, or 2) the specified sizes less the allowance for the loss of thickness in accordance with 4.5.6,
or 3) the measured sizes.
NOTE The reduction due to corrosion (see 8.7) can be ignored in the global analysis.
7.4 Construction in stages [BS5400-3, Add new clause 7.4]
Where the actual construction sequence is known in the assessment of an existing bridge, this actual construction sequence shall be used in the analysis.
Where the construction sequence is not known or is uncertain, a worst possible sequence shall be assumed which leads to maximum effects in the structural element being considered. For this purpose, the worst possible sequence shall be chosen from among a realistic set of possible construction sequences likely to have been considered at the time of construction.
NOTE 1 More than one possible sequence might be required for a bridge, each appropriate to different groups of structural elements.
7.5 Plastic methods of analysis [BS5400-3, Add new clause 7.5]
Where a plastic method is employed it shall take account of all parts of the structure which can participate in the global response and shall be able to follow the progressive development of plastic hinges (in parts which are essentially linear in configuration) and of yield lines.
Plastic methods of analysis shall be in accordance with 7.2.4 in BS 5400-1.
Where a plastic method of analysis is used, the following requirements shall be met:
1) The steel materials shall satisfy the appropriate requirements of 6.3 and 6.4. 2) The member cross sections shall satisfy the requirements of 9.3.8. 3) The structure shall be assessed in addition for the serviceability limit state using an
elastic method of analysis.
32
4) The assessment of supports, supporting structures, webs and connections shall be based on the most onerous of the load effects derived from plastic and elastic analysis respectively. Where a plastic method is used consideration shall be given to all adverse patterns of loading and potential failure mechanisms to determine those providing the least safety margins.
5) Lateral restraint to plastic hinges shall be provided as required in 9.12.6. 6) Slenderness of members shall satisfy the requirements of 9.7.6.
NOTE 1 Compact stocky beams designed by use of elastic methods of global analysis could have
some reserve of strength which could usefully be taken into account by means of the use of plastic analysis for assessment at the ultimate limit state.
7.6 Membrane action [BS5400-3, Add new clause 7.6]
Membrane action shall not be used except for accidental wheel loads to central reserves and outer verges.
33
8 Stress analysis 8.2 Analysis general [BS5400-3, Add at end of clause 8.2]
The effective breadth ratio, 𝜓, for assessment of composite bridges shall be in accordance with CS 457.
8.3 Distortion and warping stresses in box girders [BS5400-3, Add at end of clause 8.3]
Where the stiffness of a crossframe or diaphragm does not comply with the requirements of Annex B, distortional and warping stresses shall be calculated for 9.2.1.2 and 9.2.3.2 by analysis using a Finite Element plate model of the box girder and its diaphragms.
The Finite Element plate model for calculating distortional and warping stresses shall be of sufficient extent to ensure that the effects calculated are insensitive to the end conditions assumed.
8.5 Imperfections [BS5400-3, Add at start of clause 8.5]
Measurements of imperfections shall be carried out as necessary in accordance with Annex I.
In deciding on the criticality of components with strengths influenced by imperfections in accordance with Annex I, a preliminary assessment should be made of the differences between predicted strengths using values of imperfections of one half and twice the tolerances given in BS 5400-6.
Where the adequacy of any component depends on its actual imperfections or that preliminary inspection has indicated relatively large imperfections, accurate surveys should be carried out where possible in accordance with Annex I.
Measures shall be taken to determine the accuracy of the surveys.
The level of inaccuracy of the surveys shall be reviewed and an appropriate allowance made for the values used in subsequent assessment.
Where surveys are impractical the worst credible values of imperfections should be assumed, making use of remote visual observations or experience with other similar structures or any other available information.
NOTE 1 The assessment additions provide a basis for allowing for measured geometric imperfections in calculating load effects and strength. The need to survey the actual imperfections depends on the sensitivity of strength predictions to the magnitude of imperfection and on the potential benefits of reducing allowance. The sensitivity to imperfections depends on the structural configuration, particularly in relation to slenderness parameters.
34
8.5.1 Imperfections allowed for [BS5400-3, Add at end of clause 8.5.1]
Where bridges do not comply with the specification requirements of BS 5400-6 and BS 5400-9, the assessment shall use values of imperfection for bearing misalignment, errors in level, bearing inclination and imperfections in flatness and straightness that are determined by inspections and as described in Annex I.
Where measured imperfections of a structural element are greater than the BS5400 tolerances and explicit provision is not made in the assessment additions to include measured imperfection, the strength and stiffness of that element shall be assumed to be zero.
Where measured imperfections are less than the BS5400 tolerances, the benefit from reduced imperfections may be taken into account or the design strengths given in BS 5400-3 may be used.
Where imperfections are to be taken into account in assessment, they shall be assumed to be 1.2 times the measured imperfections to allow for inaccuracies of measurement.
NOTE 1 This factor of 1.2 is embodied into the relevant assessment additions, and could only be varied with the approval of the Overseeing Organisation where the nature and accuracy of the survey so warrants.
8.5.2.1 Torsionally stiff girders [BS5400-3, Add at end of clause 8.5.2.1]
For assessment the imperfections in common planarity of bearings shall be assumed to be 1.2 times the tolerances specified for the bridge or 1.2 times the imperfections recorded in as-built information.
Where specified tolerances or as-built information for common planarity is absent, imperfections shall be measured during preliminary inspections as described in Annex I and adopted in analysis of load effects.
8.5.2.2 Columns [BS5400-3, Add at end of clause 8.5.2.2]
For assessment all eccentricities of rocker bearings to the axes of columns shall be measured during detailed inspections as described in Annex I and the measured values allowed for in assessments of column strengths.
8.5.2.3 [BS5400-3, Add new clause 8.5.2.3] Other imperfections
Where inspection reveals detrimental imperfections or effects other than those described above, due allowance shall be made in the calculations for assessment in accordance with 8.5.1 and Annex I.
35
Members should be examined for presence of sharp notches, evidence of cracking, or curvature beyond twice the material thickness. For compression elements the remaining effectiveness of the section should be determined.
Where there is evidence of differential settlement having occurred then monitoring of such movements should take place over a period of time to determine the rate of settlement or whether seasonal movements are involved.
NOTE 1 Guidance on other defects is given in the Inspection Manual for Highway Structures (reference 8.5.1). In particular for steel bridges these defects could include:
1) Local damage to members, such as distortion of beam flanges due to accidental impact. 2) Differential settlement, which might be evident by observations of:
a. deformation of cracking in finishes; b. tilting of supports; c. departures from even road profiles.
Where as-built levels are available from the time of construction, the settlement shall be based on movement from the as-built profile to the current profile.
NOTE 2 It is assumed that the steelwork would have been adjusted during its erection (e.g. at the site splices as is usual practice) to suit any discrepancies of support levels. In this case the effects of such apparent differential settlement would not be present.
Where no as-built levels are available, the specified levels should be used instead.
8.7 Variations in structural dimensions [BS5400-3, Add new clause 8.7]
Measured section sizes shall be determined according to Annex I and used in assessment of strength of all critical sections.
Due account shall be taken of any existing losses of section due to corrosion.
Where it is impossible or impracticable to measure the actual dimensions of sound steel remaining in a corroded section (e.g. in unpainted non-corrosion resistance steel), an estimate should be made based on the original nominal dimensions minus a loss derived from an assumed rate of corrosion.
Where remedial action to reinforce the damaged part and to reliably protect it is not taken, allowance shall be made in the strength assessment for existing and future losses .
In the absence of other information the annual rates of corrosion at any surface of a section may be assumed to be equal to the extra thicknesses required under 4.5.5.1 divided by 240.
NOTE 1 Attention is drawn to the possibility that deep pitting corrosion can reduce not only the static strength of an element, but also its toughness and fatigue life.
NOTE 2 Section sizes for analysis in 7.2 can be based on specified or measured sizes, i.e. with or
without corrosion loss.
36
9 Assessment of beams 9.2.1.2 Effects to be considered [BS5400-3, Add at end of clause 9.2.1.2]
e) permanent stresses due to temporary works that is added and later removed during construction.
For composite girders, the loads considered at ULS shall be in accordance with CS 457 instead.
9.2.1.3 Effects that may be neglected [BS5400-3, Add at end of clause 9.2.1.3]
e) item (e) of 9.2.1.2 may be neglected at ULS provided that the requirements (1) and (2) of (d) are met.
For composite girders, the loads neglected at ULS shall be in accordance with CS 457 instead.
9.2.3.1 Serviceability limit state [BS5400-3, Add at end of clause 9.2.3.1]
NOTE 2 Studies have shown that the limiting value of 𝜓 can be typically less than 0.77(𝜎𝑚𝑎𝑥 > 1.30 𝜎𝑎𝑣), for which the SLS check governs. This is more likely to occur in cases where 𝛾 factors at ULS are reduced or where dead load effects are relatively high in proportion to live load effects. Both of these aspects can be common in assessment, e.g.:
1) Reduced surfacing and other superimposed load factors might be used for Assessment. 2) Reduced live load might be used for structures with a reduced load rating. 3) Other factors might be derived as part of the assessment procedure, e.g. material factors.
NOTE 3 The typical value referred to above is equivalent to:
𝛾𝑓3𝛾𝑚𝛾𝑓𝐿 = 1.1 × 1.05 × 1.125
= 1.3 (i.e. limiting 𝜓 = 0.77)
9.3.2.1 Flange outstands in compression [BS5400-3, Add at end of clause 9.3.2.1]
Non-complying outstands in compression shall be assessed according to 9.3.1.
NOTE 1 Although a limit is desirable for new structures to assist in avoiding wide outstands which may be prone to welding distortion by fabrication and to accidental damage, there appears to be no reason to downgrade strength if such limit is exceeded for assessment. It appears unlikely that the limit will actually be exceeded because of its historical use.
9.3.3.1 General [BS5400-3, Add at end of clause 9.3.3.1]
Where one or more of the following applies to openings:
37
1) openings are rounded with a radius of less than ¼ of the least dimension of the hole, or 2) openings do not comply with 9.3.3.2,
the openings shall be inspected individually for evidence of cracking and assessed for the effects of stress concentrations on fatigue life and on brittle fracture propensity.
For this purpose, stress concentrations shall be assessed using detailed local analyses, e.g. finite element analysis, where appropriate.
9.3.4.1.1 General [BS5400-3, Add at end of clause 9.3.4.1.1]
NOTE 1 For the assessment of non-complying stiffener configurations see 9.3.1 and Annex S.
Stiffeners with shapes other than those described shall be assessed on the basis of the nearest standard shape, in accordance with Figure 1A(c).
NOTE 2 Open stiffeners of forms other than those described in 9.3.4.1.2 – 9.3.4.1.5 have been used in the past, for example channel stiffeners were frequent in the days of riveted construction, with one flange riveted to the parent plate. In such cases the actual stiffener can usually be represented by an equivalent standard shape.
NOTE 3 The connected flange of riveted stiffeners may be considered in the effective section for stress analysis.
[BS5400-3, Replace existing clause 9.3.4.1.3 with] 9.3.4.1.3 Bulb flat stiffeners
Bulb flat stiffeners shall be assessed using 𝜎𝑦𝑠 derived from Annex S.
[BS5400-3, Replace existing clause 9.3.4.1.4 with] 9.3.4.1.4 Angle stiffeners
Angle stiffeners shall be assessed using 𝜎𝑦𝑠 derived from Annex S.
9.3.4.2 Closed stiffeners to webs and compression flanges [BS5400-3, Add at end of clause 9.3.4.2]
Where the shape limitation criteria in a) and b) are not satisfied and the gross area of a closed stiffener is to be included in the effective section, the adequacy of the stiffener parts shall be demonstrated for a compressive stress equal to the lower yield stress, 𝜎𝑦𝑠, applied over their gross area.
NOTE 1 Closed stiffeners are not prone to lateral torsional buckling, but their elements can be prone to plate panel buckling.
NOTE 2 The methods of 9.4.2.4 could be used to demonstrate adequacy under compressive stress of the individual flat plates forming a closed section.
38
[BS5400-3, Add new clause 9.3.4.3] 9.3.4.3 Combinations of closed and open stiffener
Where stiffeners are composed of a combination of closed and open sections, the proportions of individual components shall meet the requirements of 9.3.4.1 or 9.3.4.2 as appropriate.
Where an element is not connected directly to the parent plate, benefit shall not be assumed from the restraining effect of the parent plate when using Annex S or any other method.
NOTE 1 This is intended to cover, for example, the case of “wine-glass” stiffeners (see Figure 1A). In this case the tee portion is not connected directly to the plate and hence no advantage can be taken of the restraining influence of the plate. This means that the option to use Figure 4(b) is not available (or at least b becomes very large which effectively limits
𝑑𝑠𝑡𝑠√𝜎𝑦𝑠
355
to 7 unless a higher value can be obtained from Figure 4(a)).
Figure 1A(a) – Geometric notation for rolled beam sections that may be encountered in
assessments
39
Figure 1A(b) – Geometric notation for fabricated beam sections that may be encountered in
assessments
40
Figure 1A(c) – Geometric notation for flange plate and web stiffeners that may be encountered in
assessments
41
Figure 1A(d) – Geometric notation for trough stiffeners that may be encountered in assessments
9.3.5 Flanges curved in elevation [BS5400-3, Add at end of clause 9.3.5]
Flanges that are curved in elevation but not complying with the above shall be analysed in detail allowing for the effects of curvature on the stability of the elements.
9.3.6 Circular hollow sections [BS5400-3, Add at end of clause 9.3.6]
The lower yield stress, 𝜎𝑦, may be taken as the larger of the value obtained from Equation 9.3.6 and the value satisfying the shape limitation in this clause for design.
𝜎𝑦
𝜎𝑜 = (60
𝑡
𝑑)0.5
But not greater than 1 Equation 9.3.6
where
𝑡 is the wall thickness of the circular hollow section
𝑑 is the diameter of the circular hollow section
𝜎𝑜 is the nominal yield strength of the material as defined in 6.2.
9.3.7 Compact sections 9.3.7.1 General [BS5400-3, Add at end of clause 9.3.7.1]
Where any part of a cross section fails to comply with the appropriate requirements, the complete section shall be assessed as non-compact.
42
9.3.7.2 Webs [BS5400-3, Add at end of clause 9.3.7.2]
As an alternative to the requirements for design in this clause, webs satisfying the provisions of 9.3.8.2 may be considered as compact.
[BS5400-3, Add new clauses 9.3.8 and 9.3.8.1] 9.3.8 Plastic Sections 9.3.8.1 General
The use of plastic sections and analysis shall be in accordance with 7.5.
Plastic sections shall possess adequate ductility to enable them to carry the full plastic moment whilst allowing rotation at a plastic hinge to occur.
Rolled or fabricated I-beams, channels and hollow sections may be taken to have plastic sections provided that:
a. They meet the limitations of shape defined in 9.3.8.2 to 9.3.8.4, and. b. The steel materials satisfy the requirements of 6.3 and 6.4.
Longitudinal stiffeners, if any, in areas of compression shall be ignored in calculating the section properties and in deriving the strength of a beam.
All parts of the cross section including stiffeners shall comply with the appropriate requirements.
[BS5400-3, Add new clause 9.3.8.2] 9.3.8.2 Webs
For plastic sections, the depth between the plastic neutral axis of the beam and the compressive edge of the web, 𝑑1, shall not exceed the limits of the inequality in Equation 9.3.8.2a for the case when 𝑑1 ≤ 0.5 𝑑𝑤 and Equation 9.3.8.2b for the case when 𝑑1 > 0.5 𝑑𝑤.
𝑑1 ≤ 28𝑡𝑤√355
𝜎𝑦𝑤 , for 𝑑1 ≤ 0.5 𝑑𝑤 Equation 9.3.8.2a
𝑑1 ≤ 𝑡ℎ𝑒 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑜𝑓
{
(32 −8𝑑1
𝑑𝑤) 𝑡𝑤√
355
𝜎𝑦𝑤
𝑎𝑛𝑑 24𝑡𝑤√355
𝜎𝑦𝑤
, for 𝑑1 > 0.5 𝑑𝑤
Equation 9.3.8.2b
where
𝑡𝑤 is the thickness of the web plate
𝑑𝑤 is the depth of the web as defined in Figures 1 and 1A
𝜎𝑦𝑤 is the nominal yield stress of the web material as defined in 6.2.
43
NOTE 1 Generally the rules in BS EN 1993-1-1 are less severe for Class 1 sections than the rules for compact sections in BS 5400-3. The one exception is for webs primarily in compression, but with the neutral axis within the depth of the web. As in plastic design, the stress blocks are rectangular rather than triangular, the web will be more prone to instability when the distance from the plastic neutral axis to the compression edge is fairly large. The rules quoted are always more stringent than those in BS EN 1993-1-1, and follow it for 𝑑1 ≤ 0.5 𝑑𝑤. For larger 𝑑1 there is a linear reduction until the whole web is in compression.
For comparison, BS EN 1993-1-1 gives 29.3𝑡𝑤 for 𝑑1 ≤ 0.5 𝑑𝑤 falling off (not linearly) to 26.85𝑡𝑤 for 𝑑1 = 𝑑𝑤. It is noted however, that BS EN 1993-1-1 defines the depth of the web differently from BS5400-3 and in consequence the Figures are not exactly comparable. The necessary correction has been made to allow for the fact that BS EN 1993-1-1 is based on a yield of 235 N/mm2 instead of 355 N/mm2.
[BS5400-3, Add new clause 9.3.8.3] 9.3.8.3 Compression flanges
For plastic sections the compression flanges shall comply with the provisions for compact flanges given in 9.3.7.3.
NOTE 1 In all cases the BS EN 1993-1-1 rules for Class 1 sections are less severe than the BS 5400-3 rules for compact sections, hence the latter are adopted for assessment.
[BS5400-3, Add new clause 9.3.8.4] 9.3.8.4 Circular hollow sections
For plastic sections the ratio of the outside diameter to the wall thickness of a circular hollow section shall not exceed:
33 (355
𝜎𝑦)
where
𝜎𝑦 is the nominal yield stress of the material of the circular hollow section as defined in 6.2.
9.5.6 Transverse stresses in webs [BS5400-3, Add at end of clause 9.5.6]
In the case of riveted construction, transfer of load by direct bearing between flange plate and web shall not be assumed unless reasonable evidence of direct contact is available, for example by sight of the end of the beam.
9.6.1 General [BS5400-3, Add at end of clause 9.6.1]
Where the resistance of the restraining systems is less than required to resist force 𝐹𝑆 under 9.12.5.2.1, then the slenderness parameter 𝜆𝐿𝑇 appropriate to the length 𝑙𝑒 at the support under consideration, shall be taken as 𝜆′𝐿𝑇 from Equation 9.6.1.
44
𝜆′𝐿𝑇 =𝜆𝐿𝑇
√1
8(5𝐹𝑆𝐷𝐹𝑆
+3) Equation 9.6.1
where
𝜆′𝐿𝑇 is a modified value of 𝜆𝐿𝑇
𝜆𝐿𝑇 is as defined in 9.7.2
𝑙𝑒 is as defined in 9.6.2
𝐹𝑆 is as defined in 9.12.5.1
𝐹𝑆𝐷 is the available resistance which is less than 𝐹𝑆 excluding the effects of wind, frictional and other applied forces.
Stiffeners at supports shall be checked to ensure that they can withstand the applied load effects.
NOTE 1 The assessment addition allows for the case where the restraining system at supports does not comply with the strength requirements in 9.12.4.
9.6.4.1.1.1 Beams with fully effective lateral restraints at the level of a compression flange [BS5400-3, Amend clause 9.6.4.1.1.1]
The note shall be deleted.
9.6.4.1.2 Beams with discrete torsional restraints [BS5400-3, Amend clause 9.6.4.1.2]
The definition of 𝑙𝑤 shall be replaced with:
𝑙𝑤 is the assumed half-wavelength of buckling. The value of 𝑙𝑤 should generally be taken as the span length 𝐿. However, to guard against the possibility of a mode of buckling with multiple half-wavelengths within the length 𝐿, the limiting moment of resistance 𝑀𝑅 in accordance with 9.8 should also be checked considering values of 𝑙𝑤 corresponding to sub-multiples of the span 𝐿.
The parameter 𝑚 shall be replaced by the parameter 𝑛, in the definitions of 𝜃𝑅, 𝜃𝑅1, 𝜃𝑅2.
The parameter 𝑚 and its definition shall be replaced by the parameter 𝑛, defined as:
𝑛 is the number of discrete restraints in the half wavelength of buckling ( = 1 for a single restraint in the centre of a half wavelength).
NOTE 2 shall be replaced with: “NOTE 2 Note is deleted.”
In the expression for 𝜃𝑅2 in NOTE 5, the parameter 𝑚 shall be replaced by the parameter 𝑛 and the remainder of the sentence deleted after “the spacing of the beams”.
45
9.6.4.1.3 Beams restrained by U-frames [BS5400-3, Add at end of clause 9.6.4.1.3]
NOTE 2 Where the end supports in half-through bridges do not provide sufficient torsional restraint, the critical buckling stress for the compression flanges can be significantly less than that for rigid supports. Such supports could, for example, consist of U-frames similar to intermediate frames with the posts supported on knuckle bearings.
9.7.2 Uniform I, channel, tee or angle sections [BS5400-3, Amend clause 9.7.2]
In NOTE 3 in Table 9, the expression for v shall be replaced by:
𝑣 = [{4𝑖(1 − 𝑖) + 0.05𝜆𝐹2 +𝜓𝑖
2}0.5+ 𝜓𝑖]
−0.5
The existing definition for k4 shall be deleted and replaced by the new definitions as follows:
𝑘4 should be taken as:
= [4𝑍𝑝𝑒
2(1−𝐼𝑦
𝐼𝑥)
𝐴2ℎ2]
0.25
, for flanged beams symmetrical about the minor axis, or as
= [𝐼𝑦𝑍𝑝𝑒
2(1−𝐼𝑦
𝐼𝑥)
𝐴2𝐶𝑤]
0.25
. for flanged beams symmetrical about the major axis, or as
= 1 , for all other beams.
For composite beams in which the area of longitudinal reinforcement in the slab is at least 25% of the area of the steel top flange, the value of 𝑘4 may be taken as:
= [0.64 −0.213
𝑑𝑓2 𝐵𝑓
2]0.25
, but not less than 0.6
𝐶𝑤 is the warping constant. 𝐶𝑤 may be taken equal to
𝑑𝑓2𝑡𝑓𝑡𝑡𝑓𝑏𝐵𝑓𝑡
3𝐵𝑓𝑏3
12(𝑡𝑓𝑡𝐵𝑓𝑡3 + 𝑡𝑓𝑏𝐵𝑓𝑏
3)
𝑍𝑝𝑒 is as defined in 9.7.1
𝐴, 𝐼𝑥, 𝐼𝑦 are as defined in 9.7.3.1
𝑑𝑓 is as defined in 9.9.3.1
𝑡𝑓𝑡 , 𝐵𝑓𝑡 are the thickness and width respectively of the top flange
𝑡𝑓𝑏 , 𝐵𝑓𝑏 are the thickness and width respectively of the bottom flange
ℎ is the distance between centroids of the flanges
𝐵𝑓 is the average width of the two flanges, the top flange width being taken as the effective width of the slab
46
The following text shall be added at the end of the definition for 𝜂, after "other loading patterns;"
Where ‘𝑀𝐴/𝑀𝑀’ is greater than + 1.0 the value of "𝜂" shall be taken as 1.0.
[BS5400-3, Add at end of clause 9.7.2, before Table 9]
NOTE 3 For composite flanges described in note 2, the composite properties and thickness "𝑡𝑓" of the flange will have contributions from both the steel flange plate and equivalent properties of attached concrete or reinforcement as appropriate.
NOTE 4 Angle sections used alone as beams are not covered by the above. The behaviour of angle sections is affected by the non-coincidence of the principal U-U and V-V axes.
NOTE 5 The 𝑘4 factor (taken on 0.9 for rolled sections and 1.0 for all other beams) is an approximation that is reasonably conservative for design and is a simplification of the factor u given in BS 5950 Annex B. The replacement factors that can be used for assessment can be less conservative for general cases of beams symmetrical about either of the main axes and can thus be of benefit in assessment. Similarly for rolled sections symmetrical about either of the main axes, the buckling parameter given in published tables can be used in lieu of 𝑘4. The expression given for composite beams has is based on a practical range of composite sections, and could have a significant benefit for assessment in some cases.
9.7.6 Slenderness limitations for plastic analysis [BS5400-3, Add new clause 9.7.6]
Where sections are assessed using plastic methods of analysis (see 7.5), the slenderness parameter 𝜆𝐿𝑇√𝜎𝑦𝑐 355⁄ shall not exceed 30.
[BS5400-3, Replace existing clause 9.8 and Figure 11 with] 9.8 Limiting moment of resistance
The limiting moment of resistance, 𝑀𝑅, shall be obtained from Figure 11a) for beams fabricated by welding (excluding local welding of stiffeners) or Figure b) for all other sections (including stress relieved welded sections) according to the value of:
𝜆𝐿𝑇√(𝜎𝑦𝑐
355) (
𝑀𝑢𝑙𝑡
𝑀𝑝𝑒)
where
𝜆𝐿𝑇 is obtained from 9.7
𝑀𝑢𝑙𝑡 is the moment of resistance of the cross-section if lateral torsional buckling is prevented, i.e.: 𝑀𝑢𝑙𝑡 = 𝑀𝑝𝑒 , for compact sections, or 𝑀𝑢𝑙𝑡 =the least of 𝑍𝑥𝑐𝜎𝑦𝑐, 𝑍𝑥𝑡𝜎𝑦𝑡 or 𝑍𝑥𝑤𝜎𝑦𝑤 for non compact sections.
𝑀𝑝𝑒 is equal to 𝜎𝑦𝑐𝑍𝑥𝑐,𝑔𝑟𝑜𝑠𝑠 for beams restrained in accordance with 9.6.4.1.3 or 9.6.4.2 for which 𝑙𝑒 is greater than 𝑙𝑅, where 𝑍𝑥𝑐,𝑔𝑟𝑜𝑠𝑠 is the elastic modulus of the effective section with respect to the extreme compression fibres without deduction for any holes in the flanges or webs, or for all other beams is as defined in 9.7.1.
47
𝑍𝑥𝑐 , 𝑍𝑥𝑡 , 𝑍𝑥𝑤 are as defined in 9.7.1
𝜎𝑦𝑐 is the nominal yield stress value as defined in 9.3.1 for the compression flange material. Where gross section properties have been used in accordance with note 2 of 9.4.2.4, 𝜎𝑦𝑐 should be taken instead as the nominal yield stress value from 9.3.1 multiplied by 𝐴𝑒 𝛴𝑏𝑒 𝐴𝐵𝑓⁄ .
𝐴𝑒 , 𝐵𝑓 , 𝛴𝑏𝑒 are as defined in 9.4.2.4
𝐴 is the gross cross-sectional area of the flange
𝜎𝑦𝑡 is the nominal yield stress of the tension flange material as defined in 6.2.
𝜎𝑦𝑤 is the nominal yield stress of the web material as defined in 6.2.
The limiting moment of resistance, 𝑀𝑅, shall under no circumstances be greater than 𝑀𝑝𝑒 from 9.7.1.
NOTE 1 For assessment, the quickest and most accurate results are often obtained using 9.7.5 in conjunction with Finite Element methods to determine the bending moment for elastic critical buckling, 𝑀𝑐𝑟.
Note Expressions for replacement curves are given in Annex G.
Figure 11 – Limiting moment of resistance, 𝑴𝑹
Where in assessment of the adequacy of a beam allowance is to be made for initial departures from straightness of the flanges 𝛥𝐹 (measured in accordance with Table 8 of BS5400-6), 𝑀𝑅/𝑀𝑈𝐿𝑇 shall be calculated from the equation in G.8 with 𝜂 taken as:
𝜂 = 0.008(𝛽 − 30) + (𝛽−30
𝛽) [1.2𝛥𝐹 − 0.0012𝑙]
𝑦
𝑟𝑦2 for beams fabricated by welding, or
48
𝜂 = 0.0035(𝛽 − 30) + (𝛽−30
𝛽) [1.2𝛥𝐹 − 0.0012𝑙]
𝑦
𝑟𝑦2 for other sections,
but in no case less than zero.
where
𝛥𝐹 is the greater of the values measured in accordance with 4(a) and 4(b) respectively of Table 5 of BS 5400-6 over a gauge length equal to the length of the beams between points of effective lateral support.
𝑦 is the distance in the x-direction from the y-y centroid axis to the extreme fibre of the compression flange (see Figure 1).
𝑟𝑦 is the radius of gyration of the gross cross section about its y-y axis.
𝑙 is the gauge length to measure 𝛥𝐹 .
NOTE 2 The replacement form of the term, 𝜂, is based on the equivalent Perry coefficient adopted in
BS5400-3 but modified to allow for differences between actual out-of-straightness and the tolerances assumed in BS5400-3. The formula follows the empirical equation used in the calibration of BS5400-3 against test results as given in G.8.
9.9.4.2 Buckling of beam [BS5400-3, Add at end of clause 9.9.4.2]
As an alternative to the requirements of this clause for design, a uniform beam of I section subject to combined bending and axial compression may be deemed to pass assessment provided the following inequality is satisfied:
𝛾𝑚𝛾𝑓3𝑃𝑚𝑎𝑥
𝐴𝑒+𝛾𝑚𝛾𝑓3𝑀𝑥𝑚𝑎𝑥
𝑍𝑥𝑐+𝛾𝑚𝛾𝑓3𝑀𝑦𝑚𝑎𝑥𝑁𝑦
𝑍𝑦𝑐+ 𝜋2𝐸𝜂 (
𝑟𝑦
𝑙𝑒)2
(𝐾𝑦
1 − 𝐾𝑦) ≤ 𝜎𝑦𝑐
where
𝐴𝑒 is the effective cross-sectional area of the beam as defined in 10.5.2
𝑍𝑥𝑐 is the section modulus with reference to the x-x axis and the extreme fibres of the compression flange
𝑍𝑦𝑐 is the section modulus with reference to the y-y axis and the extreme fibres in bending compression
𝑁𝑦 = 1 +4
𝜋(𝐾𝑦
1+𝐾𝑦) (1 + (
𝑀𝑥𝑚𝑎𝑥
𝑀𝑐𝑟) 𝑣2)
𝐾𝑦 =𝑃𝑚𝑎𝑥𝑙𝑒
2
𝜋2𝐸𝐼𝑦+ (
𝑀𝑥𝑚𝑎𝑥
𝑀𝑐𝑟)2
𝐾𝑝 =𝑃𝑚𝑎𝑥𝑙𝑒
2
𝜋2𝐸𝐼𝑦
𝑀𝑐𝑟 =𝜋2𝐸𝑍𝑥𝑐
𝜆𝐿𝑇2
𝜎𝑦𝑐 is as defined in 9.8
49
𝜆𝐿𝑇 , 𝑣, 𝑙𝑒 are as defined in 9.7.2
𝜂 is:
= 0.0062(𝑙𝑒
𝑟𝑦− 15)
𝐾𝑝
𝐾𝑦+ 0.008(𝛽 − 30)
𝑀𝑥𝑚𝑎𝑥2
𝑀𝑐𝑟2𝐾𝑦
(1 +𝑣2𝑀𝑐𝑟
𝑀𝑥𝑚𝑎𝑥) for beams fabricated
by welding, or
= 0.0062(𝑙𝑒
𝑟𝑦− 15)
𝐾𝑝
𝐾𝑦+ 0.0035(𝛽 − 30)
𝑀𝑥𝑚𝑎𝑥2
𝑀𝑐𝑟2𝐾𝑦
(1 +𝑣2𝑀𝑐𝑟
𝑀𝑥𝑚𝑎𝑥) for all other sections.
𝛽 is as defined in G.8
NOTE 2 The alternative criterion has been developed from work on beams subject to axial
compression and combined bending about the major and minor axes. It has been particularly developed for the most common case of I-beams but could be potentially applicable to other sections such as hollow sections, channels and (possibly) tees, provided the validity is demonstrated. The alternative criterion could be less conservative when neither axial compression nor bending effects individually are near to their limiting values.
9.9.5 Beam built in several stages 9.9.5.1 General [BS5400-3, Add at end of clause 9.9.5.1]
Where temporary overstress is identified in the structure during the stages of construction, the temporary overstress may be deemed not to affect the final condition provided the structure is examined for possible signs of damage in areas which the calculations suggest have been overstressed.
9.10.2.2 Effective section for longitudinal flange stiffeners [BS5400-3, Add at end of clause 9.10.2.2]
As an alternative to the requirements of this clause for design, stiffeners may be assessed using an alternative effective section to calculate longitudinal stress, 𝜎𝑎, in accordance with a), b) and c) below.
NOTE 1 Where these alternative methods are used to calculate longitudinal stress, 𝜎𝑎, the values of 𝑘𝑙1, 𝑘𝑠1, 𝑘𝑙2 and 𝑘𝑠2 are calculated differently according to 9.10.2.3 and 9.10.3.3.2.
NOTE 2 The calculations are complicated by the differences between the secant stiffness (related to 𝐾𝑐′) and the tangent stiffness (related to 𝐾𝑐′′) and the need for iterative calculations. The parameters are listed below in the sequence of calculation with the iteration steps described. Where 𝐾𝑐′ or 𝐾𝑐′′ are used for multiple flange panels in one cross section, the iterations are carried out for all the panels together.
a) For checking against criterion (a) in 9.10.2.3
𝜎𝑎 may be calculated using an effective section of the beam based on 𝐾𝑐 = 𝐾𝑐′.
where
𝐾𝑐′ (step 1) is obtained by iteration from Figure 5a using parameters 𝜆 and 𝜎𝑎′/𝜎𝑦𝑒. For the first iteration, 𝐾𝑐′ can be guessed, or taken as 𝐾𝑐 from Figure 5.
50
𝜎𝑦𝑒 is according to 9.10.2.3
𝜆 is the slenderness parameter of the plate for use in Figure 5a and 5b, 𝜆 =
𝑏
𝑡𝑓√𝜎𝑦𝑒
355
𝜎𝑎 (step 2) is the stress at the stiffener centroid, calculated using an effective section of the beam and stiffener based on 𝐾𝑐 = 𝐾𝑐′.
𝜎𝑎′ (step 3) is the assumed mean stress over the gross area of the plate taken as:
𝜎𝑎′ = 𝐾𝑐′𝜎𝑎𝛾𝑚𝛾𝑓3
𝜎𝑎′
𝜎𝑦𝑒 (step 4) is the parameter for use in Figure 5a for the next iteration (from step 1).
Iteration continues until 𝜎𝑎′
𝜎𝑦𝑒 converges.
The tangent modulus, 𝐾𝑐′′, should be calculated from Figure 5b after the above iterations have converged and using the converged parameters.
NOTE 3 The strength of a stiffener with a large outstand is commonly governed by compressive
failure of the outstand (by 9.10.2.3). In such cases the coincident stress in the plate when yield occurs in the outstand is less than the average stress on the effective section. Consequently, the section properties to be used in assessing strength for outstand failure are based on plate effective width coefficients relating to a stress on the plate of 𝜎𝑎𝛾𝑚𝛾𝑓3. The effective width coefficients based on this stress are typically larger than the plate effective width coefficients that would otherwise be used (i.e. larger than 𝐾𝑐 relating to strength, from Figure 5).
b) For checking against criterion (b) in 9.10.2.3 and criterion (c) in 9.10.3.3.2
𝜎𝑎 and 𝜎𝑓𝑧 may be calculated using a beam effective section and stiffener effective section based on 𝐾𝑐 = 𝐾𝑐′.
where
𝐾𝑐′ is obtained from Figure 5a using 𝜆 and 𝜎𝑎′/𝜎𝑦𝑒
𝜆 is the slenderness parameter of the plate for use in Figure 5a and 5b, 𝜆 =
𝑏
𝑡𝑓√𝜎𝑦𝑒
355
𝜎𝑎′/𝜎𝑦𝑒 is the parameter for use in Figure 5a and 5b. For this case, 𝜎𝑎′/𝜎𝑦𝑒 = 𝐾𝑐 , where
𝐾𝑐 is according to Figure 5.
The tangent modulus, 𝐾𝑐′′, should be calculated similarly from Figure 5b using the parameters above.
c) For checking against criterion (b) in 9.10.3.3.2
𝜎𝑎, 𝜎𝑓𝑜 and 𝜎𝑓𝑧 may be calculated using a beam effective section and stiffener effective section based on 𝐾𝑐 = 𝐾𝑐′.
where
51
𝐾𝑐′ (step 1) is obtained by iteration from Figure 5A using the parameters 𝜆 and 𝜎𝑎′/𝜎𝑦𝑒. For the first iteration, 𝐾𝑐′ can be guessed, or taken as 𝐾𝑐 from Figure 5.
𝜎𝑦𝑒 is according to 9.10.2.3
𝜆 is the slenderess parameter of the plate for use in Figure 5a and 5b, 𝜆 =
𝑏
𝑡𝑓√𝜎𝑦𝑒
355
𝜎𝑎 (step 2) is the stress at the stiffener centroid due to global effects, calculated using an effective section of the beam and stiffener based on 𝐾𝑐 from Figure 5.
𝜎𝑎′ (step 3) is the assumed mean stress over the gross area of the plate,
𝜎𝑎′ = 𝐾𝑐′(𝜎𝑎 − 𝜎𝑓𝑧)𝛾𝑚𝛾𝑓3
𝜎𝑓𝑧 is the stress in the flange plate due to local bending, calculated using an effective section of the stiffener based on 𝐾𝑐 = 𝐾𝑐′. 𝜎𝑓𝑧 is taken from the same longitudinal position as the stiffener stress, 𝜎𝑓𝑜. 𝜎𝑓𝑧 is assumed to be tensile (for which it is taken as +ve) when 𝜎𝑓𝑜 is in compression.
𝜎𝑎′/𝜎𝑦𝑒 (step 4) is the parameter for use in Figure 5a for the next iteration (from step 1).
Iteration continues until 𝜎𝑎′
𝜎𝑦𝑒 converges.
The tangent modulus, 𝐾𝑐′′, should be calculated from Figure 5b after the above iterations have converged and using the converged parameters.
NOTE 4 Since the tangent stiffness is lower it is conservative to use 𝐾𝑐′ = 𝐾𝑐′′ , for each of a), b) and c) above, for the appropriate criterion in calculating 𝜎𝑎 and 𝜎𝑎′ , thereby obviating the need for using different section properties to calculate the values of the different parameters.
The Figures 5a and 5b shall not be used for plates with imperfections exceeding the BS 5400-6 tolerances.
Annex P may be used in place of Figures 5a and 5b for determination of 𝐾𝑐′ and 𝐾𝑐′′.
NOTE 5 Annex P can be applied where tolerances of a plate are smaller or larger than the BS5400-6 tolerances.
NOTE 6 The rules for calculation of the effective widths of flange given in 9.4.2.4 were derived so that the compressive strength of plate panel is given by 𝐾𝑐𝜎𝑦 × 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑡𝑒. As a conservative simplification the axial tangent stiffness and secant stiffness of a panel are also taken as those corresponding to the same effective width. The plate strength effective widths apply to plates having residual stresses equal to 0.1𝜎𝑦.
NOTE 7 The effective width coefficients 𝐾𝑐′ and 𝐾𝑐′′are derived for plates unrestrained in-plane along their edges and are consequently conservative for restrained plates.
52
Figure 5a – Coefficient for plate panels under direct compression
53
Figure 5b – Coefficient for plate panels under direct compression
54
9.10.2.3 Strength of longitudinal flange stiffeners [BS5400-3, Add at end of clause 9.10.2.3]
Allowance may be made for orthotropic action of a stiffened flange with or without intermediate transverse stiffeners by calculating 𝑟𝑠𝑒 instead by Equation 9.10.2.3 and assuming 𝑘𝑠1 = 𝑘𝑠2 = 0.
𝑟𝑠𝑒 = √𝜎𝑐𝑟1∗′ 𝑙2
𝜋2𝐸 Equation 9.10.2.3
where
𝜎𝑐𝑟1∗′ is the modified critical buckling stress derived in accordance with Annex N.
Where overall buckling under the complete stress field is considered in calculation of 𝜎𝑐𝑟1∗′ for a multi-stiffened panel between its boundaries or between intermediate transverse stiffeners, 𝑘𝑠1 and 𝑘𝑠2 may be taken as zero.
𝜎𝑐𝑟1∗′ shall be calculated according to Annex N.
Where in accordance with 8.5 assessment is to be based on measured imperfections in straightness of stiffeners, l/625 in the equation for 𝛥 shall be replaced by 1.2|𝛥𝑠𝑥|𝑒𝑓𝑓.
The parameter |𝛥𝑠𝑥|𝑒𝑓𝑓 shall be determined from the measurements in accordance with Annex J and be taken with a positive sign when applied in this clause.
Where imperfections are measured and allowance is made for orthotropic action, values of 𝛥𝑠𝑥 may be measured using the gauge length G according to Annex N.
Where the longitudinal stress, 𝜎𝑎, is calculated using the secant modulus 𝐾𝑐′ instead of 𝐾𝑐, the radius of gyration of the effective section of the longitudinal stiffener, 𝑟𝑠𝑒, should be calculated from one of the following two methods:
1) Using Equation 9.10.2.3a above, accounting for orthotropic action.
2) According to 𝑟𝑠𝑒 = √𝐼𝑜𝑥
𝐴𝑠𝑒, where 𝐼𝑜𝑥 is the second moment of area of the effective section
according to 9.10.2.2 with 𝐾𝑐 taken as the tangent modulus 𝐾𝑐′′ and 𝐴𝑠𝑒 is the area of the effective section according to 9.10.2.2 with 𝐾𝑐 taken as the secant modulus 𝐾𝑐′.
NOTE 2 The use of different moduli, 𝐾𝑐′ and 𝐾𝑐′′ in (2) above ensures that the elastic critical buckling is given with respect to the total load in the stiffener and based on a stiffness derived using the tangent modulus.
Where in criterion (b) the modified values of 𝐾𝑐 = 𝐾𝑖 given in 9.10.2.2 are used to calculate stress, the following shall apply:
1) 𝑘𝑙2𝜎𝑦𝑒
𝛾𝑚𝛾𝑓3 shall be factored by [𝐾𝑐
𝐾𝑐′], and
2) 𝑘𝑠2 and 𝑘𝑙2 shall be derived from Figure 19 using 𝜆 = 𝑙
𝑟𝑠𝑒√𝐾𝑐
𝐾𝑐′
𝜎𝑦𝑒
355.
where
𝐾𝑐 is as defined in 9.4.2.4
55
𝐾𝑐′ is as defined in 9.10.2.2
NOTE 3 There can be a benefit in allowing for the orthotropic action of a longitudinally stiffened panel and deriving 𝜆, for the determination of more favourable values of 𝑘𝑙 or 𝑘𝑠. Such benefit can prove particularly advantageous when a panel contains intermediate transverse stiffeners between cross-beams or diaphragms or when the transverse plate stiffeners are relatively high in comparison with that of the longitudinal stiffeners or when stiffeners have high torsional rigidity. The BS 5400-6 design rules do not apply to transversely stiffened panels in which the transverse stiffness is not stiff enough to prevent overall buckling. In such instances recourse can be made to the rules for calculating the critical buckling stresses for orthotropic plates given in Annex N. Those rules are derived from classical elastic buckling theory and may be used to calculate stress levels to cause overall buckling of a panel between rigid boundary or buckling between intermediate transverse stiffeners, the lowest of which will govern the appraisal strength. In the context of these rules the boundaries of the panels are taken as being at webs, plated diaphragms or other transverse members satisfying the requirements of 9.15.3. The tolerance on initial bow of stiffeners in BS 5400-6 is l/750 and the rules of BS5400-3 allow for 1.2 times that tolerance.
9.10.3.3.2 Longitudinal stiffeners [BS5400-3, Add at end of clause 9.10.3.3.2]
Where in criterion (c) the modified values of 𝐾𝑐 = 𝐾𝑐′ given in 9.10.2.2 are used to calculate stress, the following shall apply:
1) 1
𝛾𝑚𝛾𝑓3 shall be replaced by [𝐾𝑐
𝐾𝑐′
1
𝛾𝑚𝛾𝑓3], and
2) 𝜆 shall be taken as 𝜆 = 𝑙
𝑟𝑠𝑒√𝐾𝑐
𝐾𝑐′
𝜎𝑦𝑒
355.
9.10.5 Curtailment of longitudinal flange stiffeners [BS5400-3, Add at end of clause 9.10.5]
Where longitudinal flange stiffeners are curtailed prematurely beyond the theoretical cut off point, due account of this shall be taken in application of the foregoing clauses.
The arrangement shall always be checked to ensure the extension beyond any assumed cut off point is sufficient to develop the assessment loads in the stiffener.
The assessment procedure shall take due account of the actual end of the stiffener in deriving the capacity of the arrangement, by working back to the cut-off point where the stiffener can be assumed to be effective.
The resulting extension of the stiffener beyond the assumed cut-off point shall be ignored for calculating stresses and other strength checks.
9.11.4.3.1 General [BS5400-3, Add at end of clause 9.11.4.3.1]
Where the out-of-flatness imperfection of the plate panels exceeds the tolerance in BS 5400-6, allowance shall be made for this in the assessment of strength.
56
Where the out-of-flatness of the plate panels is less than the tolerance in BS 5400-6, a beneficial allowance may be made for this in the assessment of strength.
NOTE 1 A method for assessing the strength of panels with any out-of-flatness imperfection is given in Annex T.
9.11.5.2 General [BS5400-3, Add at end of clause 9.11.5.2]
Where in assessment of the adequacy of a longitudinal web stiffener allowance is to be made for initial departures from straightness, the parameters 𝜎𝑙𝑠 and 𝑘𝑠 shall be calculated from the equations in G.13 with the value of 𝜂 taken according to Equation 9.11.5.2.
𝜂 = 0.0083(𝜆 − 15) + (𝜆−15
𝜆) [
(1.2𝛥𝑠𝑥−0.0016𝑎)𝑦
𝑟𝑠𝑒2 ] Equation 9.11.5.2
But not less than zero.
where
y is the distance from the neutral axis of the effective stiffener to the extreme fibre under consideration
𝛥𝑠𝑥 is the initial departure from straightness measured in accordance with BS 5400-6 over a gauge length taken as a. 𝛥𝑠𝑥 is taken as positive when the bowing is in the direction away from the extreme fibre under consideration
The benefit of orthotropic action may be utilised by using the modification to 𝑟𝑠𝑒, 𝑘𝑠1 and 𝑘𝑠2 in accordance with 9.10.2.3.
Where the stresses (or stiffener properties) vary and orthotropic action is considered, checks shall be made for each stiffener using the stress field at the position of the stiffener.
NOTE 2 The strengths given in this clause for design are deemed to allow for initial out-of-straightness equal to 1.2 times the tolerance in BS 5400-6, i.e. a/625, as well as the effects of residual stresses.
The value of 𝜂 corresponding to an initial departure from straightness equal to 1.2Δ𝑠𝑥 is 1.2 Δ𝑠𝑥𝑦 𝑟𝑠𝑒
2⁄ Adjustment of the 𝜂 value is therefore made in the assessment addition to allow for
differences between measured imperfections and the tolerance. The adjustment made allows for the empirical relationship between 𝜂 and 𝜆 used in Annex G.13 whereby 𝜂 = 0 for 𝜆 ≤ 15.
9.11.6 Curtailment of longitudinal web stiffeners [BS5400-3, Add at end of clause 9.11.6]
Where longitudinal web stiffeners are curtailed prematurely beyond the theoretical cut off point, due account of this shall be taken in application of the foregoing clauses.
The arrangement shall always be checked to ensure the extension beyond any assumed cut off point is sufficient to develop the assessment loads in the stiffener.
57
The assessment procedure shall take due account of the actual end of the stiffener in deriving the capacity of the arrangement, by working back to the cut-off point where the stiffener can be assumed to be effective.
The resulting extension beyond the assumed cut-off point shall be ignored for calculating stresses and other strength checks, except to assess stability in accordance with 9.11.7.
[BS5400-3, Add new clause 9.11.7] 9.11.7 Discontinuous longitudinal stiffeners not connected to transverse stiffeners
Where longitudinal stiffeners are discontinuous and stop short of transverse stiffeners or are not adequately connected to them, their area shall be ignored in calculating the stresses in the cross section.
Discontinuous longitudinal stiffeners may be used in assessing the stability of the web under shear and/or compression, provided they are terminated not more than four times the web thickness from the transverse stiffeners.
In carrying out stability checks for discontinuous longitudinal stiffeners the longitudinal stiffeners shall be assumed to carry a compressive stress equal to that in the web plate.
9.12.1 General [BS5400-3, Amend clause 9.12.1]
In line 3 1.5 shall be deleted and substituted with 1.2.
9.12.2 Elements providing discrete intermediate restraints [BS5400-3, Amend clause 9.12.2]
In the definition of 𝜎𝑓𝑐, the text “strength” shall be replaced by “stress”.
[BS5400-3, Add at end of clause 9.12.2]
Where measured imperfection is used, the forces shall be modified as follows:
1) for lateral restraints
𝐹𝑅 = (𝜎𝑓𝑐
𝜎𝑐𝑖−𝜎𝑓𝑐)1.2𝛥𝑓
𝛿𝑅
But not greater than ( 𝜎𝑓𝑐
𝜎𝑐𝑖−𝜎𝑓𝑐)(𝑛+1)48𝛥𝑓𝐸𝐼𝑐
𝑛𝑙𝑅3
2) for torsional restraints
𝐹𝑅 = (𝜎𝑓𝑐
𝜎𝑐𝑖−𝜎𝑓𝑐)1.2𝛥𝑓
𝛿𝑅𝜃
Or when 𝑙𝑤 > 13.3𝐷
= (𝜎𝑓𝑐
𝜎𝑐𝑖−𝜎𝑓𝑐)
𝐷
50𝛿𝑅𝜃
58
where
𝛥𝑓 is the measured imperfection taken over a gauge length normally equal to the beam's distance between points of support in accordance with BS5400-6.
NOTE 3 Where the restraints at supports are not effectively rigid, the mode of buckling of the compression flange adjacent to supports will be such that the end supports will deflect in a direction opposite to that of the intermediate U-frames. For a given lateral deflection of an intermediate frame relative to the end support the absolute deflections of the intermediate frame will be reduced. The rule given for factoring 𝐹𝑅 has been derived for the case in which there are a number of intermediate frames within the critical buckling half-wave length. Where there are only one or two frames within that length, the rule becomes conservative but can still be applied.
NOTE 4 Where several half-waves occur in a span, the influence of end support flexibility on the forces 𝐹𝑅 in frames within half-wavelengths remote from the supports is slight.
9.12.4.2 Deck not at compression flange level [BS5400-3, Add at end of clause 9.12.4.2, part (a)]
Where assessment uses measured deviations of the flanges from straightness for a bridge with compression flanges restrained by the webs, the horizontal forces per unit length, 𝑓𝑅, shall be calculated by either:
1) nonlinear elastic analysis with the measured deviations allowed for in the initial geometry, or
2) from the equation 9.12.4.2.
𝑓𝑅 = (𝜎𝑓𝑐
𝜎𝑐𝑖−𝜎𝑓𝑐)1.2𝛥𝐹𝑚𝑎𝑥
𝛿𝑅. Equation 9.12.4.2
where
𝛥𝐹𝑚𝑎𝑥 is the maximum value of 𝛥𝐹 obtained in accordance with Table 8 in BS 5400-6 with a gauge length G equal to 𝑙𝑤 traversed along the critical parts of the flange.
9.12.5.2.2 Force due to bow of compression flange [BS5400-3, Add at end of clause 9.12.5.2.2]
Where the force is determined using the measured bow of the compression flange, the force 𝐹𝑆1 shall be according to Equation 9.12.5.2.2:
𝐹𝑆1 =3.8𝛥𝐹𝑚𝑎𝑥
𝐿
𝑀
𝑑𝑓{1−(𝜎𝑓𝑐 𝜎𝑐𝑖⁄ )2} Equation 9.12.5.2.2
where
𝛥𝐹𝑚𝑎𝑥 is the measured value as defined in 9.12.4.2
𝐿 is the distance between the supports
59
[BS5400-3, Add new clause 9.12.6] 9.12.6 Restraint to plastic hinges
Where structures are assessed using plastic methods of analysis in accordance with 7.5, lateral restraint shall be present at locations of all plastic hinges and satisfy the following:
1) be within a distance along the member from the theoretical plastic hinge locations not exceeding half the depth of the member.
2) be adequate to resist the lateral restraint force, in addition to any other lateral forces.
NOTE 1 The requirement for torsional restraint close to plastic hinge positions is consistent with BS EN 1993: Part 1. BS EN 1993: Part 1 does not offer guidance in determining this force but a reasonable value, consistent with other treatment in BS EN 1993: Part 1, would be that obtained as follows:
1) for each beam in which a plastic hinge is taken to be developed as a result of the applied loading, a lateral force is calculated as 1% of the value of the plastic moment capacity divided by the depth of the beam, then
2) each (and all) of these lateral forces are applied to the restraint system at the level of the compression flange at the appropriate beam, together with any other applied lateral forces. Lateral forces are applied such as to induce the greatest effects in the bracing system.
9.13 Transverse web stiffeners other than supports 9.13.1 General [BS5400-3, Add at end of clause 9.13.1]
For each case of the following:
1) a transverse web stiffener is absent at the crossbeam connection to the web, or 2) a transverse web stiffener is absent where a sloping flange changes direction, or 3) a transverse web stiffener does not extend over the whole depth of the web, or 4) a transverse web stiffener is not fitted closely to the flange at a point of application of a
concentrated load to the flange, or 5) cut outs in a transverse web stiffener are not properly connected to the longitudinal
stiffener,
then detailed analysis shall be carried out to cater for local effects in the areas concerned.
The assessment may utilise the relevant aspects of 9.14.6 and 9.15.6.
The adequacy of transverse web stiffeners for deep webs with longitudinal stiffeners may be assessed using the methods of 9.15.6 as an alternative to the requirements of 9.13.3 to 9.13.6.
Where a transverse web stiffener does not extend the full depth of the web (or is not provided), a conservative check may be made with 9.11 by assuming that the load that would otherwise be carried in the stiffener is applied to the web panel as a transverse stress, σ2. For this purpose the transverse stress σ2 may be determined by applying the load over a length of web equal to twice the connected length of the stiffener or cross beam.
60
Where a transverse web stiffener is missing or not full depth, assessment of the web may alternatively be carried out using finite element analysis that includes non-linear effects associated with web buckling and tension field action.
NOTE 1 Finite element analysis can be particularly appropriate for the case of a cross beam of a box girder connected to a deep web other than at the position of a web transverse stiffener.
NOTE 2 Advice given in Eurocode on structural modelling could be of assistance.
Where the transverse web stiffener is stopped short of a flange and local loading is applied to the flange, the unstiffened part of the web shall be assessed for the effects of the applied load.
The connections between the girder and the transverse web stiffeners should be adequate to resist an assumed shear equal to 2.5% of the axial force in the transverse web stiffener. For this purpose the load effects to be included in calculating the axial forces are given in clause 9.13.3.1.
9.13.3.3 Axial force representing the destabilizing influence of the web [BS5400-3, Add at end of clause 9.13.3.3]
Where assessment of a transverse web stiffener makes allowance for measured imperfection Δ𝑠𝑥, 𝑘𝑠 shall be calculated as described in 9.11.5.2.
9.13.5.3 Buckling of effective stiffener section [BS5400-3, Add at end of clause 9.13.5.3]
Where assessment of a transverse web stiffener makes allowance for initial departures from straightness Δ𝑠𝑥, 𝜎𝑙𝑠 shall be calculated as described in 9.11.5.2.
9.14 Load bearing support stiffeners 9.14.1 General [BS5400-3, Add at end of clause 9.14.1]
In each case of the following:
1) the bearing stiffener does not extend over the whole depth of the web; or 2) the bearing stiffener is not fitted closely to the flange; or 3) cut outs are not properly connected to the longitudinal stiffener;
then detailed analysis shall be carried out to cater for local effects in the areas concerned.
Where bearing stiffeners are not provided in accordance with the above, the adequacy of the web under transverse loading shall be checked in accordance with 9.14.6.
Where the end of a bearing stiffener is not fitted and there is evidence of more than a small gap, the welds or other connecting parts shall be assessed to carry the load rather than by contact at the end of the bearing stiffener.
Where there is a gap and an inadequate weld (or no weld), a check shall be made in accordance with 9.14.6.
61
NOTE 1 In welded construction, it can generally be presumed that bearing stiffeners are fitted as a matter of formal fabrication practice, with such fitting achieving good contact over the end of the stiffener or at worst only a small gap. For ULS considerations it is assumed that local deformation would occur if there is a small gap and that the bearing stress check of 9.14.4.2 remains valid.
NOTE 2 A gap at the end of a bearing stiffener is considered small if the connecting parts have sufficient ductility for the gap to close without loss of strength.
For riveted connections, the bearing area should include areas within the dispersal lines of the flange angles and stiffener cleat angles which are riveted to the flange.
Where the end of a bearing stiffener has a cleated connection, one of the following shall be applied for assessment:
1) a check of the cleated connection for adequacy; or 2) a check of the web in accordance with 9.14.6.
NOTE 3 Riveted construction will normally not have fitted stiffeners.
The connections between the girder and the bearing stiffeners should be designed for an assumed shear equal to 2.5% of the axial force in the bearing stiffener, with axial force calculated to include load effects in accordance with clause 9.14.3.1.
9.14.3.3 Eccentricity [BS5400-3, Add at end of clause 9.14.3.3]
Where error in positioning or any unevenness of seating on a flat bearing is measured, assessment shall take into account the following values of eccentricity in respect of (c) and (d) above:
1) half the width of the flat bearing surface plus the measured error in positioning for flat topped rocker bearing in contact with flat bearing surface; or
2) the measured error in positioning for radiused upper bearing resting on flat or radiused lower part or for flat upper bearing resting on radiused lower part.
9.14.4.3 Buckling of effective stiffener section [BS5400-3, Amend clause 9.14.4.3]
The definition for 𝑃 shall be replaced by:
𝑃 is the axial force in the stiffener. Where the bearing stiffener forms part of a u-frame or vertical cantilever providing horizontal restraint to the flanges, 𝑃 is taken as the maximum force from anywhere on the stiffener. In other cases 𝑃 may be taken as the maximum axial force within the middle third of the stiffener length.
[BS5400-3, Add new clauses 9.14.6 and 9.14.6.1] 9.14.6 Unstiffened web at supports 9.14.6.1 Strength of web
The strength of an unstiffened web shall be taken as the limiting value of patch load, 𝑃, as determined in accordance with Annex D.
62
[BS5400-3, Add new clause 9.14.6.2] 9.14.6.2 Buckling resistance of web
The buckling resistance, 𝑃𝐷 of an unstiffened web over a bearing shall be according to Equation 9.14.6.2:
𝑃𝐷 =𝜎𝑐𝑏𝑒𝑓𝑓𝑡𝑤
𝛾𝑚𝛾𝑓3 Equation 9.14.6.2
where
𝜎𝑐 is the ultimate compressive stress about an axis along the centre line of the web obtained from 𝜎𝑐 𝜎𝑦⁄ in accordance with curve C of Figure 37. 𝑙𝑒 is taken as the effective length for web buckling determined taking into account of the lateral and rotational restraint of the flange.
𝑏𝑒𝑓𝑓 is the effective breadth of web obtained as 𝑏𝑒𝑓𝑓 = √𝑑2 + 𝑠2 but not beyond the extent of the beam.
𝑑 is the overall depth of the beam.
𝑠 is the bearing length.
𝛾𝑚 is taken as 1.05 for ultimate limit state.
This method may also be applied for checking stiffened webs with poorly fitting stiffeners or riveted construction, as described in 9.14.1.
Where a cross beam is present, the load effects due to the cross beam shall be taken into account.
9.15.1.2 Compression flanges [BS5400-3, Add at end of clause 9.15.1.2]
Compression flange transverse members not complying with 9.15.3 or 9.15.5, shall be assessed in accordance with 9.15.6.
9.15.4.4 Profile deviation in compression flanges [BS5400-3, Add at end of clause 9.15.4.4]
Where compression flange transverse members are assessed based on surveyed imperfections, the factors of 200 and 160 in the denominator of (a), (b) and (c) above shall be replaced by 𝐺
3Δ𝑐 and 𝐺
3.75Δ𝑐 respectively.
where
𝐺 is defined in Table 8 of BS5400-6.
𝛥𝑐 is defined in Table 8 of BS 5400-6. The value of 𝛥𝑐 is taken as the largest measured value at any point of the span of the transverse member being considered, but not less than 3mm in any circumstances.
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NOTE 1 The use of measured imperfections can give benefit where strength is initially assessed as insufficient.
NOTE 2 For assessment this clause includes a built-in factor on the measured imperfection of 1.2. When assessment is made using measured imperfections equal to the BS 5400-6 tolerance, this gives a slightly different result from BS 5400-3.
[BS5400-3, Add new clauses 9.15.6 and 9.15.6.1] 9.15.6 Compression flange transverse members with insufficient stiffness to prevent overall
buckling of the flange, or with insufficient strength 9.15.6.1 General
Where the stiffness of the effective transverse member does not comply with 9.15.3, assessment shall be made by one of the following alternative methods which cater for overall buckling of flanges:
1) a full analysis using a structural model, in accordance with 9.15.6.2, or 2) an assessment for overall buckling of the flange based on calculated critical stress in
accordance with Annex K.
The methods in this section may also be used to assess transverse stiffeners with insufficient strength.
The effective sections for the approaches 1 and 2 above shall be as set down in 9.15.2.
The effects to be considered for the approaches 1 and 2 above shall be as set down in 9.15.4.
Further to the above, advantage may be taken of the reduced destabilising effects that can be obtained by using more exact stress proportions and distributions in the flange (e.g. shear lag).
The assessment may also derive benefit from using measured imperfections.
NOTE 1 The criterion for stiffness of a transverse member on a compression flange in 9.15.3 is based on ensuring that the overall buckling mode for the flange is one in which the transverse members alternate up and down. Under certain circumstances (and particularly when the span of the transverse members is large compared with their spacing) this can be a very onerous and, indeed, unnecessary requirement.
It is known that some compression flanges perform perfectly adequately without meeting the criterion of 9.15.3 and this can be shown by a detailed non-linear three-dimensional analysis.
NOTE 2 Some further guidance on the stability of transverse members is given in references 9.15.1 to 9.15.4.
[BS5400-3, Add new clause 9.15.6.2] 9.15.6.2 Structural model when a full analysis is utilised
The model shall be in the form of a non-linear analysis that takes fully into account the stiffness of the orthotropic deck systems and the magnified stresses resulting from deformation of the cross girders due to combined actions of longitudinal deck stresses and imperfections of the cross girders.
64
Treatment of imperfections
The structural model shall include imperfections of the flange as an initially deformed shape.
Where measurements of the actual flange imperfection are not available, the relevant imperfection specified in Item 5 of Table 8 of BS 5400-6 may be used as a peak value. Where the imperfection is derived from a specified imperfection, the peak values shall be applied at the mid points of each span of the transverse member and at the cantilever tips, with a smooth curve between. Alternate spans of a particular transverse member shall be deformed up and down.
Adjacent transverse members along the bridge shall be deformed up and down either alternately, or alternately in groups of two, three ... etc., whichever eventually gives the highest forces and moments. Consideration shall also be given to having an undeformed transverse member between the up and down groups.
Measured imperfections may be used instead in the model, subject to a minimum of 3mm. This measured imperfection shall be increased by a factor of 1.2.
Where the result of the analysis shows a deflected form at collapse radically different from the measured form, further analyses shall be made with the initial deformation conforming more closely to the final deflected pattern.
NOTE 1 The required multiplier of 1.2 when using actual deformations allows for minor departures of the deflected member from the mode of buckling and small variations which may cause overestimates of strength. This is consistent with various clauses in BS 5400-3 where the design imperfections is 1.2 times the specified maximum value.
Computer program requirements
The computer program shall be capable of analysing displacement in all six primary degrees of freedom (three linear, three rotational).
The computer program shall take into account the effect on stiffness due to the change of geometry under load.
Material behaviour
Member material behaviour may be taken as linear elastic with no allowance for plasticity.
Loading
The compressive load in the flange shall be applied at the end and side boundaries of the model, as appropriate for the actual loading conditions. The transverse loads on the flange and transverse members shall be those defined in 9.15.4.1(a) to (f) insofar as they are not otherwise taken into account in the model.
Loading between transverse members shall be applied directly at the appropriate position rather than distributed as described in 9.15.4.5.
The loads should not be magnified by the destabilising factors i1 and i2.
Extent of model
The width of the model shall include at least one whole segment as defined in 9.15.3.1.
65
NOTE 2 Where multiple segments of different spans are analysed together, benefit can occur for the long segments due to partial end fixity from the adjacent short segments.
The number of transverse members to be included longitudinally shall extend to cover a minimum of two half wavelengths of buckling. For this purpose, the wavelength for overall buckling may be obtained either theoretically or by progressively lengthening the model to be used for analysis until the critical length is found.
Idealisation
The analysis model shall be constructed of either beam elements, shell elements or a mixture of both.
NOTE 3 It is generally sufficiently accurate to represent all elements of the flange by beams with their neutral axes in a common plane.
NOTE 4 In some cases (eg a flange with no longitudinal stiffeners) ‘equivalent’ beams can be used to represent the plate stiffness and area.
The distribution of stiffness and area in the analysis model shall correspond to that of the flange being assessed.
Where beam properties are used to represent stiffeners, an appropriate effective width of plating should be included in the effective stiffener section.
The analysis model shall be subdivided into elements which are sufficiently short to represent the buckling behaviour accurately.
NOTE 5 This will to some extent be dependent on the program used – for example, if it is a simple iterative extension to a linear stiffness analysis, a much finer subdivision will be needed than if it includes stability functions.
NOTE 6 Accurate representation of the buckling behaviour requires the analysis model to reproduce accurately the internal forces, moments and displacements in the buckled shape of the flange. The number of elements required to do this depends on their capability to represent internal variation in forces, moments and displacements (e.g. linear or quadratic finite elements).
Boundary conditions.
The boundary conditions should be simple pinned supports with no moment continuity.
Where moment continuity is used at supports, the analysis should consider a larger portion of the flange such that the effects of the support stiffness are insignificant
NOTE 7 The basic notes on the structural model in this clause are not considered as all encompassing, and each specific case demands individual attention.
9.16.1 General [BS5400-3, Add at end of clause 9.16.1]
Plated intermediate diaphragms shall be assessed in accordance with 9.18.
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9.16.2.1 Girder layout [BS5400-3, Add at end of clause 9.16.2.1]
Where cross frames do not comply with the requirements of this clause for design, assessment shall be made in accordance with 9.16.6.
9.16.2.2 Cross frames [BS5400-3, Add at end of clause 9.16.2.2]
Cross frames not complying with the limitations of this clause for design shall be assessed using analytical models that fully account for the plane direction of the frames and the interconnection between the frames and longitudinal members.
The methods in this document may be applied to cross frames not complying with these limitations, with the exception of Annex B.
9.16.3 Load effects to be considered [BS5400-3, Add at end of clause 9.16.3]
The forces and stresses carried by a cross frame due to torsion shall be determined according to either:
1) elastic analysis (see 9.16.4.2), or 2) in accordance with Annex B.3.4, for boxes with web inclination and provided that the
cross frames comply with 9.16.2.2.
Where the webs of the box girder are inclined to the vertical, the assessment shall include the effects of any horizontal components of load induced in top and bottom transverse members.
[BS5400-3, Add new clause 9.16.4.4] 9.16.4.4 Ring frame corners
The strength of the connection between web transverse members and flange transverse members shall be adequate to transfer the forces and moments from one member to the other.
The assessment shall account for how both shear and the forces in the flanges of the transverse member are transferred.
NOTE 1 At the corner of a box the junction of web and flange members is required to transfer moment, shear and axial forces. The magnitude of each of these components depends very much on the configuration of the cross section. For example, the moments at the bottom corner of a small rectangular box will be quite small whilst those at the top corner of a large trapezoidal box will be quite large. For the former a simple lapped connection can be adequate whilst for the latter a stiffened portal knee can be required.
In determining the strength of the connection at corners of the box, the requirements of 9.16.2.3 for corner stiffening shall apply.
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NOTE 2 The web and flange of the box generally act as flanges to the transverse members. At the corners of the box they can only be considered to do so if there is stiffening along the junction line. This is covered by the limitation in 9.16.2.3.
[BS5400-3, Add new clause 9.16.6] 9.16.6 Cross frames not complying with limitations
Where cross frames do not comply with the limitations defined in 9.16.2, the strengths of the components of the frames shall be determined from this document in accordance with the following requirements:
1) Global analysis is undertaken in accordance with 7.1 and 7.2. 2) The structure is analysed either by a finite element method with all its primary
components modelled or an equivalent grillage provided that the elastic properties of the equivalent members are derived from finite element analysis of the box girders.
Analysis to determine load effects from local loads and reactions including distortional effects shall be undertaken using a finite element method on a model of sufficient extent to ensure that the effects calculated are insensitive to assumed end conditions.
[BS5400-3, Add new clause 9.16.7] 9.16.7 Cross girder stiffness
Where distortional and warping stresses in the box girders are calculated in accordance with Annex B, the stiffness of a cross girder shall comply with the requirements of B.3.4. Where the stiffness requirements are not complied with, the stresses shall be derived in accordance with 8.3.
9.17 Diaphragms in box girders at supports 9.17.1 General [BS5400-3, Add at end of clause 9.17.1]
Stiffened diaphragms not complying with the limitations in 9.17.2 shall be assessed using the procedures in Annex L.
NOTE 1 For diaphragms not complying with 9.17.2, more refined analysis id required which is described in Annex L.
9.17.6.7 Buckling of Diaphragm Stiffeners [BS5400-3, Add at end of clause 9.17.6.7]
The benefit of orthotropic action may be utilised by using the modification to 𝑟𝑠𝑒, 𝑘𝑠1 and 𝑘𝑠2 given in 9.10.2.3.
NOTE 1 Due to the general presence of stresses in the direction of the diaphragm stiffener, transverse to the stiffener and the likely presence of significant shear stresses, sub-panel modes as well as overall buckling are important for the determination of 𝑟𝑠𝑒.
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[BS5400-3, Add new section 9.18] 9.18 Intermediate plated diaphragms in box girders 9.18.1 General
Intermediate plated diaphragms in box girders that transfer deck loads to the webs, resist forces due to local changes in slope of the flanges or restrict distortion of the cross-section shall meet the requirements of 9.18.
NOTE 1 The rules from BS5400-3 do not necessitate the use of finite element methods and are valid only with the limitations given in 9.17.2 for support diaphragms.
Unstiffened and stiffened intermediate plated diaphragms shall meet the requirements of 9.18.5 and 9.18.6 respectively.
Stresses derived by finite element analysis should not be substituted directly for the stresses used in 9.18.5 and 9.18.6.
NOTE 2 The methods given in 9.18.5 and 9.18.6 use strength provisions that are compatible only with the assumed methods of stress derivation given therein.
9.18.2 Limitations
Intermediate plated diaphragms shall comply with the limitations given in 9.17.2, other than those limitations relating to bearings.
9.18.3 Loading on diaphragms 9.18.3.1 Derivation
The load effects in intermediate diaphragms and associated parts of box girders shall be derived from global and local analysis in accordance with 7.1, 7.2 and 9.4.1.
9.18.3.2 Effects to be considered
The loads for assessment of intermediate plated diaphragms shall include the applicable load effects given in 9.13.3 and 9.15.4.
In this context the diaphragm/web junction shall be assessed as equivalent to a transverse web stiffener.
9.18.4 Effective sections
The effective section of intermediate plated diaphragms to be used in deriving stresses shall be in accordance with 9.17.4.
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9.18.5 Unstiffened intermediate diaphragms 9.18.5.1 General
Unstiffened diaphragms that comply with the limitations of 9.18.2 shall be assessed to the yield criterion of 9.18.5.4 and the buckling criterion of 9.18.5.3 using reference stress values of 9.18.5.2 and buckling coefficients of 9.18.5.3.
Unstiffened diaphragms that do not comply with the limitations of 9.18.2 shall be assessed using finite element methods or by reference to relevant research papers.
NOTE 1 Where finite element methods are used, some of the guidance in Annex L may still be applicable.
Web/diaphragm junctions shall be in accordance with 9.18.7.
Diaphragm stiffness shall be assessed in accordance with 9.18.8.
9.18.5.2 Reference values of in-plane stresses 9.18.5.2.1 General
The stresses in an unstiffened diaphragm resulting from the load effects given in 9.18.3 shall be determined in accordance with 9.18.5.2.2 to 9.18.5.2.4.
9.18.5.2.2 Vertical stresses
The reference value of the in-plane vertical stress, 𝜎𝑅1, shall be taken as the greater of 𝜎𝑅1𝑇 and 𝜎𝑅1𝐵.
where
𝜎𝑅1𝑇 is the maximum value of compressive vertical stress on the effective horizontal section of the diaphragm plating beneath the top flange due to deck loading.
𝜎𝑅1𝐵 the maximum value of compressive vertical stress on the effective horizontal section of the diaphragm plating above the bottom flange due to change in slope of the flange or other applied vertical loading.
9.18.5.2.3 Horizontal stresses
By reference to Figure 9.18.5a, the reference value of the in-plane horizontal stress 𝜎𝑅2 at a section distance 𝑆 from the centre of the web, shall be taken as the greater of:
[𝜎𝑅2𝑇 + (𝜎2)] 𝑎𝑛𝑑 [𝜎𝑅2𝐵 + (𝜎2)]
where
𝜎𝑅2𝑇 =𝑀
𝑍𝑇
𝜎𝑅2𝐵 =𝑀
𝑍𝐵
𝑀 = 𝑀𝑒 + 𝐹1𝑌𝑇 + 𝐹2𝑌𝐵 +𝑄
2𝐷(𝐵𝑇 − 𝐵𝐵) (𝑌𝐵 −
𝐷
2) − 𝑄𝑇𝑆
70
𝐹1 =𝑄𝑉
𝐷[𝑆 +
(𝐵𝑇−𝐵𝐵)
4] {1 −
1
𝐵𝑇[𝑆 +
(𝐵𝑇−𝐵𝐵)
4]} +
𝑄𝑇
𝐷[𝑆 +
(𝐵𝑇−𝐵𝐵)
4]
𝐹2 =𝑄𝑉
𝐷[𝑆 +
(𝐵𝑇−𝐵𝐵)
4] {1 −
1
𝐵𝑩[𝑆 +
(𝐵𝑇−𝐵𝐵)
4]} +
𝑄𝑇
𝐷[𝑆 +
(𝐵𝑇−𝐵𝐵)
4]
𝑀𝑒 is the bending moment at the section under consideration due to externally applied loads transmitted to the diaphragm (see 9.15.4) and changes in slope of the bottom flange. For this purpose, the diaphragm is treated as a simply-supported beam spanning between the mid points of the webs.
𝑌𝑇 , 𝑌𝐵 are the distances to the top and bottom diaphragm/flange junctions from the centroid of the effective diaphragm section.
𝑄 = 𝑄𝑉 + 𝑄𝑇
𝑄𝑉 is one half of the total resultant load transmitted to the diaphragm (see 9.15.4).
𝑄𝑇 = (𝑇
𝐵𝐵+𝐵𝑇)
𝑇 is the torque about the centreline of the diaphragm due to any eccentricity of externally applied loads transmitted to the diaphragm.
(𝜎2) = (𝑉𝑇 − 𝑉𝐵)𝑡𝑎𝑛(𝛽)
2𝐴𝑒
𝑉𝑇 is the total factored vertical load applied to the top of the diaphragm, taken for the case causing maximum stress when combined with 𝑉𝐵.
𝑉𝐵 is the total factored vertical load applied to the bottom of the diaphragm, taken for the case causing maximum stress when combined with 𝑉𝑇.
𝑍𝐵, 𝑍𝑇 are the effective section moduli of the diaphragm and flanges on the diaphragm centre line with respect to the bottom flange and the top flange respectively.
𝐴𝑒 is the effective area of the diaphragm and flanges at the vertical section under consideration.
𝛽 is the greater angle of inclination to the vertical of either web.
𝐵, 𝐵𝑇 , 𝐵𝐵 are as defined in Figure 9.18.5a.
𝐷 is the diaphragm depth as defined in Figure 9.18.5a.
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Figure 9.18.5a
Figure 9.18.5b
9.18.5.2.4 Shear stresses
The reference value of the in-plane shear stress 𝜏𝑅 shall be taken from Equation 9.18.5.2.4.
𝜏𝑅 =𝑄𝑣+𝑄𝑇−(∑𝑃𝑖)+𝑄𝑓𝑣
𝐴𝑣𝑒 Equation 9.18.5.2.4
where, as shown in Figure 9.18.5b,
72
𝑄𝑣, 𝑄𝑇 are as defined in 9.18.5.2.3.
𝐴𝑣𝑒 is the minimum effective vertical shear area, as given in 9.17.4.3
∑𝑃𝑖 is the sum of the vertical applied loads transmitted to the diaphragm between the section considered and the edge of the top flange at point A.
𝑄𝑓𝑣 is the vertical force transmitted to the diaphragm by the portion of the bottom flange over a width 𝑙𝑓 when there is a change of flange slope.
𝑙𝑓 is the horizontal distance from the section considered to the edge of the bottom flange at point B.
The value of 𝜏𝑅 to be used in yield checks in accordance with 9.18.5.4 shall be the maximum value within the middle third of the median width, 𝐵, of the diaphragm, with B as shown in Figure 9.18.5a.
Additionally, the value on the sections adjacent to the webs may be applied in yield checks with 𝜎2 = 0.
For buckling checks 𝜏𝑅 shall be taken as the average shear stress in the diaphragms.
9.18.5.3 Buckling of diaphragm plate
The diaphragm plate shall comply with the criterion given in 9.11.4.4 using the buckling coefficients for an unrestrained panel given in clause 9.11.4.3 in which the parameters 𝜎1, 𝜎𝑏 , 𝜎2, 𝜏, 𝑏 and 𝑎 shall be taken as:
𝜎1 = [𝜎2]
𝜎𝑏 = 𝜎𝑅2𝑇 or 𝜎𝑅2𝐵, whichever is compressive
𝜎2 = 𝜎𝑅1
𝜏 = 𝜏𝑅
𝑏 the panel dimension ‘𝑏’ in Figure 19 shall be taken as the depth of the diaphragm (D in Figure 34)
𝑎 the dimension ‘𝑎’ shall be taken as the maximum width between box webs.
9.18.5.4 Yielding of diaphragm plate
The values of 𝜎𝑅1, √3𝜏𝑅 and √𝜎𝑅22 + 3𝜏𝑅2 shall not exceed 𝜎𝑦𝑑
𝛾𝑚𝛾𝑓3.
where
𝜎𝑦𝑑 is as defined in 9.17.5.4.
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9.18.6 Stiffened intermediate diaphragms 9.18.6.1 General
Intermediate plated diaphragms stiffened by an orthotropic system of stiffeners shall comply with 9.18.6 and the following criteria:
1) plate panels comply with the yield and buckling criteria for the plating given in 9.18.6.3.1.
2) Stiffeners comply with the yield and buckling criteria given in 9.18.6.3.2, for which stiffeners that span between box walls are treated as primary and all other stiffeners are treated as secondary.
3) Web/diaphragm junctions comply with 9.18.7.
4) Diaphragm stiffness are assessed in accordance with 9.18.8.
9.18.6.2 Values of in-plane stresses 9.18.6.2.1 General
The stresses in a stiffened diaphragm resulting from the load effects given in 9.18.3 shall be determined in accordance with 9.18.6.2.2 to 9.18.6.2.4.
9.18.6.2.2 Vertical stresses
The vertical stress shall include the effects of any concentrated loads applied to the top or bottom flanges.
Vertical stresses 𝜎𝑑, due to concentrated loads applied to the deck may be calculated by assuming dispersion of load at 45° from the width of contact and diminishing linearly to zero from the level of intersection of the lines of dispersion with the web to the bottom of the diaphragm.
Stresses due to changes in slope of the bottom flange shall be calculated from the vertical components of flange force and assumed to diminish linearly up the height of the diaphragm.
The vertical stresses due to concurrent top and bottom loads shall be added.
9.18.6.2.3 Horizontal stresses
The horizontal stresses shall be derived in accordance with 9.17.6.2.3.
In-plane bending 𝜎2𝑏 shall be calculated by treating the diaphragm with the associated effective widths of flanges as a simply supported beam spanning between the box webs (span B).
Horizontal stress 𝜎2𝑞 due to inclination of webs to the vertical shall be calculated in accordance with 9.18.5.2.3.
9.18.6.2.4 Shear stresses
The values of the in-plane shear stresses, 𝜏, on any section shall be taken as the reference value 𝜏𝑅 as defined in 9.18.5.2.4.
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9.18.6.2.5 Stresses in diaphragm stiffeners
The equivalent stress in a stiffener for the buckling check shall be determined from 9.17.6.3.4 as appropriate for intermediate stiffeners, with parameters taken as:
𝜎2𝑏, 𝜎2𝑞, 𝜏 calculated in accordance with 9.18.6.2.3 and 9.18.6.2.4,
𝜎𝑎 is not necessarily zero for vertical intermediate stiffeners but shall include any loading effects due to tension field action in accordance with 9.13.3.2 and 9.13.4.
Loading from clause 9.13.3.3 should be excluded.
All additional load effects as defined in 9.18.3.2 shall be included.
9.18.6.3 Strength criteria 9.18.6.3.1 Diaphragm plating
Plate panels between stiffeners or between stiffeners and box walls shall be assessed in accordance with the criteria in 9.17.6.4 and 9.17.6.5.
9.18.6.3.2 Stiffeners
Stiffeners shall be assessed in accordance with the criterion given in 9.17.6.7.
9.18.7 Intermediate diaphragm web junctions
The web junction at intermediate plated diaphragms shall be assessed as a stiffener to the box web spanning between box flanges, unsupported in the plane of the diaphragm, in accordance with 9.17.7.2 to 9.17.7.4, and using effective sections derived in accordance with 9.17.4.5.
9.18.8 Intermediate diaphragm stiffness
Where distortional and warping stresses in the box girders are calculated in accordance with Annex B, the stiffness of an intermediate diaphragm shall comply with the requirements of B.3.4.
Where the stiffness requirements are not complied with, the stress shall be derived in accordance with 8.3.
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10 Assessment of compression members 10.3.4 Circular hollow sections [BS5400-3, Add at end of clause 10.3.4]
Non-complying sections may be assessed according to the criteria of 9.3.6.
10.6.1.1 Strength [BS5400-3, Add at end of clause 10.6.1.1]
Where in assessment of the adequacy of a compression member allowance is made for initial departures from straightness, 𝜎𝑐 shall be calculated from the Equation in G.16 with 𝜂 taken from Equation 10.6.1.1:
𝜂 = 𝛼(𝜆 − 15) + (𝜆−15
𝜆) [
(1.2𝛥𝑠−0.0012𝐺)𝑦
𝑟2] Equation 10.6.1.1
but not less than zero.
where
𝛼, 𝜆 are as defined in G.16.
𝑟, 𝑦 are as defined in 10.6.1.1.
𝛥𝑠 is the initial departure from straightness measured in accordance with BS5400-6 using gauge length G.
𝐺 is the gauge length for measurement equal to the clear length of the compression member.
NOTE 2 The curves given in Figure 37 are derived empirically by reference to test data and include
allowances for the effects of residual welding and rolling stresses as well as accidental eccentricities and initial bows.
NOTE 3 Since they are applicable to members within the tolerances in straightness given in BS 5400-6, it is justifiable to adjust the limiting compressive stresses when departures from straightness differ from the tolerances. The term β in the Perry formula is given by 𝛥𝑦/𝑟2
NOTE 4 The tolerance in BS 5400-6 is 𝛥𝑠 =𝐺
1000 and throughout the design rules allowance has been
made for 1.2 times the tolerance. NOTE 5 The modified 𝜂 equation consequently provides allowance for 1.2 times the difference
between measured imperfections and tolerances with the same empirical reduction factor to allow for the plastic capacity of stocky members.
10.6.2.1 Strength [BS5400-3, Add at end of clause 10.6.2.1]
For assessment of the adequacy of a uniform member of I-section subject to combined bending and axial compression, the buckling criterion given in 9.9.4.2 shall be used instead of the criterion above.
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10.7.2 Evaluation of stresses [BS5400-3, Add at end of clause 10.7.2 part (c)]
Where measured initial departures from straightness are used in assessment of a compression member with longitudinal stiffeners, Δ𝑖 shall be taken as:
𝛥𝑖 = 1.2 Δ𝑠, determined separately for the X-X and Y-Y axes.
where
Δ𝑠 is the departure from straightness measured in accordance with BS 5400-6 over a gauge length 𝐺 equal to the distance between points of restraint appropriate to the axis being considered.
10.8 Battened compression members 10.8.1 General [BS5400-3, Add at end of clause 10.8.1]
Where the arrangements of the member do not comply with any of the above requirements, the strengths of the battens and of the battened member shall be assessed in accordance with 10.8.5.3 and 10.8.5.4 respectively.
NOTE 1 The rules for battened strut design stem from those in BS 153 which is based on the work of Koenigsberger (ref 10.8.1). The arrangements and proportions of the members defined are intended to be such that the member as a whole has a compressive strength of at least 80% of that of a corresponding member free from shear distortion of battens and of the individual components.
NOTE 2 Members having more flexible and widely spaced battens can be structurally adequate but allowance is made in their strength assessment for shear flexibility and buckling of battens and of individual components between them.
NOTE 3 The rules for assessment are based on the theory and experimental evidence forming the basis for the rules for design.
10.8.2 Radius of gyration of the member [BS5400-3, Add at end of clause 10.8.2]
Where the battened member does not comply with the requirements of 10.8.1, the radius of gyration of the member shall be taken as 𝛷0.5 times the actual radius of gyration where 𝛷0.5 is as defined in Annex M.
NOTE 1 The reduction factor of 0.9 on radius of gyration given in 10.8.2 of BS 5400-3 allows only for the loss of full effectiveness due to battening of a member complying with design requirements. Provision is made in assessment for reduction factors for less effective arrangements.
10.8.3 Spacing of battens [BS5400-3, Add at end of clause 10.8.3]
Where the spacing of the battens exceed the limits derived from the above requirements, the strengths of the battened member shall be assessed in accordance with 10.8.5.4.
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10.8.4.1 Length [BS5400-3, Add at end of clause 10.8.4.1]
Where the length of any batten is less than the criteria above, the strength of the battened member shall be assessed in accordance with 10.8.5.4.
10.8.4.2 Thickness [BS5400-3, Add at end of clause 10.8.4.2]
Where the thickness of any batten is less than that the criteria above, the adequacy of the batten shall be assessed in accordance with 10.8.5.3.
NOTE 1 The batten thickness defined in 10.8.4.2 of BS5400-3 is such that the battens so sized can be accepted without consideration of their buckling. Smaller thicknesses can be accepted in assessment provided that they are checked against buckling.
10.8.5.1 Arrangement of battens [BS5400-3, Add at end of clause 10.8.5.1]
Where the arrangement of battens does not comply with the recommendations above, the battened compression member shall be assessed in accordance with 10.8.5.4.
10.8.5.2 Loads and moments on battens [BS5400-3, Amend clause 10.8.5.2]
For assessment, (a) and (b) shall be modified to read:
(a) a longitudinal shear force equal to 𝐾𝑏𝑄𝑠𝑛𝑏
(b) a bending moment, acting in the plane of the batten, equal to𝐾𝑏𝑄𝑠2𝑛
[BS5400-3, Add at end of clause 10.8.5.2]
where
𝐾𝑏 = 0.5 for end battens, or
= 0.5 (𝑐𝑜𝑠𝜋𝑥1
𝑙+ 𝑐𝑜𝑠
𝜋𝑥2
𝑙) for intermediate battens
𝑙 is the overall length of the battened member
𝑥1, 𝑥2 are the respective distances from one end of the member to points a distance s/2 either side of the centre line of the batten under consideration.
NOTE 1 The shearing forces and moments defined in 10.8.5.2 of BS5400-3 are those due to the
effects of axial load on a deformed member, and are treated as constant irrespective of the location of the batten. The assessment values take account of the variation in slope from the nominal axis of a bowed member in relation to the initial imperfection implicitly assumed.
78
Where the arrangement of battens does not comply with the limits of 10.8.1, 10.8.4 or 10.8.5.1, the lowest values of elastic critical buckling loads 𝑃𝐸𝑌′ and 𝑃𝐸𝑋′ shall be determined for the battened member in accordance with Annex M and used instead of 𝑃𝐸𝑌 and 𝑃𝐸𝑋.
Where in assessment of the adequacy of a battened member, account is to be taken of measured departure from straightness exceeding that permitted by [BS 5400-6], the number 200 in the denominator of equations (1) and (2) above shall be replaced by:
1
3.8𝛥𝑠𝑙𝑒+
1815
where
𝛥𝑠 is the departure from straightness measured over a gauge length equal to 𝑙𝑒.
𝑙𝑒 is the effective length of the battened member, ie 𝑙𝑦 for equation (1) and 𝑙𝑥 for equation (2).
[BS5400-3, Add new clause 10.8.5.3] 10.8.5.3 Strength assessment of non-complying battens
Where the arrangement or dimensions of the battened member do not comply with the requirements 10.8.1, 10.8.4 or 10.8.5.1, the battens shall comply with the following:
1) maximum bending stress not exceeding 𝜎𝑦
𝛾𝑚𝛾𝑓3 ; and
2) maximum average shear stress, 𝜏𝑚𝑎𝑥 not exceeding the lesser of 𝜎𝑦
1.5√3𝛾𝑚𝛾𝑓3 and
𝐾
𝛾𝑚𝛾𝑓3(𝑡𝑏
𝑑𝑏)2.
where
𝜏𝑚𝑎𝑥 is the maximum average shear stress calculated using:
𝜏𝑚𝑎𝑥 = 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒
𝐴𝑏𝑛𝑒𝑡
𝐴𝑏𝑛𝑒𝑡 is the net cross sectional area of the batten
𝐾 is obtained from Table 10.8 in N/mm2
𝑡𝑏 is the thickness of the batten
𝑑𝑏 is the depth of the batten in the direction parallel to the axis of the member
𝑏 is as defined in 10.8.5.2
NOTE 1 The limiting shear stresses in battens given in 10.8.5.3 for assessment are taken as two
thirds of the elastic critical buckling stresses derived by Girkmann (ref 10.8.3).
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Table 10.8
db/b 1.5 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
K (x104) 87.3 36.8 32.2 25.1 19.1 14.1 9.9 6.7 4.2 2.3 1.0
[BS5400-3, Add new clause 10.8.5.4] 10.8.5.4 Strength assessment of non-complying battened members
Where the arrangements of the battened member do not comply with the requirements of 10.8.1, 10.8.4 or 10.8.5.1, the compressive strength of the battened member shall be calculated in accordance with Clauses 9.1 to 9.9, 10.1 to 10.7 using effective radii of gyration defined in 10.8.2.
The adequacy of each main component of the battened member shall be checked assuming it to resist all of the following:
1) the axial force assuming its effective length to be equal to 𝑙𝑏1, where 𝑙𝑏1 is as defined in 10.8.3;
2) a bending moment about each of the X-X and Y-Y axes equal to Qs/4, where Q is as defined in 10.8.5.2;
3) the effects of transverse external forces, if any.
Members with planes of battens in opposite faces in which the centres of the battens are staggered may be treated as if the battens were not staggered.
[BS5400-3, Delete existing clause 10.8.6.2 and replace with] 10.8.6.2 Loads and moments on battens For assessment, each batten and its end connections to the main components shall be
proportioned to resist simultaneously:
1) a longitudinal shear force equal to 𝐾𝑏𝑄𝑟𝑠/𝑏 2) a bending moment acting in the plane of the batten equal to 𝐾𝑏𝑄𝑟𝑠/2
where
𝐾𝑏 is as defined in 10.8.5.2
10.9.1 General [BS5400-3, Amend clause 10.9.1]
The following text shall be inserted in the fourth paragraph after ‘The strength’:
‘of a member as a whole and’.
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10.9.2 Inclination of lacing bars [BS5400-3, Add at end of clause 10.9.2]
Where a laced member has lacing bars not complying with the above limits to inclination, the critical buckling loads and strength of the whole member shall be determined as follows:
The critical loads for buckling about the Y-Y or X-X axes respectively shall be taken as 𝑃𝐸𝑌′ = 𝛷𝑃𝐸𝑌 and 𝑃𝐸𝑋′ = 𝛷𝑃𝐸𝑋 where 𝛷 shall be derived from Equation 10.9.2:
𝛷 = {1 + 𝜋2𝐴𝑒𝑟
2
𝑙2[
1
𝐴𝑙 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛2 𝜃]}−1
Equation 10.9.2
where
𝐴𝑙 is the total cross-sectional area of the lacing bars within a laced panel in the appropriate plane of the bracings.
𝜃 is the angle of inclination of the lacing bars to the axis of the member.
𝑙 is 𝑙𝑥 or 𝑙𝑦 as appropriate.
𝑟 is the radius of gyration of the laced member as a whole about the X-X and Y-Y axes as appropriate.
𝐴𝑒 is the effective area of the laced member determined in accordance with 10.5.
𝑃𝐸𝑌, 𝑃𝐸𝑋 are as defined in 10.8.5.2.
The strength of the member as a whole shall be determined in accordance with 10.9.1 with the radius of gyration about the appropriate axis taken as 𝜑0.5 times the actual radius of gyration using the value of 𝜙 appropriate to the axis considered.
NOTE 1 The rules in BS5400-3 for design of laced compression members ensure that the buckling loads of the members as a whole are not diminished significantly as a result of shear flexibility in the planes of the bracings and that individual components do not fail prematurely. Where the bracing is inclined to the axis of a member at smaller angles or is relatively light, allowance needs to be made for shear flexibility in the assessment procedure.
NOTE 2 The reduction of critical buckling loads given was derived by Timoshenko (ref 10.9.1).
10.9.3 Spacing of lacing bars [BS5400-3, Add at end of clause 10.9.3]
Where the spacing of lacing bars does not comply with the requirements above, the main components of the member shall satisfy Equation 10.9.3:
𝑃
𝐴𝑒+𝑀𝑥
𝑍𝑥(
1
1−𝑃
𝑃𝐸𝑋′
) +𝑀𝑦
𝑍𝑦(
1
1−𝑃
𝑃𝐸𝑌′
) ≤𝜎𝑐
𝛾𝑚𝛾𝑓3 Equation 10.9.3
where
Ae is the effective area of cross section of the laced member (see clause 10.5.2.1).
P is the axial load applied to the laced member.
𝑍𝑥 , 𝑍𝑦 are the section moduli of the laced member about the X-X and Y-Y axes respectively related to the centroid of the main component considered.
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𝑃𝐸𝑌′ , 𝑃𝐸𝑋
′ are as defined in 10.9.2.
𝑀𝑥 = 𝑀𝑜𝑥 + 1.2𝑃𝛥𝑥
𝑀𝑦 = 𝑀𝑜𝑦 + 1.2𝑃𝛥𝑦
𝑀𝑜𝑥 ,𝑀𝑜𝑦 are any applied bending moments about the X-X and Y-Y axes respectively in the plane of the lacing including that due to eccentricity of axial load to the centroid of the laced member.
𝛥𝑥 , 𝛥𝑦 are the maximum departures from straightness of the laced member in the directions normal to the X-X and Y-Y axis respectively, measured in the plane of the lacings over a length between points of effective lateral restraint to the laced member in the relevant direction.
𝜎𝑐 is the ultimate compressive stress for buckling of the main component about its centroidal axis perpendicular to the plane of lacing obtained from 𝜎𝑐 𝜎𝑦⁄ in accordance with Figure 37 using 𝑙𝑒 equal to the spacing of the lacing bar intersections along the component.
𝑟 is the least radius of gyration of the section of the main component.
𝑦 is the distance from the axis of least radius of gyration to the extreme fibre of the section of the main component.
𝜎𝑦 is the nominal yield stress of the material.
NOTE 1 The verification above checks against local buckling of the main components, which is
required where the spacing of the lacing bars exceeds the design limits. The limiting equation given allows approximately for the use of measured initial departures from straightness.
NOTE 2 For initial assessment, recommended departures from straightness are given in 8.5 and Annex I.
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11 Assessment of tension members 11.1 General [BS5400-3, Add at end of clause 11.1]
This section shall be applied only to nominally straight members subjected to axial tension or subjected to combined tension and bending.
Where members are subjected to compression in some loading scenarios and it cannot be shown that sufficient redundancy or alterative load path exists for such compression to be ignored, the members shall be assessed in accordance with 10.
NOTE 1 Where structures are designed to earlier standards such as BS 153, the assessment provisions (and the provisions of recent design codes) can often be used to demonstrate a much greater load carrying capacity. This is because earlier codes used a much larger factor of safety than the current codes and typically imposed a maximum slenderness for tension members.
11.3.2 Effective area [BS5400-3, Add at end of clause 11.3.2]
For assessment of steels not listed in 6.1.2 the value of 𝑘2 shall be taken from Table 11.3.2.
Table 11.3.2
Member steel type 𝒌𝟐
BS 4360 grade 43 or BS 15 steel 1.2
BS 4360 grade 50 or BS 968 steel 1.1
BS 4360 grade 55 or Thirty Oak steel 1.0
steel not complying with BS 4360, BS 15, BS 548 or BS 968 1.0 + 0.5 {
𝜎𝑈𝐿𝑇
𝜎𝑦− 1.2}
but not exceeding 1.2 or less than 1.0
Note 𝜎𝑦 and 𝜎𝑈𝐿𝑇 are the nominal yield stress and ultimate stress derived in accordance with 6.2
and 6.3 respectively. NOTE 2 The rules in BS4500-3 for tension members and connections together with the associated
safety factors relate to materials which have specified ultimate tensile stresses which exceed their yield strengths by certain amounts depending on the grade of steel. The margins provided by BS 15 and BS 968 correspond to those for grades 43 and 50 steel in BS 4360.
NOTE 3 For steels of other qualities allowance is made for the ratio of ultimate/yield stress. The modifications to the factor 𝑘2 provide compatibility with a ratio of 1.1 for grade 50 steel and 1.2 for grade 55 steel.
NOTE 4 The combined factors of 𝛾𝑚𝛾𝑓3 for tension members is 1.16. In order to limit the risk of yielding on a line of holes under serviceability limit state conditions the value of k2 is limited to 1.2 as permitted for grade 43 steel for which the ratio of ultimate/yield stress is of the order of
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1.75. Since the factor only applies to members with holes, overall yielding on the gross section is therefore avoided.
11.3.5 Pin connected members [BS5400-3, Add at end of clause 11.3.5]
Where this requirement is not met, it shall be ensured through additional checks that tearing will not occur beyond the pin hole.
11.4 Thickness at pin holes [BS5400-3, Add at end of clause 11.4]
Where this requirement is not complied with, it shall be ensured through additional checks that local buckling will not occur beyond the pin hole.
11.6.1 General [BS5400-3, Add at end of clause 11.6.1]
Where battens have been incorporated to cater for lateral loading or vibration (or for erection and handling during construction), and the requirements of 11.6.2 to 11.6.7 are not complied with, the battens and their fixings shall be assessed to resist the effects of all loading to which they are subjected including wind.
11.7.1 General [BS5400-3, Add at end of clause 11.7.1]
Where lacing has been incorporated to cater for lateral loading or vibration (or for erection and handling during construction), and the requirements of 11.7.2 to 11.7.5 are not complied with, the lacing bars and their fixings shall be assessed to resist the effects of all loading to which they are subjected including wind.
11.8.1 General [BS5400-3, Add at end of clause 11.8.1]
Where the above requirements are not met, the perforated plate shall be assessed to resist the effects of all loading to which it is subjected including wind.
11.9 Tension members with components back to back [BS5400-3, Add at end of clause 11.9]
Where the requirements of 10.11.1 and 10.11.3 are not complied with, the members and their fixings shall be assessed to resist the effects of all loading to which they are subjected including wind.
NOTE 1 Where any requirements are not complied with there is a potential for local effects to be significant. However, stability criteria are not applied and battens/lacings can be thinner and lighter than for compression members.
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12 Assessment of trusses 12.1 General [BS5400-3, Add at end of clause 12.1]
Where joints between members are formed using untensioned bolts or rivets in clearance holes such that any secondary bending developed can be relieved by joint movement, bending of members that is solely due to axial deformation of truss members may be ignored for fatigue and serviceability limit states in 12.2.2 and 12.2.3.
NOTE 1 BS 5400-3 permits deformation stresses to be ignored in the middle third of the length of compression members at the ultimate limit state, but other secondary stresses due to eccentricity and off joint loading are included. The assessment method permits that secondary stresses may be ignored altogether provided joints are formed using untensioned bolts or rivets in clearance holes because any developed secondary bending will be relieved by joint movement. As far as fatigue is concerned it is generally unlikely that this will govern highway bridges except where poor details were used.
Vierendeel or other non-triangulated girders or frameworks may be assessed using the requirements of this section. In this case bending and other secondary effects shall be included in assessment of the joints and members.
12.5.2 Restraint to compression chord [BS5400-3, Add at end of clause 12.5.2]
Where assessment of an intermediate U-frame uses measured initial departures from straightness of the compression chord, the value of 𝐹𝑅 shall be calculated in accordance with 9.12.2 with 𝑙𝑒 in accordance with 9.6.4.1.1.2 or 9.6.4.1.3 as appropriate and with the chord treated as a compression flange.
[BS5400-3, Add new clause 12.6.1] 12.6.1 Lateral bracing not providing adequate restraint
Where any provisions of 12.6 are not met, such bracing shall either be:
1) ignored and assumed to provide no restraint, or 2) assumed to provide partial restraint, provided it can be justified using a rigorous non-
linear analysis of the complete system.
12.7 Curved members [BS5400-3, Add at end of clause 12.7]
Members not curved to a circular arc or not complying with any of the requirements (a) to (d), shall be assessed for the following effects instead of using (a) to (d) above:
1) The forces and stresses according to 9.5.7 or the adequacy of flanges to resist the radial component of the flange force, and
2) The effects of the change in neutral axis position due to curvature, and 3) The buckling resistance of sections that do not satisfy the criteria for a compact section.
85
NOTE 1 Assuming the axial force in the flange is distributed uniformly across the width, the line load radial force per unit width across the flange per unit length of the flange can be expressed as: 𝜎𝑓𝑡𝑓𝑜
𝑅𝑓 for a flange outstand, or
𝜎𝑓𝑡𝑓
𝑅𝑓 for a plate panel between longitudinal stiffeners and/or webs
where 𝜎𝑓, 𝑡𝑓𝑜, 𝑡𝑓 and 𝑅𝑓 are all as defined in 9.5.7.1.
12.8.2 Detailing [BS5400-3, Add at end of clause 12.8.2]
Where gusset plates have severe changes in geometric shape such as the presence of sharp re-entrant cuts, the effect of stress concentrations shall be included to determine stress in the gusset plate.
Where 𝑏𝑔/𝑡 exceeds the above limit then the gusset plates shall be checked for local buckling either by means of a detailed analysis or by means of reducing the yield stress 𝜎𝑦 given in 12.8.1 to a value given by Equation 12.8.2.
𝜎𝑦 = 0.9 × 106 (𝑡
𝑏𝑔)2
Equation 12.8.2
NOTE 1 If the limit on gusset plate thickness from BS5400-3 is exceeded, then gusset plates are
assessed for instability. There is no guidance on this item in previous bridge codes, but exceedance is not often expected because the limit is similar to limits for proportions of bottom plates in earlier codes.
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14 Assessment of connections 14.1 General [BS5400-3, Add at end of clause 14.1]
For assessment the term ‘fastener’ shall apply also to the components of members such as screwed tie rods and turnbuckles.
14.2.3 Serviceability limit state [BS5400-3, Add at end of clause 14.2.3]
The criteria to prevent slip at connections under serviceability factored loading in accordance with 14.5.4.1.2 may be disregarded provided all of the following criteria are met: 1) no distress is apparent at the joints; 2) the connection strength is adequate for ultimate factored loading in accordance with
14.5.4.1.1(b); 3) fatigue endurance is adequate in accordance with 14.2.2 with the fasteners assumed to
be black bolts; 4) the calculated deflections due to bolt slip do not cause unserviceability.
NOTE 1 SLS criteria for assessment are described further in 4.2.2.
Where there is evidence of loose rivets in riveted connections then the fatigue endurance of the joint shall also be checked in accordance with 14.2.2 by assuming the fasteners to be black bolts.
[BS5400-3, Add new clause 14.3.3.3] 14.3.3.3 Assessment
Elastic analysis in accordance with 14.3.3.1 shall be used for:
1) checking of HSFG bolts under 14.2.3 to the serviceability limit state, and 2) assessment of welds under 14.2.2 for fatigue endurance.
Plastic analysis in accordance with 14.3.3.2 shall be used in all other cases.
NOTE For the assessment of connections in beams at the ultimate limit state it can normally be assumed that all the bending is resisted by the flanges (along with any associated flange angles) and that shear only is resisted by the web, provided that this is compatible with the basis of the assessment of the member.
NOTE 2 Prior to 1949, practice is known to have been to design the flanges of girders to resist the bending, and the web to resist the shear, though one-eighth of the web plates could have been included in the estimated sectional area of each of the flanges if the web plates are efficiently covered to transmit the horizontal stresses. This means that girder web splices in pre-1949 bridges are likely to be found deficient if, as is now usual practice, the webs and splices are assumed to share in the bending resistance. However, except in the case of HSFG bolts which do not appear in pre-1949 bridges (except as replacements for rivets) 14.3.3.2 permits “plastic analysis” which can be taken to mean flanges resist all of the bending and web splices resist only shear.
87
14.3.4 Distribution of load to the connected members [BS5400-3, Add at end of clause 14.3.4]
Where any part of a member is connected so that the load is not distributed over its effective section, the load dispersion from the fastener shall be determined by detailed analysis or by assuming the load is dispersed from a fastener onto a connected part within an angle of ± 45° from the direction of the force.
14.3.5 Connection of restraints to parts in compression [BS5400-3, Add at end of clause 14.3.5]
Where the connection cannot resist the forces in (a) and (b) above, the intermediate restraint shall be ignored or the system checked by making allowance for the maximum restraint that can be provided, in accordance with 9.6.
14.3.6 Prying force [BS5400-3, Replace existing clause 14.3.6 with]
Where more than one line of bolts or rivets is present and in the absence of more detailed analysis or effective stiffening to reinforce the connection, only the inner line of fasteners adjacent to the web shall be assumed as effective in resisting the tensile load.
The value of additional bolt force, 𝐻 due to prying shall be taken as the greater of 𝑃𝑡/10, 𝐻1 and 𝐻2, taken according to Figure 45a, Equation 14.3.6a and Equation 14.3.6b.
𝐻1 = 𝑃𝑡 {
1
2−(
𝐿𝑡4
30𝑎𝑏2𝐴𝑒)
𝑎
𝑏(𝑎
3𝑏+1)+(
𝐿𝑡4
6𝑎𝑏2𝐴𝑒)} Equation 14.3.6a
𝐻2 = [𝑐
2𝑎−1
8] [𝑃𝑡 − (
𝐹𝑣𝐿𝑡4
18𝑎𝑏2𝐴𝑒)] Equation 14.3.6b
where symbols are as defined in Figure 45a.
NOTE 1 More detailed expressions are provided for deriving values of prying force for assessment, since the minimum value given for design could be unsafe for some situations where the design arrangements are not met or unnecessarily excessive for other cases.
NOTE 2 The value of the prying force developed in the fasteners of a connection is dependent on a complex relationship between the bending stiffness of the flange and the axial stiffness of the fastener but generally for a given connection geometry, as the stiffness of the flange is reduced then the prying force increases.
NOTE 3 The requirement that a lower bound value for prying force of 10% of the applied tension in the fastener be considered is an attempt to limit any possible loss of preload due to yielding of the fastener under overload conditions.
As a simplified alternative for initial assessment the additional bolt force, 𝐻 may be taken instead as the greater of 𝐻3 and 𝐻4 according to Equation 14.3.6c and Equation 14.3.6d.
𝐻3 = 𝑃𝑡 [3𝑏
8𝑎− (
𝑡
69)3] Equation 14.3.6c
𝐻4 = [𝑐
2𝑎−1
8] 𝑃𝑡 Equation 14.3.6d
where
88
t is the plate thickness in mm
other symbols are as defined in Figure 45a NOTE 4 It is unlikely that the effect of prying forces on tensile connections will have been considered
in the design of existing bridges designed prior to [BS 5400-3]. Riveted structures generally avoided the use of fasteners in tension so the absence of prying treatment in previous codes is not likely to be serious for these cases.
NOTE 5 Further background data on prying action is given in references 14.3.2 to 14.3.5. NOTE 6 The Equations 14.3.6c and 14.3.6d are conservative simplifications of Equations 14.3.6a and
14.3.6b, based on references 14.3.5 and 14.3.4.
Figure 45a – Notation for prying forces
Note The terms in this figure are defined as:
L is the limitation on the length of section 1 or 2.
60° is the maximum value of these angles that may be assumed for the spread of 𝑃𝑡 from the normal.
𝐴𝑒 is the relevant bolt or rived area in accordance with 14.5.3.2 or 14.5.3.3.
𝐹𝑣 is any prestress, see 14.5.4.3.
14.4.1 Cover material 14.4.1.1 General [BS5400-3, Add at end of clause 14.4.1.1]
Where only one surface of the spliced part is provided with covers, bending effects due to eccentricity between the cover plate and the spliced part shall be included for calculation of stress in the connected parts except where stated otherwise below.
These bending effects due to eccentricity may be ignored in the following situations:
1) at ultimate limit state except for compression components that may be vulnerable to buckling, or
89
2) with the presence of surrounding or adjacent concrete or other solid infill that prevents bending, or
3) with the presence of an element that prevents bending of either the parent material or the cover and provided that this element is within a distance of 12t from the furthest fastener, where t is the thickness of the parent material to which the cover plate is attached.
NOTE 1 Where single sided covers only are present, it is likely that use of the full eccentricity of the cover and spliced part will significantly reduce the assessed capacity because of the bending stress apparently created. Although the effect of eccentricity is important for single sided splices, the stresses can be much lower than adding the product of eccentricity and load as a moment in the cover. Tests have demonstrated, for example, that in some circumstances welded single sided covers can develop the full capacity of bulb flats.
NOTE 2 Where splices are in tension at ultimate load the bending stresses would tend to be redistributed as the joints distort, so requirements are given only for serviceability.
For the calculation of bending effects due to eccentricity it may be assumed that the line of action of the axial force in the splice is located along the interface between the parent material and the cover.
14.4.5 Obsolete splicing methods [BS5400-3, Add at end of clause 14.4.5]
Where splices occur in multi-layered plates similar to Figures 14.4a or 14.4b, the load path through the joint shall be checked to ensure no single component is overloaded.
Figure14.4a – Force flow in plate shingle joint
Figure 14.4b – Types of filler plates
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14.5 Connections made with bolts, rivets or pins [BS5400-3, Delete existing clause 14.5.1.3 and replace with] 14.5.1.3 Staggered spacing
Where bolts or rivets are staggered at equal intervals and the gauge is not greater than 80mm, the maximum distance between centres of bolts or rivets, permitted by 14.5.1.2.2 and 14.5.1.2.3, may be increased by 50%.
NOTE 1 The value of 80mm has been used for assessment since it is believed that existing bridges might have a gauge length of 3 inches, i.e. greater than the 75mm used in [BS5400-3], but for which no reduction is really needed.
[BS5400-3, Add new clause 14.5.1.5] 14.5.1.5 Assessment of non-complying arrangements
Where the spacing of fasteners does not comply with 14.5.1.1, 14.5.1.2, 14.5.1.3 or 14.5.1.4, the following shall apply:
1) Where there is evidence of plate bulging, distortion near or to fasteners or excessive rust forming, allowance shall be made for the reduction in strength.
2) Where the spacing between fasteners is less than 2.5d, the friction capacity shall be reduced in linear proportion from a value of 100% of the normal capacity at 2.5d to 80% of the normal capacity at 2.0d. Where the spacing is less than 2.0d, the friction capacity of one fastener shall be ignored.
3) Where the spacing between two fasteners away from an edge is less than 2.5 times the diameter of the shank of the bolt or rivet, the strength of each shall be reduced in linear proportion to a value of zero when the spacing is 1.5 times the shank diameter. Where a fastener is close to more than one other, the reduction factors shall be multiplied together
4) Where the maximum pitch requirements in 14.5.1.2 are exceeded and the parts joined are in tension or shear, the connections shall be examined carefully to determine whether any corrosion has occurred. In the absence of evidence for such corrosion, a reduction of strength shall not be required.
NOTE 1 The maximum pitch requirements in [BS5400-3] are intended to avoid corrosion by ensuring that the plates are kept sufficiently close together for the paint film to be able to seal any gaps between the plates.
NOTE 2 Away from edges, this examination might be limited to any signs of corrosion around bolt heads or nuts, or bulging of plates.
5) Where the parts joined are in compression and the limits that are given as a multiple of t are exceeded, a reduced yield stress of the outer plies shall be used, with the reducing factor, 𝑘𝑟, taken from Equation 15.5.1.5a. Where the limits are exceeded in two directions, the lesser value of the reducing factor in the two directions shall be used.
𝑘𝑟 = (𝑘0
𝑘𝑎)2, but in no case greater than 1 Equation 14.5.1.5a
where
𝑘0 is the permitted maximum multiple of t
𝑘𝑎 is the actual multiple of t.
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NOTE 3 Where the plates are in compression, the requirements for spacing given as a multiple of t are intended also to prevent local buckling of the plates.
6) Where the parts joined are in compression and the limits quoted as absolute dimensions are exceeded, the connections shall be examined carefully to determine whether any corrosion has occurred.
7) Where spacing is staggered, the same approach as in (1) to (6) above may be used. 8) A similar approach to (5) above may be used in cases of non-compliance with 14.5.1.4.
However, in this case the reducing factor, 𝑘𝑟, for yield stress, to be applied to the plate or other part subjected to compression or shear should be taken from Equation 14.5.1.5b:
𝑘𝑟 = (𝑏
4𝑆𝑎)2, but in no case greater than 1 Equation 14.5.1.5b
where
𝑏 is as defined in 14.5.1.4.
𝑆𝑎 is the actual spacing between the centres of the two consecutive bolts or rivets connecting the stiffener to the plate or other part subjected to compression or shear.
14.5.2 Edge and end distance [BS5400-3, Add at end of clause 14.5.2]
Where for assessment purposes any of the above limits for design are not complied with, the strength of the fastener or plate shall be reduced as follows:
1) Where a fastener is adjacent to an edge that is parallel to the direction of force, the value of 𝑘2 in 14.5.3.6 shall be linearly reduced from the value 2.5 when the edge distance is 1.2𝑑 to a value of zero when the edge distance is 0.8𝑑.
2) Where the end distance of a fastener at the end of a plate is not less than 0.8𝑑 and the load is applied from the fastener to the plate in a direction away from the plate edge, no reduction shall be required due to end distance. Fasteners closer than 0.8 to the end of the plate shall be ignored.
3) Where a fastener is adjacent to the end of a plate and the load is applied from the fastener to the plate in a direction towards the plate edge, the value of 𝑘2 in 14.5.3.6 shall be reduced linearly from the value of 1.2 when the edge distance is 1.2𝑑 to a value of zero when the edge distance is 0.9𝑑.
4) Where the edge distance is less than 1.5𝑑, the friction capacity shall be reduced linearly to a value of zero when the distance is 1.0𝑑.
5) Where strengths are mutually affected by more than one limit, the resulting reduction factors shall be multiplied together.
14.5.3 Strength of other fasteners and HSFG bolts not acting in friction 14.5.3.1 General [BS5400-3, Add at end of clause 14.5.3.1]
Where for assessment purposes any of the general or specific requirements of this clause or any of the following sub-clauses are not met, due allowance shall be made on the strength of the fasteners.
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NOTE 1 For rivets tests have shown that the actual strength capacity often exceeds that shown by calculations. Consequently testing of connections could show greater strength than that specified in the standards.
Where black bolts have been used in permanent main structural connections, their assessment shall include a fatigue check.
NOTE 2 Fatigue check of black bolts is generally as Class G detail.
Bolts shall be assumed to be black bolts and rivets shall be assumed to be hand driven unless there is evidence to the contrary.
As an alternative, the requirements in BS EN 1993-1-8 together with the partial factors for materials in BS EN 1993-1-8 may be used to determine the strength capacity.
NOTE 3 Capacity from BS EN 1993-1-8 is based on the ultimate strength of the bolts or rivets rather than the yield stress.
The diameter of the hole shall be taken as given on record drawings.
Where the hole diameter is not known, it may be taken as a normal clearance hole of 2mm greater than the bolt diameter for bolts smaller than 27mm and 3mm greater than bolt diameter for bolts of 27mm and over.
For structures to imperial units, reference should be made to contemporary standards for the limiting sizes of holes.
NOTE 4 Typically, clearance holes were taken to be 1/16"(1.6 mm) larger than the bolt; rivets were driven in holes 1/16" (1.6 mm) greater than their nominal diameters.
Where there is reason to suggest that the holes are oversize, this shall be investigated or a suitable allowance made.
NOTE 5 To determine the actual diameter, d, of the holes in individual plies, and whether holes have been reamed, it can be necessary sometimes to remove sample bolts.
Where the bolt holes are larger than clearance holes, the capacity of the connection shall be taken as a lower bound capacity which is calculated to prevent excessive deformation or premature failure of individual bolts.
For the application of 14.5.3.1, all connections that are subjected to live or wind load effects shall be considered to be “permanent main structural connections”.
Where HSFG bolts are used in connections with mixed bolts and rivets, the HSFG bolts should be considered only to act in friction at ULS, as the rivets cannot accommodate the slip necessary for clearance bolts to act in bearing/shear.
14.5.3.2 Bolts subjected to axial tension [BS5400-3, Add at end of clause 14.5.3.2]
Where the manufacturing standard of bolts is BS 3692, BS 4190, BS 4395, or other known standards, values of tensile area and 𝜎𝑡 shall be taken from the relevant standard.
Where the relevant manufacturing standard of bolts is not known, the tensile area may be taken as 60% of the shank area.
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Where the relevant value of 𝜎𝑡 is not known, a worst credible value shall be assumed.
NOTE 1 A worst credible value for 𝜎𝑡 of 230 N/mm2 can be presumed in most cases.
Alternatively, tensile tests may be carried out on a statistically significant sample of bolts taken from the structure.
NOTE 2 See also 4.3.3.
High Strength Friction Grip (HSFG) bolts specified to BS 4395-2 shall not be used to resist applied axial tension.
NOTE 3 BS 4395-2 covers HSFG grade 10.9 bolts.
14.5.3.3 Rivets subjected to axial tension [BS5400-3, Add at end of clause 14.5.3.3]
Where there is significant loss of rivet heads, the tensile capacity shall be reduced.
Where rivets are subject to tension due to live loads, 𝜎𝑓 shall be reduced to that for countersunk rivets, for which the remaining effective head diameter is not more than 1.3 times the nominal diameter.
Where rivets are subject to tension due to live loads and the remaining effective head diameter is less than 1.3 times the nominal diameter, 𝜎𝑓 shall be reduced to zero.
Where the sizes of the rivet holes are not known, sample rivets of each head size and diameter shall be removed to determine the size of the hole.
14.5.3.4 Bolts subject to shear only [BS5400-3, Add at end of clause 14.5.3.4]
For bolts other than turned barrel bolts, the bolt shank area should only be taken as the shear area if it can be ensured from bolt dimensions on drawings or otherwise that the threaded length is clear of the shear planes.
When checked for the shear capacity of HSFG bolts that are in accordance with BS 4395 Parts 1 and 2 in accordance with 14.5.4.1.1 (b), the shear planes should be assumed to pass through the threaded length.
NOTE 2 For HSFG bolts in accordance with BS 4395 Parts 1 and 2, it would have been desirable at installation to have a reasonable thread length within the grip length of the bolt, as the major proportion of bolt extension takes place in this length.
14.5.3.8 Long grip rivets
Where the grip length of a rivet exceeds eight times the diameter of the hole, the connection shall be inspected carefully for any signs of slip or separation at the interfaces.
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14.5.4.1.1 Ultimate limit state [BS5400-3, Add at end of clause 14.5.4.1.1]
Friction group bolts of types, arrangements or tightness not in accordance with this or any of the following sub clauses shall be assessed by reference to 14.2 and published data relating to the bolt type or by tests on selected bolts in the structure.
Where waisted shank bolts are used and evidence of slip indicates that the bolts are acting in bearing/shear, the following shall apply:
1) each bolt should be inspected to confirm that it has not fractured, and 2) the strength of the fastener shall be calculated as for a bolt in bearing/shear based on the
waisted diameter.
NOTE 1 Normally only ULS is to be assessed and not SLS, but see assessment criteria given in 14.2.3. In most cases the shear/bearing capacity will determine the strength of the fasteners.
14.5.4.2 Friction Capacity [BS5400-3, Add at end of clause 14.5.4.2]
Where bolts have been tightened in accordance with BS 4604 and the condition of the friction surface during installation is known with confidence and there is no evidence of contamination,
1) the partial factor 𝛾𝑚 shall be taken as 1.30 at the ultimate limit state and 1.20 at the serviceability limit state, and
2) 𝜇 may be taken as given in 14.5.4.4.
Where circumstances are different from the above, the following shall apply:
1) determine appropriate partial factors and 𝜇 factors by taking into account the probable prestress in the bolts and the condition of the friction surfaces.
2) determine values for 𝛾𝑚 based on the methods given in 4.3.3. 3) Where the condition of the friction surface is unknown and it is impracticable to remove
any cover for inspection, use a value of not greater than 𝜇 = 0.10.
NOTE 1 For blasting carried out in accordance with the Specification for road and bridge works (1976 Edition), 1st quality to BS 4232 would have been required, for which a value of 𝜇 = 0.5 is appropriate. The value of 𝜇 = 0.45 was recommended for other qualities of blast cleaned surfaces to BS 4232 (by BA19/85 - withdrawn).
NOTE 2 Departmental Standard BD 7/81 (now CD 361) specified a 3rd quality blast cleaning to BS 4232 for weathering steel, for which 𝜇 = 0.45 was recommended.
14.5.4.4 Slip factor [BS5400-3, Amend clause 14.5.4.4]
The text “to the satisfaction of the Engineer” on the last line shall be deleted.
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14.5.4.5 Oversized and slotted holes [BS5400-3, Add at end of clause 14.5.4.5]
Where the size of the holes is larger than the limits in the Table 12 or cannot be confidently taken to lie within the limits, the performance of the connection shall be assessed on an individual basis, paying particular attention to the likely condition of the interfaces and the consequences if slip were to occur.
Alternatively, the capacity of all bolts in holes which do not comply with the limits may be taken as zero and the adequacy of the connection determined from the capacity of the remainder of the bolts.
Where it is known or confidently believed that the size of the holes complies with Table 12, 𝑘ℎ may be taken as 0.85 for over-sized and short slotted holes, or 0.70 for long slotted holes.
Table 12 may be interpolated for use with imperial sizes and minor infringements arising from conversion ignored.
The reduction factor 𝑘ℎ should be applied if the hole in any of the plies is greater than normal.
Values of 𝑘ℎ shall not be extrapolated to less than those quoted above except after verification by testing.
NOTE 1 Where the clearance around HSFG bolts is greater than that in normal clearance holes, the potential movements if slip should occur is greater. There is also a greater risk of impact and consequent fracture of the stressed bolt if a sudden slip occurs. In such circumstances it is usual to specify a higher factor against slip and this is achieved by applying the reduction factor 𝑘ℎ to the calculated friction capacity.
14.6 Welded connections 14.6.1 General [BS5400-3, Add at end of clause 14.6.1]
Welded connections known to have been welded in accordance with BS EN 1011, BS 5400-6, BS 5135: 1974 or BS 5135: 1984 may be assessed using the strengths in 14.6.2.3 for butt welds and in 14.6.3.11 for fillet welds.
Welded connections not known to comply with the above standards may be assessed using the following alternative criteria for strength:
1) Where butt welds are in compression the strength may be taken as defined in 14.6.2.3 2) Where butt welds are in tension or shear and are free from surface cracks the strength
may be taken as:
a. equal to the strength as defined in 14.6.2.3, for welds complying with the re-inspection criteria in Annex I, or
b. 85% of the strength defined in 14.6.2.3, for other cases.
3) Where fillet welds are constructed to BS 153: Part 1: 1958 or BS 153: Part 1: 1972 and are free from surface cracks, the strengths may be taken as:
a. equal to those derived from 14.6.3.11, for welds complying with the re-inspection criteria in Annex I, or
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b. 90% of the strength derived from 14.6.3.11, for other cases.
4) Where fillet welds are not in accordance with (3) but are free from visible surface cracks, the strengths may be calculated in accordance with 14.6.3.11, but replacing the term 𝜎𝑊 = 0.5(𝜎𝑦 + 455) by:
a. 𝜎𝑊 = 0.5(𝜎𝑦 + 400), for welds complying with the re-inspection criteria in Annex I, or
b. 𝜎𝑊 = 0.4(𝜎𝑦 + 400), for other cases.
Where any of the general or specific requirements of this or any of the following sections are not met, due allowance shall be made in the assessment of the strength of welds.
Crack like defects in critical tensile regions shall not be permitted.
NOTE 1 Welded connections in existing bridges can also be deficient in terms of their toughness properties, which cannot be measured in-situ by non-destructive testing. The requirements for toughness are given in 6.5.
Where welds are not detailed in accordance with requirements of this document, any reduction of strength or fatigue implications should be taken into account.
NOTE 2 Examples of non-complying details might be:
1) welds not detailed to BS 5135 or of yield stress less than that of parent material (14.6.1); 2) intermittent or partial penetration butt welds (14.6.2); 3) fillet welds with excessive gaps, incomplete end welds or returns, end connections with
non-complying side fillets or overlaps and packings not trimmed flush (14.6.3); 4) non-complying plug welds (14.6.4); 5) welds with defects.
NOTE 3 Often it will not be known whether welds had been detailed to BS 5135, (ie with root face and gap dimensions as recommended), but this would not be detrimental provided appropriate procedural and production testing was undertaken at the time of construction.
NOTE 4 It can reasonably be argued that bridges constructed since 1974 (ie at publication of BS 5135) will have been welded to BS 5135 such that their weld metal yield strength is at least equal to that of the parent metal, and that full penetration was likely to have been achieved in the butt welds where this was intended.
NOTE 5 The same are also likely to be true for bridges welded to the earlier standards BS 1856 and BS 2642. However at that time the sensitivity of equipment for non-destructive testing of welds was such that significant hidden defects could remain undetected, whereas visible defects would have been discovered and repaired. Except in cases where other evidence is available, it would therefore appear prudent to downgrade the strength of welds in bridges built prior to 1974 where hidden defects or lack of penetration could be significant, i.e. in butt welds.
NOTE 6 It is a fact that all welds contain defects of one sort or another, there being no such thing as a perfect weld. Many defects such as porosity and minor lack of penetration do not significantly affect strength. BS 153: 1972 allowed butt welds to be treated as parent metal. Permissible stresses in fillet welds were between 0.43𝜎𝑦 for Grade 43 to 0.37𝜎𝑦 for Grade 50. Allowing for the factor of safety of 1.7 in BS 153: 1972, the corresponding values from BS 5400-3 are 0.43𝜎𝑦 for side fillets in Grade 43 and 0.35𝜎𝑦 for side fillets in Grade 50. It appears, therefore, that although BS 5135 was not available, the BS 5400-3 strengths were considered to be satisfactory in 1972.
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NOTE 7 The value of 𝛾𝑚 used at ultimate limit state in BS5400-3 for fillet weld strength is increased from 1.1 to 1.2 by BD 13/90. The value of 1.1 was based on the calibration of pre-1974 results. The strengths of welds in bridges built before 1974 are therefore downgraded unless evidence is available that welds comply with modern standards. It is not easy to stipulate a value for 𝛾𝑚 to represent a downgrading because 𝛾𝑚 already varies depending upon the type of member. The simplest way is to reduce the yield stress of the weld metal. The measure of strength reduction due to the presence of weld defects is addressed by BS 7910 in detail, but a basis for assessment is to assume that the strength of the welds are downgraded by a maximum of 15% unless there is evidence that the weld complies with the re-assessment criteria in Annex I by results of n.d.t either at the time of construction or since.
[BS5400-3, Delete existing clause 14.6.2.1 and replace with] 14.6.2.1 Intermittent butt welds
For the assessment of intermittent butt welds, a length equal to three times the throat thickness at each end of any intermittent length shall be ignored in the calculation of strength.
NOTE 1 It is unlikely that the intermittent butt welds will exist often. The assessment provisions ignore a length at the weld ends because full penetration is difficult to achieve here. Arbitrarily it is proposed to deduct the contribution of the weld ends equal to approximately three times the throat thickness.
14.6.2.2 Partial penetration butt welds [BS5400-3, Add at end of clause 14.6.2.2]
The strength of partial penetration butt welds shall be calculated as for fillet welds.
For single sided joints where transverse bending causes tension across the root then the yield stress of the weld metal shall be taken as 50% of the weaker of the parts joined in assessing the resistance to transverse bending.
NOTE 1 BS5400-3 effectively bars the use of partial penetration butt welds under tensile stress and was drafted to avoid designs where cross bending is applied to single sided welds such that the root is operating at peak tension. However, in many cases partial penetration welds are provided as part of a two sided joint and cross bending does not put the root into peak tension.
NOTE 2 In assessment it is reasonable that partial penetration welds be treated as for fillet welds when they are not eccentric. Where single sided welds occur then the tensile stress in the root is limited arbitrarily by assuming that the yield stress of the weld metal is 50% of the strength of the weaker part joined.
Partial penetration butt welds in non-fatigue prone connections may be assessed by reference to BS 5950.
NOTE 3 BS 5950 does not apply for eccentric welds carrying tension or compression.
Where welds are not known to have been tested through procedure trials at the time of construction nor demonstrated by testing, the throat thickness of a partial penetration butt weld shall be taken as 90% of the nominal.
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14.6.3.9 Effective throat of a fillet weld [BS5400-3, Amend clause 14.6.3.9]
The text on paragraph 2, line 2, “to the satisfaction of the Engineer” shall be deleted.
[BS5400-3, Add at end of clause 14.6.3.9]
NOTE 1 Until 1995, UK practice for showing the sizes of fillet welds on drawings was normally by indicating the leg length. Stating throat thicknesses on weld drawings, instead of leg lengths, only started coming into British practice with the introduction of BS EN 22553 in May 1995.
14.7.2 Other combinations [BS5400-3, Amend clause 14.7.2]
The text on line 3, “to the satisfaction of the Engineer” shall be deleted.
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[BS5400-3, Add new clause 15] 15 Outmoded forms of construction 15.1 General
This section shall be used to assess the buckle plate, joggled stiffener and knee stiffener forms of construction.
Any outmoded forms not covered within this section shall be assessed using the relevant section of this document where possible.
NOTE 1 In some cases additional studies, special analyses and tests could be beneficial to the type and form of outmoded construction encountered, to supplement the assessment checks carried out.
15.2 Buckle plates 15.2.1 General
Buckle plates consisting of vertically curved steel plates with ballast or non-structural filling and spanning between supporting steel members shall be assessed by 15.2.2 or 15.2.3 as appropriate.
NOTE 1 Buckle plates are an outmoded form of construction in which curved or "buckled" steel (or wrought iron) plates span between supporting beams as shown in Figure 15.2. Buckle plates can either be arched (bowing upwards) or suspended (bowing downwards) and are normally riveted or bolted down to the supporting steelwork. It is noted by one reference that buckle plates were unsuitable for supporting block pavement under concentrated moving loads.
Figure 15.2 – Buckle plates
NOTE 2 There appears to be little published information or methods of design for buckle plates.
However some capacities are provided by the 1920 “Arrol’s Bridge & Structural Engineer’s Handbook” from experiments with arched wrought iron plates 0.91m square and with 50mm rise (see ref 15.2.1). Comparison of these capacities with notional calculations based on various design approaches are shown in Table 15.2. The capacities calculated for comparison assume a uniformly distributed loading and a “working stress” approach with mild steel at 165 N/mm2 bending stress.
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Table 15.2 – Buckle plate capacity compared with 1920 Arrol Handbook
Plate Thickness,
mm
Arrol 1920 Handbook
Flat Plate Suspended Arched
Encastré Simply supported
Thrust= 𝑤𝐿2/8𝑟 Buckling assuming strut with 𝑙𝑒 = 𝑠𝑝𝑎𝑛/2
6.2 54 24 18 502 40
7.9 75 38 28 629 76
9.5 100 55 41 757 129
Note Buckle plate 0.91m2, supported 4 sides. Table shows capacity for uniformly distributed loading compared with 1920 Arrol Handbook, safe u.d.l. in kN/m2.
NOTE 3 The comparisons in Table 15.2 show that buckled plates derive some benefit from arching
action, but that full horizontal thrust capacity is probably not available. It is seen that a reasonable comparison is reached assuming that the plate when acting as an arch is analogous to a strut having an effective length equal to half the span. Clearly in practice the capacity depends on:
1) Span, plate thickness and rise; 2) Whether supported, or stiffened, on 2 or 4 sides; 3) Form of filling, loose or solid; 4) Resistance to thrust by connections and capacity of supporting members; 5) Uniform or concentrated loading.
NOTE 4 In order to establish a fully reliable assessment method it would be necessary to undertake research by testing. The number of different forms of buckle plates means that this could be extensive. It is unwarranted compared with the number of bridges likely to be remaining in service carrying traffic loading on buckled plates, because often they occur beneath footways only. A simple and conservative approach is therefore proposed for checking the capacity of buckle plates typically encountered based on the available information given above and upon judgment. A simplified approach based on arch or catenary action is considered appropriate for spans up to 1.2m only, with rise between 1/12th and 1/18th of the span, where the plates are riveted or bolted down on at least 2 sides. In other cases and where the structure is limited by the thrust capacity of the fixings or supporting members, then a flat plate approach is used.
15.2.2 Spans of 1.2 m or less
Where the clear span measured between edges of supporting members is 1.2 m or less and complies with the following:
1) the rise is between 1/12th and 1/18th of the clear span, and 2) the plate thickness is at least 6 mm,
the strength may be assessed assuming arch or catenary action with the horizontal thrust taken as 𝐻 from Equation 15.2.2.
𝐻 =𝑤𝐿2
8𝑟 per unit width Equation 15.2.2
where
𝑤 is the pressure on surface of plate due to dead loads and dispersed live load. Concentrated wheel loads over the plate can be dispersed at 1:1 for solid filling
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and at 1(horizontal) to 2(vertical) for loose filling. The maximum pressure calculated is assumed to occupy the full area of the plate.
𝐿 is the span of buckle plate between edges of supporting members.
𝑟 is the rise of buckle plate.
Where arching action is used, the capacity of the arch for horizontal thrust may be checked as a straight compression members in accordance with 10.6, with parameters taken instead to be the following when calculating the value of 𝜎𝑐:
𝜂 is the buckling parameter to be taken as 𝜂 = [𝑎(𝜆 − 15)].
𝑙𝑒 is the effective length, to be taken as extending from the end of the span to the intersection point with the wheel distribution, but not less than 0.5𝐿.
NOTE 1 This 𝜂 value is consistent with the BS5400-3 clause, i.e. without using measured imperfections.
Where catenary action is used, the capacity for tension in the plate shall be checked as a tension member in accordance with clause 11.
Where arch or catenary action is assumed, the fixings and the supporting members shall be capable of resisting the horizontal load.
Alternatively to the methods above, the buckle plate may be checked as a flat plate without the effects of catenary or arch behaviour.
15.2.3 Spans of more than 1.2 m
Domed buckle plates of spans greater than 1.2m shall be checked as flat plates unless testing or detailed analysis is carried out demonstrating greater capacity.
Suspended buckle plates of spans greater than 1.2m may be checked as a flat plate or as a tension member according to the method in 15.2.2.
15.3 Joggled stiffeners 15.3.1 Assessment of joggled stiffeners
The criteria for assessment of joggled stiffeners shall use the additional requirements of 15.3.2 or 15.3.3 combined with the relevant sub-clauses of 9.13 or 9.14 as appropriate, to derive effective sections and loading and assess the strength.
In addition, the limitations on shape shall be addressed in accordance with 9.3.
NOTE 1 Joggled stiffeners to beams are an outmoded form which occurs in riveted construction where the necessity to employ flange angles interrupted the web depth. This means that stiffeners are “joggled” to clear the vertical leg of the flange angles. The alternative was to insert packings between stiffener and web as practised when the stiffeners acted as bearing stiffeners. The different types are shown in Figure 15.3.
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Figure 15.3 – Stiffener types in riveted construction
NOTE 2 Joggled or knee stiffeners ((i) & (iv) above) introduce a local eccentricity which could reduce their strength (although no experimental work is known) in carrying axial load, i.e. as a bearing stiffener, but much less likely to reduce their effectiveness as intermediate stiffeners. This had been appreciated in the drafting of old codes such that it is unlikely in practice that joggled or knee stiffeners will exist except as purely intermediate stiffeners.
15.3.2 Joggled stiffeners acting as transverse web stiffeners other than at supports
Joggled or knee type transverse stiffeners shall be assessed as transverse web stiffeners.
Where an axial force resulting from application of 9.13.3.1 (c), (d), (e) and (f) is applied to joggled or knee type stiffeners other than within the straight portion between joggles, the additional bending stress introduced by the shape of the stiffener shall be included within the joggle height when checking yielding of the stiffener under 9.13.5.2.
The additional bending stress shall be in accordance with 1 for joggled stiffeners and in accordance with 2 for knee stiffeners:
1) For joggled stiffeners the bending stress shall be calculated assuming that a bending moment is applied to each stiffener leg equivalent to its axial load multiplied by an eccentricity equal to one half of the joggle offset. The joggle height over which the bending stress can be included shall be taken as at the level of the joggle and extending to the first fastener either side which connects the stiffener to the web.
2) For knee stiffeners the bending stress shall be calculated assuming that a bending moment is applied to each stiffener leg equivalent to its axial load multiplied by an eccentricity equal to one half of the horizontal distance from the centroid of the stiffener to the point of intersection of its flange with the beam flange. The height, over which the bending stress is to be included, shall be taken as from the flange in contact with the stiffener to the first fastener where the stiffener is connected to the web.
15.3.3 Joggled stiffeners acting as load bearing support stiffeners
Where joggled stiffeners or knee stiffeners occur as load bearing support, the additional bending stress introduced due to the shape of the stiffener shall be assessed when applying 9.14.4.1. The additional bending stress may be calculated in accordance with 15.3.2.
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NOTE Where stiffeners act as bearing stiffeners then either packed or gusseted stiffeners would appear to require no special assessment over existing BS 5400-3 requirements. Joggled or knee types deserve consideration, although it seems unlikely that many will exist because of the requirements of the old codes. Joggled gusseted stiffeners and knee gusseted stiffeners can be assessed more easily by ignoring the joggled region from assessment.
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[BS5400-3, Add new clause 16] 16 Bearings and bearing areas 16.1 General
Bearing types within scope of BS 5400-9 shall be assessed to BS 5400-9.
Steel bearings of types outside the scope of BS 5400-9 shall be assessed using BS 5400-3 (as implemented by this document).
Bearings may alternatively be assessed to BS EN 1337 where applicable.
Where movement of a bearing is impaired or restricted, then load effects shall be included in the assessment in accordance with CS 454.
NOTE 1 The transfer of horizontal loadings, especially longitudinal forces, can also be uncertain. As far as temperature restraint effects are concerned it is likely that structure will be showing signs of distress, such as by local spalling of masonry, where temperature effects have been relieved. The specific assessment of inbuilt temperature effects is therefore considered of secondary importance because it is mainly a question of unserviceability.
16.2 Beams without bearings
Where beams do not have discrete bearings and bear directly on concrete, brickwork, or masonry substructures with or without a bearing plate or other distributive layer, then the local distribution of load to the substructure shall be assessed taking due account of any rotation or movement.
Patch loading to the web of the beam shall be assessed in accordance with 9.9.6 where appropriate.
16.3 Pressure distribution under bearing areas
Where the end of a beam bears directly on a substructure without bearings a linear pressure distribution shall be assumed varying from a maximum at the inner face of the contact area down to zero at the far face or free end of the girder.
The assumed length of the contact area shall not exceed the length of girder in contact, or the depth of the beam if less.
For distribution transversely or in other directions as appropriate, a dispersal angle of 2 horizontal to 1 vertical shall be assumed through any flange angles, flange plate(s) and bearing plate (s) present onto the surface of concrete, brickwork, masonry or other material of the substructure.
NOTE 1 This assumption follows that in BS 153.
The effective span of the beam shall be assumed to extend from the centroid of the contact area determined.
NOTE 2 The dispersal angle and the extent of effective span are illustrated in Figure 16.3.
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Figure 16.3: Distribution of pressure through bearing areas
16.4 Maximum pressures under bearing areas
For concrete substructures the compressive stress in the contact area shall not exceed the allowable limits given by CS 455.
For masonry bed stones the bearing stresses shall not exceed 0.4 𝑓𝑐𝑢, with 𝑓𝑐𝑢 being the characteristic compressive strength of the masonry. Where inspection has shown evidence of no local spalling, no cracking and no other distress, this value may be increased to 0.6 𝑓𝑐𝑢.
The compressive strength of the masonry should be derived by testing where possible. Failing this, published information of guidance on strengths of different materials quoted in CS 454 should be used.
Bearing loads shall be assumed to disperse at an angle of 1:1 through masonry bed stones down to supporting coursed masonry or brickwork.
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Annex G - Equations used for production of curves in Figures
G.8 Limiting moment of resistance 𝑴𝑹 [BS5400-3, Amend clause G.8]
In the definition of 𝜂, the term 𝑙𝑤/𝑙𝑒 shall be omitted in the expressions for both Figure 11a and Figure 11b.
The definitions of 𝑙𝑤 and 𝑙𝑒 shall be deleted.
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[BS5400-3, Add new Annex H]
Annex H - Derivation of nominal yield stress for assessment
H.1 General
The nominal yield stress, 𝜎𝑦, for use in the assessment of existing bridges shall be derived using one of the methods from this Annex. Although written in terms of yield stress some methods may also be used to assess ultimate tensile stress.
NOTE 1 The choice of methods given in Annex H for deriving the assessment yield stress depend on the extent of knowledge of the origin and properties of the steel used in a structure. Some methods can also offer advantages for recent structures when there are several relevant mills’ test certificates showing a mean strength substantially greater than the specified minimum.
H.2 Yield stress based on specifications
The nominal yield stress may be determined depending on the specification of the steel from construction using Table H.2.
Table H.2
Known specification of steel from construction
Nominal yield stress
BS EN 10025, BS 4360 or other steels in accordance with BS 5400-6.
nominal yield stress to be taken as the minimum value specified in the relevant Standard.
BS 15, BS 548, BS 968 or BS 2762 and thickness up to 63mm
the nominal yield stress may be taken as the minimum value specified in the relevant Standard for material appropriate to the thickness of 16mm irrespective of the actual thickness of the component.
Material quality specified is not known and no test information is obtained
the steel may be assumed to be a mild steel grade with specified minimum yield stress in BS 15 or BS 4360 appropriate to the date of construction provided that the steel can be identified, by means of trade marks or names, as being made by a recognised supplier.
In all cases the material standard referred to should be that current at the date of fabrication.
H.3 Yield stress based on tests of the material in the component to be assessed
For the nominal yield stress to be taken as the measured value without adjustment, the tensile testing shall be in accordance with BS 4360 and using a sample from the particular component to be assessed.
These samples should be taken at the locations within the cross section defined in BS 4360.
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H.4 Yield stress based on mill test certificates or tests on samples H.4.1 Yield stress based on mill test certificates or tests on samples taken from existing
structures composed of BS EN 10025, BS 4360, BS 15, BS 548, BS 968 or BS 2762 steel
Where the nominal yield stress for assessment is derived from test results using this clause, the following shall all apply:
1) mill test certificates for the material used are available or tests are undertaken on the materials for representative parts, and
2) the materials were specified to one of BS EN 10025, BS 4360, BS 15, BS 548, BS 968 or BS 2762
Where mill test certificates are available which can be identified as applying to the cast number and product type of the component being assessed but not necessarily to a particular batch from which the component was rolled, the nominal yield stress of that component may be taken as the greatest of the values from H.2 above and from Equations H.4.1a and H.4.1b.
Where the results of tests in accordance with BS 4360 on samples taken from components of the same profile and the same structure as the part to be assessed are obtained, the nominal yield stress of that component may similarly be taken as the greatest of the values from H.2 above and from Equations H.4.1a and H.4.1b.
𝜎𝑦 = 𝜎𝑦𝑚 (1 − 0.128(𝑛+1
𝑛)0.5) Equation H.4.1a
𝜎𝑦 =𝜎𝑦𝑚−1.2𝑘𝑠
∗
0.93+17.4(𝑠∗ 𝜎𝑦𝑚⁄ )2 Equation H.4.1b
where
𝜎𝑦𝑚 is the mean of the yield stresses on the relevant certificates or obtained from the tests.
𝑛 is the number of relevant certificates or test results.
𝑠∗ is the standard deviation from 𝜎𝑦𝑚 of the relevant test results.
𝑘 is a statistical coefficient values of which are given in Table H.4 for various numbers, 𝑛, of relevant test results.
NOTE 1 The statistical Equation H.4.1a is based on the assumption that the coefficient of variation of
yield stress of parts of the same product type is 6.4% from one case of modern UK structural steels, and is derived by use of a one-sided confidence interval calculation as described in BS 2846: Part 2: 1981, using a 95% confidence interval. However, owing to the uncertainties involved in assessing population statistics from small numbers of samples, the equation does not provide a benefit unless the mean yield stress is relatively high and/or many relevant test results are available.
NOTE 2 The Equation H.4.1b is based on that described in BS 2846: Part 3: 1975 Table 7 in which two alterations are made: 1) a factor of 2/1.65 is introduced to allow for the overestimation of the static yield stress
due to the high strain rates used in mill testing, and
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2) a reduction factor is introduced to apply when the variability in the yield stress exceeds that of current UK structural steels in order to avoid modification to the partial safety factors in 4.3.
Where for Equation H.4.1b few results are available having a high coefficient of variation, the value of this coefficient of variation judged as the maximum credible may be used instead of the value from the tests.
NOTE 3 The Equation H.4.1b requires no prior knowledge of the coefficient of variation but can produce pessimistic values when few results are available having a high coefficient of variation.
NOTE 4 For the statistical analysis to be valid, the specimens tested are asked to be supplied from the same source as the component being assessed, and the tests are assumed to be undertaken on material from the same part of the cross section (e.g. flange when assessing flange strength) at the locations defined in BS 4360.
Where a mill test certificate is available which is identified as applying to the same cast from which the component being assessed was rolled, or the result of a test on a sample taken from the component is obtained, the nominal yield stress may be taken from Equation H.4.1c:
𝜎𝑦 = 𝜎𝑦𝑡 − 10 𝑁/𝑚𝑚2 Equation H.4.1c
where
𝜎𝑦𝑡 is the yield stress given on the certificate or obtained from the test in 𝑁/𝑚𝑚2. NOTE 5 The greatest benefit can be expected to result from testing material taken from a critical
component, but this is not always practical or desirable.
Table H.4: Values of statistical coefficient k
n 2* 3* 4* 5 6 7 8 9 10 11 k 257 66 5.14 4.20 3.71 3.40 3.19 3.03 2.91 2.82
n 12 13 14 15 16 17 18 19 20 21 k 2.74 2.67 2.61 2.57 2.52 2.49 2.45 2.42 2.40 2.37
n 22 23 24 25 26 27 28 29 30 k 2.35 2.33 2.31 2.29 2.28 2.26 2.24 2.23 2.22
n 35 40 45 50 60 70 80 90 100 Ꚙ k 2.17 2.13 2.09 2.07 2.02 1.99 1.96 1.94 1.93 1.65
Note * The use of fewer than five test results is not recommended.
H.4.2 Yield stress in existing structures composed of other or unidentified steels:
Where the steel material is not known to comply with BS EN 10025, BS 4360, BS 15, BS 548, BS 968 or BS 2723, test results shall be used from samples taken from the components or similar components in the same structure to determine the yield stress and the nominal yield stress should be derived in accordance with Equation H.4.1b above.
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In the absence of knowledge of the specification or test data related to the steel of a component, assumptions may be made as to the worst credible yield stress being the value judged to be the least that the actual yield stress would have.
The worst credible yield stress should be taken as the steel of the weakest grade of structural steel in use at the time of construction.
In this context the results of hardness testing (see 6.3) may be used to provide an estimate of the U.T.S. from which the grade of steel may be judged.
Where worst credible values are used, the sensitivity of the strength of the structure to the yield stress of the component should be reviewed.
NOTE 1 Historic structural steel information is given in Reference 6.2.4.
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[BS5400-3, Add new Annex I]
Annex I - Inspections for assessment
I.1 General
Inspections for assessment shall comply with the aims and provisions of CS 454 and where possible with the recommendations given in this Annex.
I.2 Preliminary inspection and criticality ratings
A preliminary inspection shall be undertaken with nature and extent appropriate to:
1) the prior knowledge of the construction of the bridge, including as-built drawings, construction procedures, dimensional surveys and material property data; and
2) the criticality of each part of the bridge in relation to its overall and local structural adequacy.
A preliminary inspection should establish the following:
1) In the absence of drawings or previous dimensional surveys of any part of the whole of a bridge, the layout dimensions and nominal component sizes should be recorded. Details of all accessible connections should be measured and the locations of any inaccessible parts or connections should be noted.
2) Where design drawings but no as-built drawings or previous dimensional surveys are available, the layout dimensions should be checked against the design drawings and nominal component sizes used should be verified. Connections should be visually inspected for compliance with the drawings and any variation in location or arrangement noted.
3) For bridges where the load effects are sensitive to errors in level inclination or common planarity of bearings and no as built records of these are available, the bearings should be surveyed and the errors recorded.
4) Locations of significant visible damage, deterioration or cracking should be recorded.
NOTE Where the information from 1-3 is given by as-built drawings and/or previous surveys are available, the purpose of preliminary inspection is only to determine condition.
An initial assessment of the adequacy of the structure should be undertaken using the best information then available.
The initial assessment should be used to establish the relative criticality of each part and to identify what further information is required to enable the final assessment to be undertaken.
Where information is lacking (e.g. material properties, or constructional imperfections), pessimistic assumptions should be made for the initial assessment.
Any parts assessed as likely to be inadequate or shown by the preliminary inspection to be significantly corroded or deteriorated should be identified on drawings and used for reference in the detailed inspection.
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I.3 Detailed inspections
The detailed inspection of a bridge shall be carried out as necessary to supplement the information concerning the details and conditions obtained in the preliminary survey as set out in I.4 to I.6.
NOTE 1 Inspection requirements for sealed box members and hollow sections are given in 4.5.2.
I.4 Structural arrangements and sizes
Measurements of components on the structure shall be appropriate to the level of the as-built information and the criticality of the elements.
The section dimensions of components at critical locations should be measured.
Dimensions of connections at critical locations and their connectors should be recorded, including weld sizes.
NOTE Note that fillet welds larger than specified could be to compensate for a larger root gap which does not increase the throat thickness.
I.5 Constructional imperfections
Measurements of construction imperfections shall be appropriate to the construction quality information and the criticality of the elements.
All components should be visually inspected for gross deformations from intended flatness or straightness.
Where a part is critical and the strength of the part is related to geometric imperfections, detailed measurement of deviations should be made in accordance with 5.6 of BS 5400-6 or as otherwise defined in this document.
The alignments of all bearings in relation to load bearing stiffeners and/or diaphragms should be measured.
The coincident ambient temperature of the main bridge members should be recorded during measurements of bearing alignment and appropriate adjustment made to the eccentricities or alignment to allow for the differences between the observed and the effective bridge temperature relative to the assessments required.
I.6 Condition I.6.1 General
At all locations where corrosion, deterioration and/or damage including missing components is apparent, its significance shall be assessed by reference to the criticality ratings, taking detailed measurements of loss of section and/or investigating potential influences on fatigue life or fracture propensity.
I.6.2 Welded connections
All welds shall be checked for completeness and loss of section due to corrosion.
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Welds in critical tensile areas shall be subject to 100% visual testing (VT) to confirm the minimum weld sizes and the absence of visible crack like defects.
Critical tensile areas shall include all areas in tension for which damage tolerance is poor and failure can cause premature loss of strength.
Visual testing of welds covered by paint which are not to be subject to other forms of NDT is acceptable provided the paint is less than 100 microns thick and provides a suitable contrast for inspection.
Where there is any doubt as to the effectiveness of visual inspection over paint, the paint shall be removed and the weld VT repeated.
In-line butt welds in critical regions that are underfilled or ground flush with reduced thickness shall be surveyed to measure the remaining thickness.
Where any of the following situations apply to welded connections in critical tensile areas, the welded connections shall be inspected using the re-inspection criteria in I.8:
1) where there is a lack of confidence that the workmanship meets the criteria for re-inspection and materials meet the criteria of 6.5, or
2) where the theoretical fatigue life is deficient or has been exceeded, or 3) where defects are identified in the weld from visual testing 4) where defects are suspected due to other reasons, for example if similar details
elsewhere on the structure have known defects.
The inspection criteria for welded connections subject to fatigue should be appropriate to the detail category assumed in the fatigue assessment.
Where a transverse web stiffener is stopped short of a flange by more than five times the web thickness, inspection should pay particular attention for fatigue cracking.
I.6.3 Bolted and riveted connections
The inspection of bolted and riveted connections shall be appropriate to the criticality, condition and the level of as-built information.
All bolted and riveted connections should be inspected for loss or looseness of connectors. HSFG bolted connections should be tested for tightness by application of the appropriate torque to a representative sample of nuts.
NOTE 1 The purpose of applying a torque to existing High Strength Friction Grip Bolts is to check for tightness to ensure they were originally tightened substantially beyond the bedding torque and plastically strained.
NOTE 2 Testing for tightness using a torque wrench is needed even where load indicating washers
have been used since these can be an unreliable indication of whether the correct tension has been achieved in the bolt.
HSFG bolts with obvious signs of movement (e.g. paint cracking, slackness of fit) or considered suspect after light hammer tapping should be given more detailed examination and replaced if necessary. Re-tightening of HSFG bolts shall not be permitted.
Rivets should be tested for tightness by hammer tapping.
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When a rivet is removed for inspection the rivet should be replaced by a new HSFG bolt or by reaming the hole and fitting a close tolerance bolt.
NOTE 1 Where HSFG bolts are used in connections with mixed bolts and rivets, the HSFG bolts can be considered only to act in friction at ULS. This is because slip is prevented by the rivets, preventing any clearance bolt from acting in bearing/shear.
I.7 Material testing
Where testing is required for strength according to Annex H, test specimens and tensile testing for plates and sections shall be accordance with BS EN 10025.
Strain rates in tensile testing should be similar to those used in mill testing.
Where testing is required for toughness according to 6.5, Charpy impact testing shall be carried out.
NOTE 1 Where a sample is taken which includes a weldment it is usually effective to carry out a range of tests, similar to that for weld procedure tests, including toughness testing using Charpy specimens, macroscopic sections including hardness tests, and tensile tests.
NOTE 2 Sub-size Charpy specimens can be used to minimise the size of the samples required or to suit the details being tested. Sub-size Charpy specimens test temperatures require correction from the nominal test temperature which can be done using the method described in BS 7910 and require adjustment to achieve equivalent full-size specimen values based on the ratio of net cross-section area.
The location of samples should be in accordance with the following:
1) To make use of results of such tests in accordance with Annex H, the samples should be taken in the same structure and considered to be likely to have been supplied from the same batch of material.
2) Where possible samples should be taken from a position on a member remote from its critical region.
3) The locations of the samples within a section should be relevant to the strength criteria being used (e.g. within a flange of a beam when considering bending capacity) and in accordance with BS EN 10025.
4) The location of Charpy specimens within a weldment shall be in accordance with BS 5400-6 Annex B.
Where samples are taken from an existing structure for any purpose, the introduction of stress concentrations in the structure shall be avoided.
The method and extent of removal shall avoid modification of the material properties of the samples due to heat input.
I.8 Criteria for re-inspection of welds
Where re-inspection of the welds is necessary, the criteria in this section shall be applied.
Non-destructive testing (NDT) of welds should be carried out in accordance with the recommendations of BS EN ISO 17635 including visual testing (VT) in accordance with BS EN ISO 17637 and other methods of NDT as described below.
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NOTE 1: Non-destructive testing (NDT) is now considered to include visual testing or examination of welds (VT). Refer to BS EN ISO 17635 Table 1. Note visual testing (VT) includes taking measurements of weld features.
The acceptance criteria for NDT should be in accordance with BS5400-6 as a minimum.
NOTE 3 Additional NDT or acceptance criteria can be required in some cases to comply with the assumptions of the assessment, e.g. in critical welds sensitive to fatigue or with low toughness.
The minimum extent of inspection should be in accordance table I.1 for butt welds and table I.2 for fillet welds.
Where a defect is identified in a weld by any NDT method, the extent of MT and UT (where applicable) shall be increased to 100% of the weld length.
NOTE 2 The extent of inspection in tables I.1 and I.2 is based on the requirements of BS5400-6.
For the purposes of the extent of inspection requirements of Table I.1 and Table I.2 a longitudinal weld shall be taken to be a weld for which the axis lies within 30° of the direction of tensile stress.
Welds at all other orientations including remnants of temporary attachments shall be deemed to be transverse welds.
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Table I.1 – Minimum extent of inspection in critical areas for butt welds
Test method
Transverse in Line Butt Joints
Transverse tee, cruciform and corner joints
Full penetration longitudinal butt joints, longitudinal tee, cruciform and corner joints
VT 100% 100% 100%
MT 100% 100% 1 in 10 of intermit welds joint where length of joint < 300mm
300mm or 10% whichever is greater if joint >300mm and <10m long
5% of each 10m length for joints >10m long
25mm at ends including at weld interruptions and cope holes.
UT Minimum extent (UT required for joints >12mm only)
100%
100% Entire length of joint, if joint is <300mm
300mm or 10% whichever is greater if joint >300mm and <10m long
10% of each 10m length for joints >10m long
Minimum testing levels
Class D Class E Class F Class F All fatigue classes
See Note 3
Testing Level B (see Notes 1, 4)
Testing Level B (see Notes 1, 4)
Testing Level A or B (see Notes 2, 4)
Testing Level A or B (see Note 7)
Note 1: Scans for discontinuities transverse to the weld axis not required.
Note 2: The primary purpose of UT is to detect lamellar tearing and/or toe cracking.
Note 3. Requires special UT techniques, such as PAUT, TOFD-UT. Refer to Annex A of BS EN ISO 17635 for guidance.
Note 4. Testing levels of UT are based on the recommendations in Annex A of BS EN ISO 17635 for BS EN ISO 5817 Quality Level B or C. Testing levels to be confirmed as suitable
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for detecting defects as required for the weld detail to meet the acceptance criteria of BS 5400-6. PAUT may be used instead
Table I.2 – Minimum extent of inspection in critical areas for fillet welds and temporary
attachments
Test method
Transverse Welds including tee, corner and cruciform joints and areas from which temporary attachments have been removed
Longitudinal welded joints (continuous)
Longitudinal welded joints (intermittently welded)
VT 100% 100% 100%
MT 100% 5% length of each weld
Including 25mm at the end of a weld and at cope holes
300mm or 1 in 10 welds, whichever is greater
Including 25mm at attachment ends and cope holes
UT Minimum extent (UT required for throat thickness >12mm only)
5% 5% of each 10m length for joints >10m long
300mm or 1 in 10 welds whichever is greater
Minimum testing levels
Testing Level B (see Note 1)
Testing Level A or B (see Note 1)
Testing Level A or B (see Note 1)
Note 1: Testing levels for UT are based on the recommendations in Annex A of BS EN ISO 17635 for EN ISO 5817 Quality Level B or C. Testing levels should be confirmed as suitable for detecting defects as required for the weld detail to meet the weld acceptance criteria of BS 5400-6. PAUT may be used instead.
NOTE 4 Butt and fillet welds can require preparation of the scanning surfaces to suit UT, refer to
Clause 8 of BS EN ISO 17640. NOTE 5 Phased Array UT (PAUT) to BS EN ISO 13588 can be used instead of conventional UT (as
permitted for supplementary NDT methods described in BS EN 1090-2). NOTE 6 MT is also referred to as Magnetic Particle Inspection (MPI). NOTE 7 Radiographic testing (RT) is not usually practicable on highway structures as it requires
exclusion zones to be introduced while testing using a radioactive source is being carried out, but could be appropriate in exceptional circumstances. Penetrant testing (PT) is usually less effective than MT for ferro-magnetic materials as it requires surface breaking defects to be open, but with suitable cleaning techniques it can be of benefit for non- or weakly-magnetic metals such as stainless steel, refer to BS EN ISO 3542-1.
NOTE 8 Other NDT techniques such as Time of Flight Diffraction UT (TOFD-UT) to BS EN ISO 10863, Eddy Current Testing (ET) or Potential Drop Flaw Detection and Sizing can be used
118
to provide additional information on suspected defects. All of these alternative NDT techniques require specialist knowledge as to their suitability and application.
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[BS5400-3, Add new Annex J]
Annex J - Determination of effective stiffener imperfection for stiffened compression flanges
J.1 Effective stiffener imperfection
Where in accordance with 9.10.2.3 measured imperfections are to be used in assessing the strength of longitudinal flange stiffeners, the effective imperfection |𝛥𝑠𝑥|𝑒𝑓𝑓 shall be taken as the peak stiffener imperfection in the panel or a reduced value derived in accordance with this Clause.
NOTE 1 Application of the rules in this Annex could be of benefit when the limiting stress is governed by overall buckling of a multi-stiffened panel with diverse values of stiffener imperfections.
NOTE 1 The sequence and terminology for the stiffened panels, referred to as 𝑟 − 1, 𝑟 and 𝑟 + 1 are illustrated in Figure J.1. Longitudinal stiffeners are numbered 1 to N.
For all stiffened panels except the first and last panels at each end of the bridge, the effective imperfection may be calculated using Equation J.1a.
|𝛥𝑠𝑥|𝑒𝑓𝑓(𝑟) = −1
6𝛥𝑠𝑥(𝑟−1)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ +
2
3𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ −
1
6𝛥𝑠𝑥(𝑟+1)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ Equation J.1a
where
𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ is the mean stiffener imperfection for the panel r under consideration calculated as the mean of the surveyed measurements of all the stiffeners in the panel 𝑟:
𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ = ∑ (𝛥𝑠𝑥)𝑚𝑎𝑥(𝑟,𝑛) 𝑁⁄𝑁𝑛=1
(𝛥𝑠𝑥)𝑚𝑎𝑥(𝑟,𝑛)is the peak imperfection of stiffener 𝑛 in panel 𝑟, measured in accordance with the requirements for 𝛥𝑠𝑥 in BS5400-6. The sign of the imperfection is taken as +ve when the bowing is in the direction away from the stiffener outstand and –ve when in the other direction.
N is the number of stiffeners in the stiffened panel.
𝛥𝑠𝑥(𝑟−1)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ is the mean stiffener imperfection for the adjacent panel 𝑟 − 1, calculated similarly to 𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ .
𝛥𝑠𝑥(𝑟+1)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ is the mean stiffener imperfection for the adjacent panel 𝑟 + 1, calculated similarly to 𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ .
For the first and last stiffened panels at each end of the bridge, the effective imperfection may be calculated using Equation J.1b.
|𝛥𝑠𝑥|𝑒𝑓𝑓(𝑟) =5
6𝛥𝑠𝑥(1)̅̅ ̅̅ ̅̅ ̅̅ −
1
6𝛥𝑠𝑥(2)̅̅ ̅̅ ̅̅ ̅̅ Equation J.1b
where
𝛥𝑠𝑥(1)̅̅ ̅̅ ̅̅ ̅̅ is the mean stiffener imperfection for the first or last stiffened panel calculated similarly to 𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ above.
𝛥𝑠𝑥(2)̅̅ ̅̅ ̅̅ ̅̅ is the mean stiffener imperfection for the second, or second to last stiffened panel as appropriate, calculated similarly to 𝛥𝑠𝑥(𝑟)̅̅ ̅̅ ̅̅ ̅̅ above.
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Figure J.1
121
[BS5400-3, Add new Annex K]
Annex K – Assessment of crossbeams in compression flanges
K.1 General
This Annex may be used as an alternative method for the assessment of cross beams in compression flanges.
To use this Annex, the critical longitudinal stress for buckling of the cross beams should be determined using the methods and subject to the provisions in K.2.
The destabilising factors 𝑖1 and 𝑖2 should then be calculated using the methods in K.3.
These values for the destabilising factors 𝑖1 and 𝑖2 should then be used in the assessment of the crossbeams, in place of the values from 9.15.4.5.4.
NOTE 2 This Annex gives the following benefits with respect to the design clauses:
1) assessment is made possible for cases where 9.15.3.2 is not satisfied, by considering overall buckling of the flange,
2) additional restraint from continuity can taken into account for crossbeams spanning more than 2 webs,
3) benefit can be taken from a more favourable longitudinal stress distribution due to shear lag using Finite Element methods.
4) these benefits can allow more favourable values of 𝑖1 and 𝑖2 to be calculated, thereby reducing the assessment load effects in the cross beam.
K.2 Calculation of critical stress, 𝝈𝒄𝒓
The longitudinal stress, 𝜎𝑐𝑟 to cause elastic buckling of the crossbeam shall be calculated.
The critical stress, 𝜎𝑐𝑟, may be obtained from finite element analysis using the eigenvalue for buckling load. For this purpose, the finite element analysis should be carried out in accordance with the guidance from BS EN 1993-1-5. Where it is difficult to identify the most critical mode relating to buckling of the crossbeam, it is recommended for the full analysis in accordance with 9.15.6.2 to be used.
Alternatively the critical stress, 𝜎𝑐𝑟, may be obtained from finite element analysis using the Southwell plot method. For this purpose, the analysis should be as described in 9.15.6.2.
NOTE 1 For details of the Southwell plot method see Reference 9.15.4.
For flanges without cantilevering parts, such as bottom flanges, the critical longitudinal stress may be calculated instead using Annex N.
The equations and charts given in BD56/10 and previous versions should not be used.
`
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K.3 Calculation of destabilizing factors from the critical longitudinal stress
Where the destabilising factors, 𝑖1 and 𝑖2, are to be calculated based on the critical longitudinal stress for buckling of the cross girder, 𝑖1 and 𝑖2 shall be calculated using Equations K.3a and K.3b respectively.
𝑖1 = 1 +𝑙𝑖
𝐿𝑓(
𝜎𝑓
𝜎𝑐𝑟−𝜎𝑓) Equation K.3a
𝑖2 = (𝜎𝑐𝑟
𝜎𝑐𝑟−𝜎𝑓) Equation K.3b
where
𝜎𝑐𝑟 is the critical longitudinal stress for buckling of the cross girder, related to the longitudinal stress such that 𝜎𝑐𝑟 = 𝜆𝑏𝜎𝑓, where 𝜆𝑏 is the factor of increase of stress 𝜎𝑓 in order to cause critical buckling.
𝜎𝑓 is the longitudinal compressive stress in the flange, based on the assumption of uniform in-plane stress without shear lag.
𝜎𝑎 is the longitudinal stress due to axial load (not subject to shear lag).
𝜎𝑏 is the longitudinal stress due to bending moment, = 𝜎𝑓 − 𝜎𝑎.
𝑙𝑖 is the half wavelength of buckling calculated.
𝐿𝑓 is as defined in 9.15.4.5.4.
In the cross-beam assessment, these destabilizing factors should then be used to factor the effects from the applied loads in 9.15.4.5.1 and 9.15.4.5.2 for 𝑖1 and 𝑖2 respectively.
NOTE 1 Where loading has contributions of uniformly distributed load (giving the same effects on multiple cross beams) and concentrated loading (giving differing effects on adjacent cross beams), significant benefit can be achieved by separated the load into uniform and non-uniform contributions for the application of 𝑖1 and 𝑖2.
NOTE 2 The use of destabilizing factors is described in Reference 9.15.2 for the context of the design code.
For deriving 𝜎𝑐𝑟 benefit may be utilised in the cross beam assessment by using a modified longitudinal stress distribution due to shear lag.
The benefit from shear lag shall not be utilised unless all other parts of the cross section, including girder flange and web checks, are also satisfied in this condition.
Where full non-linear analysis is used which includes stress distribution of all collapse factored loads and takes account of all destabilising magnifications, then 𝑖2 = 𝑖1 = 1.0.
K.4 Measured imperfections
The assessment imperfection (Δ𝑐𝑜) to be used shall be based on measured imperfections or the design tolerance (Δ𝑐𝑥).
The assessment imperfection, Δ𝑐𝑜, should be calculated according to Table K.4, using the buckling wavelength, 𝑙𝑖, and other terms as defined below and in Figure K.4.
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Table K.4
Mode Buckling wavelength, 𝑙𝑖 = Assessment imperfection, Δ𝑐𝑜 =
CASE I 𝑎 0.5 𝛾𝐴Δ𝑐𝑥
CASE II 2𝑎 𝛾𝐴Δ𝑐𝑥
CASE III
3𝑎 2 𝛾𝐴Δ𝑐𝑥
4𝑎 3.4 𝛾𝐴Δ𝑐𝑥
5𝑎 5.2 𝛾𝐴Δ𝑐𝑥
Where the buckling wavelength exceeds 2𝑎, the assessment imperfection, Δ𝑐𝑜, may be calculated instead from Equation K.4.
𝛥𝑐𝑜 =𝛥𝑐𝑥𝛾𝐴
1−𝑠𝑖𝑛{(𝑛−2)𝜋
2𝑛} Equation K.4
where
𝛥𝑐𝑥 is the measured imperfection or design tolerance.
𝛾𝐴 is the factor to be applied to 𝛥𝑐𝑥 to allow for statistical assessment or factor on tolerance, to be taken as 1.2 unless derived otherwise.
𝑛 is the multiple of cross beam spacings, a, within the buckling wavelength 𝑙𝑖.
a is the cross beam spacing (or average of adjacent spacing where these vary), as illustrated in Figure K.4. In the case of one cross beam between diaphragms a is half the diaphragm spacing.
𝑙𝑖 is the buckling wavelength, as illustrated in Figure K.4.
In lieu of any other information, the values should be adopted as 𝛾𝐴 = 1.2 and Δ𝑐𝑥 = 2𝑎 500⁄ .
NOTE 1 The default values are consistent with the BS 5400-6 tolerances and cater particularly for CASE II.
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Figure K.4
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[BS5400-3, Add new Annex L]
Annex L – Assessment of stiffened diaphragms not complying with limitations
L.1 General
The adequacy of stiffened diaphragms not complying with the limitations in 9.17.2 may be assessed in accordance with this Annex.
L.2 Loading on diaphragms L.2.1 Derivations
The load effects in diaphragms and associated parts of box girders should be derived from global analysis undertaken in accordance with 9.4.1.
The structure should be analysed by an elastic finite element method with shell elements to model all its primary components, including each box web and support diaphragms, so modelled as to enable the global forces transmitted to the boundaries of the diaphragms and their distribution to be determined.
Analysis to determine load effects from local loads and reactions, including distortional effects, should be undertaken using a finite element method on a model of sufficient extent to ensure that the effects calculated are insensitive to assumed end conditions.
The model should include any cross beams and cantilevers integral with the diaphragm.
The models used should reproduce the actual geometry including any skew or out of verticality in diaphragm alignment.
Supports to diaphragms should be modelled to represent their degrees of freedom and stiffnesses.
Since stress fields derived from the analysis will be complex, reference may need to be made to L.9 in deriving effective stresses for buckling checks.
The treatment of buckling of panels with large openings is not covered by this Annex and such panels should either be framed and ignored in stress analysis and strength checks or reference made to relevant research papers.
L.2.2 Effects to be considered
The effects defined in 9.17.3.2 shall be included as appropriate.
L.2.3 Effective sections
For determining stresses in a diaphragm the effective sections to be assumed should be derived in accordance with 9.17.4.2.2, 9.17.4.2.3(b) and (c), 9.17.4.4(a) and 9.17.4.5.
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L.3 Stresses in diaphragms L.3.1 General L.3.1.1 Analysis
Stresses in diaphragms should be calculated by finite element analysis of a model having the effective sections defined in L.2.3.
The analysis model should include the flexibility of support bearings and their supporting structure when this is not effectively rigid.
Where a diaphragm is not in a single plane and/or the diaphragm is subject to out-of-plane loading the analysis model shall be three dimensional.
Where diaphragm openings do not comply with the limits in 9.17.2.8, the openings should be included in the analysis model or the affected panels ignored in analysis and strength assessments.
L.3.1.2 Effective Stresses
Effective values of stresses to be used in assessment of the buckling strength of plate panels should be derived in accordance with L.9.1.
The effective values of stiffener stresses to be used in buckling strength checks should be derived in accordance with L.9.2.
L.3.2 Stresses in diaphragm plates L.3.2.1 Vertical stresses
Vertical stresses, 𝜎𝑑1, should be taken as the values derived in accordance with L.3.1.1 for yield checks and L.3.1.2 for buckling checks.
L.3.2.2 Horizontal stresses
The horizontal stresses, 𝜎𝑑2, should be taken as the values derived in accordance with L.3.1.1 for yield checks.
The effective stresses for buckling checks should be derived in accordance with L.3.1.2 with 𝜎2𝑏 taken as the effective horizontal bending stress and 𝜎2𝑞 as the effective horizontal mean stress, and 𝜎𝑑2 = 𝜎2𝑏 + 𝜎2𝑞 in the panel under consideration.
L.3.2.3 Shear stresses
The shear stresses, 𝜏, for yield checks should be derived in accordance with L.3.1.1.
L.3.3 Stresses in diaphragm stiffeners L.3.3.1 Vertical stresses in bearing stiffeners
The vertical stress, 𝜎1𝑆 + 𝜎1𝑆𝑇, in a bearing stiffener should be taken as the maximum value derived in accordance with L.3.1.1.
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L.3.3.2 Bending stresses in bearing stiffeners
The bending stress, 𝜎𝑏𝑠1, in a bearing stiffener should be derived in accordance with 9.17.6.3.3.
Where the groups of bearing stiffeners are not symmetrically placed about the diaphragm the effect of eccentricity shall be included in 𝑀𝑠 in 9.17.6.3.3.
L.3.3.3 Equivalent stress for buckling check
The equivalent axial stress, 𝜎𝑠𝑒, referred to in 9.17.6.3.4 should be calculated in accordance with the equation in that clause with the following modifications:
For bearing stiffeners the following terms should be taken instead to be:
𝜎𝑎 is the maximum value of 𝜎1𝑆 + 𝜎1𝑆𝑇 derived in accordance with L.3.3.1.
𝜎𝑑2 is the effective value derived from L.3.2.2 over the height of the stiffener.
𝜏 is the average shear stress in the panels on each side of the stiffener derived from L.3.2.3 over the length of the stiffener.
𝜎2𝑠 is the average value of 𝜎𝑑2 within the middle third of the length 𝑙𝑠.
𝑙𝑠 is as defined in 9.17.6.3.4.
For horizontal intermediate stiffeners the following terms should be taken instead to be:
𝜎𝑑2 is the effective value derived in accordance with L.3.2.2 over the unrestrained length of the stiffener.
𝜏 is the average shear stress in the panels on each side of the stiffener, over the unrestrained length of the stiffener.
For vertical intermediate stiffeners the following terms should be taken instead to be:
𝜎𝑎 is the effective value of 𝜎1𝑆 + 𝜎1𝑆𝑇 over the unrestrained height of the stiffeners derived from L.3.3.1.
𝜏 is the average shear stress in the panels on each side of the stiffener over its unrestrained height, derived from L.3.1.
𝜎𝑞 is in accordance with the equation in 9.17.6.3.4 with 𝜎2𝑠 equal to the effective value of 𝜎𝑑2, and 𝜎2𝑏𝑚𝑎𝑥 and 𝜎2𝑏𝑚𝑖𝑛 equal to the maximum and minimum values of 𝜎2𝑏 derived in accordance with L.3.2.2.
Allowance for actual imperfections should be made where appropriate in accordance with L.8.
L.4 Strength of diaphragm plate L.4.1 Yielding of diaphragm plate
Plate panels shall be checked in accordance with 9.17.6.4 using stresses derived in accordance with L.3.1.
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Stress concentrations within a distance 12td from a corner of any opening may be ignored, where td is the diaphragm plate thickness.
L.4.2 Buckling of diaphragm plate
Plate panels not satisfying any of the requirements of 9.17.6.5.1 should be checked in accordance with 9.17.6.5.2 using the effective panel stresses calculated in accordance with L.3.2 and the qualifications given therein.
In using the buckling criterion in 9.11.4 𝜎1 and 𝜎2 should be derived from L.9.1.
The buckling strength of plate panels containing openings in excess of the limits given in 9.17.2.8(a) shall be subject to special investigation.
L.5 Strength of diaphragm stiffeners L.5.1 Yielding of diaphragm stiffeners
Bearing stiffeners should be checked in accordance with 9.17.6.6 using the stresses defined in L.3.3.1 and L.3.3.2.
L.5.2 Buckling of diaphragm stiffeners
All stiffeners should be checked in accordance with 9.17.6.7 using the equivalent stresses for buckling check as defined in L.3.3.3, and allowance for actual imperfections where appropriate in accordance with L.7.
L.5.3 Yield stress for non-complying diaphragm stiffeners
The nominal yield stress, 𝜎𝑦𝑠, used in L.5.1 or L.5.2 shall be derived with due regard to the stiffener shape in accordance with 9.3.1 and 9.3.4 with b taken as the spacing of stiffeners, or the distance between the stiffener and the box wall, as appropriate.
For boxes with sloping walls, the distance between the stiffener and the box wall should be taken at the centre of the length of the stiffener between points of effective restraint.
L.6 Diaphragm/web junctions
Diaphragm/web junctions should be checked in accordance with 9.17.7.
L.7 Diaphragm stiffener imperfections for use in buckling check
In the buckling check in L.5.2 the stiffener imperfection shall be used to modify 𝜎𝑙𝑠 as follows.
Where the out-of-straightness of the stiffener exceeds the tolerance in BS 5400-6, 𝜎𝑙𝑠 shall be calculated, making allowance for the actual imperfection, by use of formula (1) given in G.13, with 𝜂 as given for assessment in 9.11.5.2.
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Where the out-of-straightness of the stiffener is less than the tolerance in BS 5400-6, the value of 𝜎𝑙𝑠 may be calculated making allowance for the actual imperfection, by use of formula (1) given in G.13, with 𝜂 as given for assessment in 9.11.5.2.
In applying formula (1) of G.13, 𝐿 shall be taken as 𝑙𝑠 as defined in 9.17.6.3.4.
L.8 Diaphragm stiffener imperfections for deriving equivalent stress
When calculating 𝜎𝑠𝑒 in L.3.3.3 the stiffener imperfection shall be used to modify 𝑘𝑠 as follows.
Where the out-of-straightness of the stiffener exceeds the tolerance in BS 5400-6, 𝑘𝑠 shall be calculated, making allowance for the actual imperfection, by use of formula (2) given in G.13, with 𝜂 as given for assessment in 9.11.5.2.
Where the out-of-straightness of the stiffener is less than the tolerance in BS 5400-6, the value of 𝑘𝑠 may be calculated making allowance for the actual imperfection, by use of formula (2) given in G.13, with 𝜂 as given for assessment in 9.11.5.2.
In applying formula (2) of G.13, 𝐿 shall be taken as 𝑙𝑠 as defined in 9.17.6.3.4.
L.9 Derivation of effective stresses in plate panels and stiffeners L.9.1 Effective values of stresses varying in a complex manner in plate panels
Where rectangular plate panels are subject to complex stress systems the following method may be used to determine effective stresses.
Each panel should be considered to be composed of rectangular elements of uniform size, forming an array of 𝑝 elements over the dimension 𝑎, and 𝑞 elements over dimension 𝑏, as shown in Figure L.9.1.
The mean values of each of the orthogonal stress components, 𝜎1 and 𝜎2, in each of the 𝑝 × 𝑞 elements in the panel should be first determined.
The mean values of each of the orthogonal stress components should then be reduced to the six effective components of overall edge stresses in the whole panel shown in Figure L.9.1 and defined as:
𝜎𝑚1 is the effective mean of stresses 𝜎1,
𝜎𝑣1 is the effective linear variation of 𝜎1 stresses in direction 1 (over half the panel length),
𝜎𝑏1 is the effective linear variation of 𝜎1 stresses in direction 2 (over half the panel width),
𝜎𝑚2 is the effective mean of stresses 𝜎2,
𝜎𝑣2 is the effective linear variation of 𝜎2 stresses in direction 2 (over half the panel width),
𝜎𝑏2 is the effective linear variation of 𝜎2 stresses in direction 1 (over half the panel length).
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These effective stress components should be calculated from the stresses in the 𝑝 × 𝑞 elements by means of the arrays of coefficients given in Tables L.9a, L.9b and L.9c.
1) To calculate 𝜎𝑚1, using the array in Table L.9a having p columns and q rows, the element stresses, 𝜎1, should be multiplied by the corresponding element coefficients, 𝑘𝑚, and summed.
2) To calculate 𝜎𝑏1, using the array in Table L.9b having 𝑝 columns and 𝑞 rows, the element stress values, (𝜎1 - 𝜎𝑚1), should be multiplied by the appropriate coefficients, 𝑘𝑏, and summed. The coefficients should be used either as presented in Table L.9b, or reversed top to bottom, to obtain the larger positive value of 𝜎𝑣1.
3) To calculate 𝜎𝑣1, using the array in Table L.9c having 𝑝 columns and 𝑞 rows, the element stress values, (𝜎1 - 𝜎𝑚1), should be multiplied by the appropriate coefficients, 𝑘𝑣, and summed. The array should be used with larger coefficients to the left or to the right in such a way as to obtain the larger positive value of 𝜎𝑣1.
4) The stresses 𝜎𝑚2, 𝜎𝑏2 and 𝜎𝑣2 should be obtained similarly from the element stresses, 𝜎2, by turning the stress array through 90°, making the direction of application of the stress coincident with that shown in Tables L.9a to L.9c.
All coefficients should to be applied algebraically with compressive stresses always being regarded as positive.
The effective uniform shear stress should be calculated using Equation L.9.1a:
𝜏 =𝑎(𝑄1+𝑄3)−𝑏(𝑄2+𝑄4)
4𝑎𝑏𝑡 Equation L.9.1a
where
𝑄1, 𝑄2, 𝑄3, 𝑄4 are the boundary shear forces acting on each edge of the panel, taken as positive if in a clockwise direction. (See Figure L.9.2)
Where the direct stress resultants on opposite edges of a panel are unequal as shown in Figure L.9.1, effective uniform stresses, 𝜎1 and 𝜎2, may be calculated as follows:
𝜎𝑚1 + 𝜎𝑣1 and 𝜎𝑚1 + 𝜎𝑣1 should be taken as the longitudinal direct stresses on the two opposite shorter edges.
Where 𝜎𝑚1 is positive (i.e. compressive) and 𝜎𝑣1𝜎𝑚1
≥3(𝜙−1)
𝜙, 𝜎1 should be calculated from
Equation L.9.1b.
𝜎1 = 𝜎𝑚1 [1 +1
3(𝜎𝑣1
𝜎𝑚1)2] Equation L.9.1b
But not greater than (𝜎𝑚1 + 𝜎𝑣1)
Where 𝜎𝑚1 is positive (i.e. compressive) and 𝜎𝑣1𝜎𝑚1
<3(𝜙−1)
𝜙, 𝜎1 should be calculated from
Equation L.9.1c.
𝜎1 = 𝜎𝑚1 [1 +𝜙−1
𝜙(𝜎𝑣1
𝜎𝑚1)] Equation L.9.1c
Where 𝜎𝑚1 is negative, 𝜎1 should be calculated from Equation L.9.1d.
𝜎1 = 𝜎𝑚1 + 𝜎𝑣1 Equation L.9.1d
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𝜎𝑚2 + 𝜎𝑣2 and 𝜎𝑚2 + 𝜎𝑣2 should be taken as the longitudinal direct stresses in the shorter direction on the two opposite longer edges, and 𝜎𝑏2 should be taken as the in-plane coexistent pure bending stresses on these two edges.
Where 𝜎𝑚2 is positive and 𝜙 > 2, 𝜎2 should be calculated from Equation L.9.1e.
𝜎2 = 𝜎𝑚2 [1 +1
3(𝜎𝑣2
𝜎𝑚2)2] + (
𝜙−2
𝜙)𝜎𝑏2 Equation L.9.1e
But not greater than (𝜎𝑚2 + 𝜎𝑣2 + (𝜙−2
𝜙)𝜎𝑏2)
Where 𝜎𝑚2 is positive and 1 ≤ 𝜙 ≤ 2, 𝜎2 should be calculated from Equation L.9.1f.
𝜎2 = 𝜎𝑚2 [1 +1
3(𝜎𝑣2
𝜎𝑚2)2] Equation L.9.1f
But not greater than (𝜎𝑚2 + 𝜎𝑣2)
Where 𝜎𝑚2 is negative and 𝜙 > 2, 𝜎2 should be calculated from Equation L.9.1g.
𝜎2 = 𝜎𝑚2 + 𝜎𝑣2 + (𝜙−2
𝜙)𝜎𝑏2 Equation L.9.1g
Where 𝜎𝑚2 is negative and 1 ≤ 𝜙 ≤ 2, 𝜎2 should be calculated from Equation L.9.1h.
𝜎2 = 𝜎𝑚2 + 𝜎𝑣2 Equation L.9.1h
where
𝜙 is the aspect ratio of the longest edge over the shortest edge,
𝜙 = 𝑎 𝑏⁄
L.9.2 Effective values of applied stresses in diaphragm stiffeners
Where stresses vary along the length of a stiffener, its length should be divided into at least four equal segments and the effective value of stress in the stiffener in the direction of the stiffener be taken as 𝜎𝑎𝑒 = ∑(𝜎𝑠𝑘𝑚′ ), being the sum of the stress in each segment, 𝜎𝑠,multiplied by the corresponding coefficient 𝑘𝑚′ , from the array of influence coefficients given in Table L.9d.
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Table L.9a: Influence coefficients, 𝒌𝒎 for effective mean stress of element array 𝒑 × 𝒒
133
Table L.9b: Influence coefficients, 𝒌𝒃 for effective in-plane bending stress of element array 𝒑 × 𝒒
134
Table L.9c: Influence coefficients, 𝒌𝒗 for effective linearly varying mean stress of element array 𝒑 × 𝒒
135
Table L.9d: Influence coefficients, 𝒌𝒎′ for determining effective stresses in stiffness
136
Figure L9.1
Figure L9.2
137
[BS5400-3, Add new Annex M]
Annex M – Critical buckling loads for battened members
M.1 General
Where the radius of gyration of a non-complying battened member is to be reduced in accordance with 10.8.1, the factor 𝜑0.5 shall be calculated from Equation M.1 for bending about the Y-Y axis or X-X axis as appropriate.
𝜑0.5 = √𝑃𝐸𝑦′
𝑃𝐸𝑦 for bending about the Y-Y axis, or
= √𝑃𝐸𝑥′
𝑃𝐸𝑥 for bending about the X-X axis. Equation M.1
where
𝑃𝐸𝑥, 𝑃𝐸𝑦 are the Euler critical buckling loads as defined in 10.8.5.2.
𝑃𝐸′ , 𝑃𝐸𝑦′ are the modified critical buckling loads calculated according to M.2 or M.3 as
appropriate.
M.2 Members where the faces parallel to the X-X axis are battened
Where the critical loads are determined by elastic buckling analysis (e.g. Finite Element analysis) of the battened member, 𝑃𝐸𝑦′ shall be taken as 𝐾 times the lowest value of the elastic critical buckling load for buckling of the member in the plane of the X-X axis.
where
𝐾 = 1 for welded or friction grip bolted battens, and
= 0.7 for battens having riveted or black bolted connections.
Alternatively, where the following criteria are all met,
1) the faces parallel to the X-X axis are battened; and 2) arrangement of battens complies with the requirements of 10.8.5.1; and 3) battens are equally spaced; and 4) main members are of the same cross-section,
𝑃𝐸𝑦′ may be determined as 𝑃𝐸𝑦′ = 𝜙𝑌𝑃𝐸𝑦 with 𝜙𝑌 calculated from Equation M.2a.
𝜙𝑌 =𝐾
1+𝜋2𝐴𝑒𝑟𝑦
2
𝑙𝑦2 {
𝑙𝑏1𝑐
12𝐼𝑏𝑛+
𝑙𝑏12
24𝐼𝑛(1−𝛽𝑏)+3𝑙𝑏1𝑐𝐴𝑏𝑛
}
Equation M.2a
where:
𝐼𝑛 is the second moment of area of a main component or the sum of the second moments of area of main components to one side of the Y-Y axis about its or their centroidal axis parallel to the Y-Y axis. Where channels are battened, one
138
component of the second moment of area is used. Where 4 corner angles are battened, the sum of two components is used.
𝛽𝑏 =𝜙𝑌𝑃𝐸𝑦
(2𝜋2𝐸𝐼𝑚𝑖𝑛
𝑙𝑏12 )
𝐴𝑒 , 𝑙𝑦, 𝑙𝑏1, 𝑟𝑦 are as defined in 10.8.3 or 10.8.5.
𝑛 is the number of layers of battens parallel to the x-x axis in a particular cross section.
𝐴𝑏 is the cross sectional area of one battened plate
𝐼𝑏 is the second moment of area of one batten in its plane about its transverse centre line.
𝑐 is the distance parallel to the X-X axis between the centroidal axes of the main components.
𝐼𝑚𝑖𝑛 is the second moment of area of the main component or the sum of the main components to one side of the Y-Y axis about its or their minor axis.
𝑃𝐸𝑦 is as defined in 10.8.5.2.
𝐾 = 1 for welded or friction grip bolted battens, or
= 0.7 for riveted or black bolted battens.
NOTE 1 In the case where channels or similar are battened, 𝐼𝑚𝑖𝑛 would be 𝐼𝑛. In the case where 4 corner angles are battened, 𝐼𝑚𝑖𝑛 would be twice the minimum I of an individual angle and 𝐼𝑛 would be twice the 𝐼 of an individual angle about the axis parallel to the Y-Y axis.
Where the battens consist solely of unstiffened plates, 𝜙𝑌 may be taken from Equation M.2b.
𝜙𝑌 =𝐾
1+𝜋2𝐴𝑒𝑟𝑦
2𝑙𝑏1
12𝑙𝑦2
{
12𝑐
𝑑𝑏3𝑡𝑏𝑛
+36
𝑐𝑑𝑏𝑡𝑏𝑛+
𝑙𝑏1
2𝐼𝑛(1−𝑙𝑏1
2𝐴𝑒𝑟𝑦2
2𝑙𝑦2𝐼𝑚𝑖𝑛
)
}
Equation M.2b
where
𝑑𝑏 is the overall length of a batten in the direction parallel to the longitudinal axis of the member.
𝑡𝑏 is the thickness of the batten.
other parameters are as defined for Equation M.2a. NOTE The Equations M.2a and M.2b are based on Timoshenko, reference 10.8.2.
M.3 Members where the faces parallel to the Y-Y axis are also battened
The modified buckling load for buckling in the Y-Y plane 𝑃𝐸𝑋′ shall be calculated in the samemanner as 𝑃𝐸𝑌′ from M.2, except by taking properties with respect to the X-X axis instead ofthe Y-Y axis and vice versa.
139
[BS5400-3, Add new Annex N]
Annex N – Modified critical buckling stress of stiffened panels utilising orthotropic actions
N.1.1 General
The methods in this Annex may be used to assess stiffened panels using the benefit of orthotropic stiffness.
For this purpose, the minimum factor against critical buckling, 𝛼𝑐𝑟,𝑚𝑖𝑛, should be calculated. 𝛼𝑐𝑟,𝑚𝑖𝑛 shall be taken as the lowest of:
1) 𝛼𝑐𝑟 according to N.2, and 2) 𝛼𝑐𝑟,𝑠𝑝𝑏1, 𝛼𝑐𝑟,𝑠𝑝𝑏2 according to N.4.
Values of 𝛼𝑐𝑟,𝑠𝑝𝑏1 and 𝛼𝑐𝑟,𝑠𝑝𝑏2 shall be derived for each stiffener in a multi-stiffened panel with due allowance for any variation of 𝜎1, 𝜏 and 𝜎2 (i.e. particular 𝜎1 in web panels).
The minimum value of 𝛼𝑐𝑟,𝑠𝑝𝑏1, 𝛼𝑐𝑟,𝑠𝑝𝑏2 and 𝛼𝑐𝑟 (as derived for the whole stiffened panel) shall then be adopted as the governing 𝛼𝑐𝑟,𝑚𝑖𝑛 for each stiffener.
Where panels have negligible coincident in-plane shear and transverse stress, the sub-panel buckling modes in 2) and the corresponding factors 𝛼𝑐𝑟,𝑠𝑝𝑏1.and 𝛼𝑐𝑟,𝑠𝑝𝑏2 may be ignored.
NOTE Additional methods are also provided in this Annex to carry out strength checks for stiffened panels under combined stress.
N.1.2 Derivation of Strength
The capacity of each effective longitudinal stiffener shall be checked at both the tip of the stiffener outstand and at the junction with the attached plate boundary, with stresses appropriately magnified for the governing (minimum) load factor against buckling, 𝛼𝑐𝑟,𝑚𝑖𝑛, derived from N.1.1.
NOTE 1 Although each stiffener strictly requires separate checks on both aspects, generally for multi-stiffened panels with uniform equally spaced stiffeners the governing stiffener will be apparent by inspection (e.g. when the maximum shear stress and maximum longitudinal compressive stress are concurrent on the same stiffener).
NOTE 2 Methods for the outstand check are given in N.1.3 and methods for the plate boundary check are given in N.1.4.
The checks shall include the effects of residual stresses and assumed values of initial imperfections.
NOTE 3 Methods for treatment of residual stresses and imperfections are given in N.1.5 and N.5.3.
N.1.3 Stiffener Outstand Checks N.1.3.1 Verification method using modified radius of gyration
Checks may be made using 9.3.2 (flanges), 9.11.5.2 (webs) and 9.17.6.7 (diaphragms) as appropriate but in each case using 𝑟𝑠𝑒 calculated from Equation N.1.3.
140
𝑟𝑠𝑒 = (𝑎𝑠
𝜋)√
𝛼𝑐𝑟,𝑚𝑖𝑛𝜎𝑠𝑒
𝐸 Equation N.1.3
where
𝛼𝑐𝑟,𝑚𝑖𝑛 is the governing (minimum) load factor against critical buckling.
𝜎𝑠𝑒 is the appropriate equivalent stress in the stiffener in accordance with 9.10.2.3(a), 9.11.5.2 and 9.17.6.3.4 for flanges, webs and diaphragms respectively.
𝑎𝑠 is the length of the stiffener (i.e. 𝑙 for flanges, 𝑎 for webs and 𝑙𝑠 for diaphragms) compatible with the use in N.4.2.
NOTE 1 Based on this expression for 𝑟𝑠𝑒, the slenderness for a stiffener can be expressed as 𝜆𝑠𝑒 =
𝑎𝑠
𝑟𝑠𝑒√𝜎𝑦𝑠
355= 75√
𝜎𝑦𝑠
𝛼𝑐𝑟,𝑚𝑖𝑛𝜎𝑠𝑒 , where 𝜆𝑠𝑒 is the equivalent 𝜆 for use on Figure 19 or 24.
NOTE 2: Note that this procedure is iterative due to the dependence of the slenderness parameter, 𝜆, as well as the buckling coefficients (𝑘𝑠 and 𝑘𝑙) on 𝑟𝑠𝑒 .
The procedure in N.1.5 and N.5.3 may be used to allow for the variation of initial imperfections (and residual stresses, if required) as well as effective stress levels in the plate via use of modified effective widths of plate.
N.1.3.2 Verification method using amplified stress
As an alternative to the method in (N.1.3.1), to obtain the maximum capacity and benefits, the stiffener outstand stress (𝜎𝑜) may be derived from IDWR clause 20.3.3 using values derived in accordance with 20.3.1, but with total assumed initial imperfection (Δ𝑜) and residual stresses (𝜎𝑅𝑏 and 𝜎𝑂𝑅𝑆) derived in accordance with N.1.5.
The stiffener outstand stress (𝜎𝑜) should then be checked against the limiting outstand stress allowing for torsional buckling (i.e. the 'lower yield stress' 𝜎𝑦𝑠 of the stiffener calculated in accordance with 9.3.1). The effective width of plating for derivation of stresses should be based on the secant effective width of plating, 𝐾𝑏𝑠, see N.5.
Torsional buckling limiting stress should not be derived from IDWR clause 20.3.4 as this may produce an overestimate of the outstand limiting stress.
N.1.4 Plate Boundary Check N.1.4.1 Verification method using modified radius of gyration
Checks may be made by using the methods in N.1.3(i) using 𝑟𝑠𝑒 also as set out in N.1.3 (i), but using the plate limiting stress in place of the outstand limiting stress.
NOTE 1 Thus for flanges the modified 𝜎𝑠𝑒 = 𝜎𝑎 + 2.5𝜏𝑖𝑘𝑠2 (as per 9.10.2.3(b)) is checked against a modified 𝑘𝑙2𝜎𝑦𝑒 𝛾𝑚𝛾𝑓3⁄ .
For webs a conservative check may be made by taking 𝜎𝑠𝑒 = 𝜎𝑦𝑤(𝑚𝑐 +𝑚𝑏 + 3𝑚𝑞), where 𝜎𝑦𝑤, 𝑚𝑐, 𝑚𝑏 and 𝑚𝑞 are derived in accordance with 9.11.4.
141
NOTE 2: Note that this procedure is iterative due to the dependence of the slenderness parameter, 𝜆, as well as the buckling coefficients (𝑘𝑠 and 𝑘𝑙) on 𝑟𝑠𝑒.
The procedure in N.1.5 and N.5.3 may be used to allow for the variation of initial imperfections (and residual stresses, if required) as well as effective stress levels in the plate via use of modified effective widths of plate.
N.1.4.2 Verification method using amplified stress
As an alternative to the method in (N.1.4.1), to obtain the maximum capacity and benefits, the stress at the plate/stiffener junction, i.e. the plate boundary stress (𝜎𝑏) may be derived from IDWR clause 20.3.2 using values derived in accordance with 20.3.1 but with total assumed initial imperfections (Δ𝑜) and residual stresses (𝜎𝑅𝑏 and 𝜎𝑝𝑟𝑠) derived in accordance with N.1.5, and then checked against the limiting boundary stress (𝜎𝐵𝐿) derived in accordance with IWDR clause 20.2.2d.
For this purpose the effective width of plating should be based on 𝐾𝑏𝑠 the secant effective width of plating, see N.5.
N.1.5 Allowance for variation of residual stresses and plate imperfections
The combined effect of variation of residual stresses and initial imperfections on effective widths of plates may be allowed for using the method in N.5.3.
NOTE 1 Residual stresses are not dealt with explicitly in either this document or BS 5400-3. All the BS 5400-3 rules have a built-in assumption of actual residual stress assumed at a level of 10% of yield. The effect of these is generally small in design, particularly in the case of non-slender elements. However for assessment, particularly for web panels, these levels of stress can be a high proportion of basic capacity when very slender panels and stiffeners are assessed. The separate effect of variation of plate and stiffener initial imperfections on strength (measured, specific or assumed) can be dealt with by the relevant rules in this document for longitudinal stiffener and plate panel checks.
In cases where residual stresses are known or can be shown to be less than 10% of yield, or where residual stresses can be treated as equivalent imperfections, the full procedure of clauses 18 and 19 of the IDWR may be used.
NOTE 2 The procedure in IDWR clauses 18 and 19 provides alternative methods to account for residual stress and initial imperfections that can give particular benefit for 𝑏 𝑡⁄ and/or 𝑙 𝑟𝑠𝑒⁄ ≥60 if the residual stress is treated as an additional imperfection.
Clause 7 of the IDWR may be used to derive residual stresses where required.
NOTE 3 The IDWR allows imperfections to be fully considered and also allows some residual stresses to be replaced as equivalent imperfection; an added benefit when assessment strength capacity is low. Again for b/t and/or l/r ≥ 60, the full procedure of clauses 18, 19 and 20.3 of the IDWR can be used to obtain additional benefit, as set out in N.1.2 to N.1.4 above for strength, N.4.3 for plate buckling factor (𝛼𝑐𝑟,𝑝) and N.5 for secant effective width (𝐾𝑏𝑠).
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N.2. Determination of critical buckling stress for stiffened flange or web panels N.2.1 General
The critical buckling stress for stiffened panels bounded by stiff supports and subject to one type of uniformly distributed edge applied stress may be determined from this section.
For panels where the boundary stress is not uniform, effective values of uniform boundary stress on such panels may be determined as described in L.9.1 by assuming stiffener forces and stiffnesses to be smeared into the effective associated plate. The aspect ratio for case in
L.9.1 should be taken as ∅ = ∅′ where ∅′ = 𝑙
𝑏𝑠(𝐷𝑦
𝐷𝑥)0.25
.
N.2.2 In-plane bending and compression
Where the critical buckling stress is to be calculated for in-plane bending and compression only, the critical value of the maximum longitudinal stress, (𝜎1𝑚𝑎𝑥)𝑐𝑟∗ shall be calculated using Equation N.2.2:
(𝜎1𝑚𝑎𝑥)𝑐𝑟∗ =
𝜋2
𝑏𝑠2𝑡𝑒𝑓𝑓
[𝐾𝑜√𝐷𝑥𝐷𝑦 + (𝐾𝑖 − 𝐾𝑜)𝐻] Equation N.2.2
where
𝜎1𝑚𝑎𝑥 = 𝜎1 + 𝜎𝑏
𝐾𝑜, 𝐾𝑖 are the buckling coefficients obtained from Figure N.4 and Figure N.3 for 𝐾𝑜 and 𝐾𝑖 respectively, by taking 𝜓 such that 𝜓(𝜎1 + 𝜎𝑏) = (𝜎1 − 𝜎𝑏) and 𝜙′ =𝑙
𝑏𝑠(𝐷𝑦1
𝐷𝑥)0.25
for overall buckling, or 𝜙′ = 𝑎
𝑏𝑠(𝐷𝑦2
𝐷𝑥)0.25
for buckling between transverse stiffeners.
𝑡𝑒𝑓𝑓 = 𝑡 (1 +𝑁𝐴𝑠𝑥
𝑏𝑠𝑡)
other parameters are as defined in N.3 and Figure N.1.
N.2.3 Shear
Where the critical buckling stress, 𝜏𝑐𝑟∗ for a panel under in-plane shear only is calculated, 𝜏𝑐𝑟∗ shall be taken as the greater of 𝜏𝑐𝑟∗ from Equations N.2.2a and N.2.2b
𝜏𝑐𝑟∗ =
𝐾𝑠𝜋2
𝑎′𝑏𝑠2𝑡√𝐷𝑥𝐷𝑦 (
𝑎′
𝑏𝑠(𝐷𝑦
𝐷𝑥)0.25
) Equation N.2.2a
𝜏𝑐𝑟∗ =
𝐾𝑠𝜋2
𝑎′𝑏𝑠2𝑡√𝐷𝑥𝐷𝑦 (
𝑏𝑠
𝑎′(𝐷𝑥
𝐷𝑦)0.25
) Equation N.2.2b
where
𝐾𝑠 is the buckling coefficient obtained from Figure N.2.
𝐷𝑦 = 𝐷𝑦1, for overall buckling, or
= 𝐷𝑦2, for buckling between transverse stiffeners.
𝑎′ = 𝑙, for overall buckling, or
143
= 𝑎, for buckling between transverse stiffeners.
other parameters are as defined in N.3 and Figure N.1.
N.2.4 Interaction between stresses for overall buckling of stiffened panels
Where the strength of a stiffened panel is assessed using N.1.3 or N.1.4 and the stiffened panel is subject to more than one coincident type of applied in-plane stress, the minimum load amplifier, 𝛼𝑐𝑟, for the design loads to reach the elastic critical load of the plate under the complete stress field shall be determined.
NOTE For rectangular panels with simple stress patterns, a method is given in BS EN 1993-1-5 for the interaction between the stress types.
N.3 Evaluation of parameters for calculating the critical stress for a stiffened panel
The values of the stiffness parameters of a panel shall be evaluated as follows, with coordinate axes and panel dimensions shown in Figure N.1.
𝐼𝑜𝑥, 𝐼𝑜𝑦 are the second moments of area for the effective stiffener cross section, for the longitudinal stiffeners (in direction 1) and for the transverse stiffeners (in direction 2) respectively. The cross section of the stiffener includes an effective width of plating on each side as defined in 9.10.2.2 with values appropriate to the effective in-plane stresses in the plating elements, with due allowance for out-of-plane bending of the stiffened panel. Where the effective cross-section of a stiffener varies along its length, the average value of I applies. For vertical web stiffeners in panels designed as having fully restrained boundaries the effective width on each side is as defined in 9.11.5.
𝐽𝑥, 𝐽𝑦 are the torsion constants for the longitudinal stiffeners (in direction 1) and for the transverse stiffeners (in direction 2) respectively.
For stiffeners having “open” type cross section, e.g. angles, flats, (see Figure N.5a): 𝐽 = 𝑑𝑡𝑠
3
3+𝑏𝑐𝑡𝑓
3
3.
For bulb flats (See Figure N.5b): 𝐽 = 𝑑𝑡𝑠3
3+(𝑏𝑐−𝑡𝑠)𝑡𝑓
3
4.8.
For stiffeners having “closed” type cross section (See Figure N.5c): 𝐽 = 4𝐴𝑐2
∑𝑑
𝑡
.
𝐴𝑐 is, for a “closed” type cross section stiffener, the area enclosed by the mid-planes of the stiffener walls.
𝐴𝑠𝑥, 𝐴𝑠𝑦 are the areas of the longitudinal stiffeners and transverse stiffeners respectively.
For stiffeners having “open” type cross section (See Figure N.5a): 𝐴𝑠 = 𝑑𝑡𝑠 +𝑡𝑓(𝑏𝑐 − 𝑡𝑠), or as given in steel section Tables.)
For bulb flat stiffeners: as is given in steel section Tables.
For stiffeners having “closed” type cross section (See Figure N.5c): 𝐴𝑠 = 𝑑2𝑡2 +𝑑3𝑡3 + 𝑑4𝑡4 .
144
𝜈, 𝜈𝑥, 𝜈𝑦 𝜈 = 0.3
𝜈𝑥 = 0.3 (𝑎𝑡
𝐴𝑠𝑦+𝑎𝑡)
𝜈𝑦 = 0.3 (𝑏𝑡
𝐴𝑠𝑥+𝑏𝑡)
𝐷𝑥 is the bending stiffness per unit width for a multi stiffened panel in the longitudinal direction (i.e. bending of the longitudinal stiffeners about the transverse axis).
For panels with uniform stiffeners at equal spacing,
𝐷𝑥 =𝐸𝐼𝑜𝑥
𝑏+ (1 − 𝐾𝑐)
𝐸𝑡3
12(1−𝜈𝑥𝜈𝑦)
Where 𝐾𝑐 is the same modulus for the effective width of plate that is used to calculate 𝐼𝑜𝑥, ie derived from 9.10.2.2.
Where the longitudinal stiffeners are unequal or unequally spaced, the critical stresses can be obtained by assuming the panel to be equivalent to one having uniform longitudinal stiffness per unit width equal to the average stiffness within the compression zone in the case of pure compression and pure in-plane bending, and to the average stiffness in the entire stiffened panel in the case of shear. In assessing the average stiffness the effective stiffness of each stiffener is related to its position in the panel as follows. For compression and shear the effective second moment of area of any longitudinal stiffener is taken as:
𝐼𝑠,𝑒𝑓𝑓 = 1.5𝐼𝑜𝑥 (1 −4𝑦𝑠
2
𝑏𝑠2 ) (
𝑁+1
𝑁+2)
Where 𝐼𝑜𝑥 is the second moment of area of the stiffener, 𝑏𝑠 is the width of the stiffened panel at right angles to the stiffener, 𝑦𝑠 is the distance from the centre of the stiffened panel to the stiffener, 𝑁 is the number of longitudinal stiffeners.
For in-plane bending the effective second moment of area is taken to vary linearly from zero, when the stiffener is on the boundary or on the neutral axis to 2𝐼𝑜𝑥 when it is located at a distance from the compression boundary equal to 0.2 times the distance from that boundary to the neutral axis.
𝐷𝑦 is the bending stiffness per unit width for a multi stiffened panel in the transverse direction (i.e. bending of the plate or transverse stiffeners about the longitudinal axis).
For overall buckling of a panel with transverse stiffeners:
𝐷𝑦1 =𝐸𝐼𝑜𝑦
𝑎+ (1 − 𝑓)
𝐸𝑡3
12(1−𝜈𝑥𝜈𝑦)
Where 𝑓 =𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑝𝑙𝑎𝑡𝑖𝑛𝑔 𝑎𝑐𝑡𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠 𝑠𝑡𝑖𝑓𝑓𝑒𝑛𝑒𝑟𝑠
𝑡ℎ𝑒 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑒 𝑠𝑡𝑖𝑓𝑓𝑒𝑛𝑒𝑟𝑠
For buckling between transverse stiffeners or overall buckling of a panel with longitudinal stiffeners only:
𝐷𝑦2 =𝐸𝑡3
12(1−𝜈𝑥𝜈𝑦)
145
Where transverse stiffeners are equally spaced but of unequal stiffness, the value of 𝐼𝑜𝑦 is the mean value for the members contained within the half wavelength or, when the half wavelength equals twice the stiffener spacing, the value for the central stiffener.
𝐻 For overall buckling of a panel with rigidly interconnected longitudinal and transverse stiffeners:
𝐻 =1
2(𝜈𝑥𝐷𝑦 + 𝜈𝑦𝐷𝑥) +
𝐺𝑡3
6+𝐺
2(𝐽𝑥
𝑏+𝐽𝑦
𝑎)
For overall buckling of a panel with stiffeners in the x-direction only or when stiffeners are not rigidly interconnected and for buckling between transverse stiffeners:
𝐻 =𝐺𝑡3
6+𝐺𝐽𝑥
2𝑏
N.4 Sub-panel buckling N.4.1 General
In addition to deriving the load factor, 𝛼𝑐𝑟, against overall buckling in accordance with N.2 which allows for the benefit of orthotropic action as several stiffeners buckle in the same direction, the sub-panel buckling modes shall also be calculated according to this section.
NOTE 1 The sub-panel modes allow for the destabilising effects of longitudinal, transverse and shear stresses in the adjacent plate panels on possible stiffener buckling modes as required in accordance with 9.10.2.3 for flange stiffeners, 9.11.5.2 for web stiffeners and 9.17.6.7 for diaphragm stiffeners.
The following two basic modes shall be considered:
1) sub-panel buckling mode 1 (spb1) in which adjacent stiffeners buckle in opposite directions; and
2) sub-panel buckling mode 2 (spb2) in which alternate stiffeners remain generally straight and the stiffeners in between buckle in opposite directions. Where there is only one longitudinal stiffener in a stiffened panel, only mode 2 applies.
The factors against sub-panel buckling, 𝛼𝑐𝑟,𝑠𝑝𝑏1 and 𝛼𝑐𝑟,𝑠𝑝𝑏2 for modes 1 and 2 respectively should be derived using the expressions given in N.4.2.
NOTE 1 The equations in N.4.2 include benefit from the stabilising effect of the plate. NOTE 2 Guidance on improved strength derivation is given in N.1.3. NOTE 3 Methods for the derivation of plate effectiveness and the associated effective widths of plates
to be used are given in N.4.3 and N.5 respectively. These are applicable to all modes.
N.4.2 Factor Against Sub-Panel Buckling
The factor against buckling for sub-panel buckling mode 1, 𝛼𝑐𝑟,𝑠𝑝𝑏1, and for sub-panel buckling mode 2, 𝛼𝑐𝑟,𝑠𝑝𝑏2, may be calculated using Equation N.4.2a and Equation N.4.2b respectively.
146
𝛼𝑐𝑟,𝑠𝑝𝑏1 =𝜎𝑐𝑟𝑒1+
𝑡
𝑡𝑒𝑓𝑓1[𝜎𝑐𝑟1∗′ +0.4(
𝑎𝑠𝑏)2(𝑡𝑒𝑓𝑓2
𝑡)𝜎𝑐𝑟2
∗′ +𝜏𝑐𝑟∗′ ]
𝜎1𝑒𝑓𝑓+𝑡
𝑡𝑒𝑓𝑓1[0.4(
𝑎𝑠𝑏)2(𝑡𝑒𝑓𝑓2
𝑡)𝜎2𝑒𝑓𝑓+𝜏𝑒𝑓𝑓]
Equation N.4.2a
𝛼𝑐𝑟,𝑠𝑝𝑏2 =𝜎𝑐𝑟𝑒1+
𝑡
𝑡𝑒𝑓𝑓1[𝜎𝑐𝑟1∗′′ +0.1(
𝑎𝑠𝑏)2(𝑡𝑒𝑓𝑓2
𝑡)𝜎𝑐𝑟2
∗′′ +𝜏𝑐𝑟∗′′]
𝜎1𝑒𝑓𝑓+𝑡
𝑡𝑒𝑓𝑓1[0.1(
𝑎𝑠𝑏)2(𝑡𝑒𝑓𝑓2
𝑡)𝜎2𝑒𝑓𝑓+𝜏𝑒𝑓𝑓]
Equation N.4.2b
where
𝜎𝑐𝑟1∗′ , 𝜎𝑐𝑟2
∗′ , 𝜏𝑐𝑟∗′are the mode 1 modified critical stresses for direct stress, transverse stress and shear stress respectively to cause buckling of the panels of size 𝑎𝑠 × 𝑏 adjacent to the stiffener under the combined actions of the component stresses 𝜎1𝑒𝑓𝑓, 𝜎2𝑒𝑓𝑓 and 𝜏𝑒𝑓𝑓 derived in accordance with the procedure in N.4.3.
𝜎𝑐𝑟1∗′′ , 𝜎𝑐𝑟2
∗′′ , 𝜏𝑐𝑟∗′′are the mode 2 modified critical stresses derived for a panel of size 𝑎𝑠 × 2𝑏 in accordance with N.4.3, ie allowing for alternative stiffeners being straight and not buckling or applying when there is only one intermediate stiffener.
𝜎𝑐𝑟𝑒1 is the Euler critical buckling stress of the effective stiffener section, calculated as:
𝜎𝑐𝑟𝑒1 =𝜋2𝐸𝐼𝑂𝑋
𝑎𝑠2𝑏𝑡𝑒𝑓𝑓
𝐼𝑂𝑋 is the second moment of area of the effective stiffener section including a total effective width of plating 𝐾𝑏𝑡 × 𝑏 (for spb mode 1) and 𝐾𝑏𝑡 × 2𝑏 (for spb mode 2).
𝐾𝑏𝑡 is the tangent effective width of plating associated with the stiffener under consideration, see N.5.1.
𝑏 is the spacing of equally spaced stiffeners, or the average spacing on each side of the stiffener for unequally spaced stiffeners.
𝑎𝑠 is the length of the stiffener in direction 1 between main cross members or other points of attachment providing full restraint against buckling.
𝑡 is the actual thickness of the attached plating on either side of the stiffener under consideration.
𝑡𝑒𝑓𝑓1 is the effective plate thickness in direction 1, given by 𝑡 (1 + ∑𝐴𝑆𝑋
𝑏𝑡), where 𝐴𝑆𝑋 is
the area of the stiffener under consideration in direction 1.
𝑡𝑒𝑓𝑓2 is the effective plate thickness in direction 2, given by 𝑡 (1 + ∑𝐴𝑆𝑌
𝑎𝑠𝑡), where ∑𝐴𝑆𝑌
is the sum of any secondary stiffeners in direction 2(i.e. orthogonal to the main stiffener under consideration.) For most cases ∑𝐴𝑆𝑌 = 0. Where there is any variation in size or spacing, ∑𝐴𝑆𝑌
𝑎𝑠 should be based on stiffeners in the middle
third of the length 𝑎𝑠.
In cases of unequal spacing, b, or of unequal thickness, t, either side of the stiffener under consideration, 𝐼𝑂𝑋 should be based on a section comprising 𝐴𝑆𝑋 together with associated effective plating given by 0.5(𝐾𝑏𝑡1𝑏1𝑡1 + 𝐾𝑏𝑡2𝑏2𝑡2), where 𝐾𝑏𝑡1, 𝑏1, 𝑡1 and 𝐾𝑏𝑡2, 𝑏2, 𝑡2 apply to the plating either side of the stiffener.
147
Elsewhere such as for 𝛼𝑐𝑟,𝑝1, 𝛼𝑐𝑟,𝑝2 and 𝑡𝑒𝑓𝑓1, 𝑏 may be taken as 0.5(𝑏1 + 𝑏2).
NOTE In all cases the sub-panel buckling mode assumes a single half wavelength of length 𝑎𝑠, for the stiffener and plate.
N.4.3 Stabilising effect of plate
Where the sub-panel buckling load factor 𝛼𝑐𝑟,𝑠𝑝𝑏1 is calculated in accordance with N.4, the modified critical stresses 𝜎𝑐𝑟1∗′ , 𝜎𝑐𝑟2
∗′ , 𝜏𝑐𝑟∗′ shall be calculated from the following expressions.
𝜎𝑐𝑟1∗′ = 𝛼𝑐𝑟,𝑝1𝜎1,𝑒𝑓𝑓
𝜎𝑐𝑟2∗′ = 𝛼𝑐𝑟,𝑝1𝜎2,𝑒𝑓𝑓
𝜏𝑐𝑟∗′ = 𝛼𝑐𝑟,𝑝1𝜏𝑒𝑓𝑓
where
𝛼𝑐𝑟,𝑝1 is the minimum load amplifier to cause elastic buckling of the combined action of component stresses 𝜎1,𝑒𝑓𝑓, 𝜎2,𝑒𝑓𝑓 and 𝜏𝑒𝑓𝑓 on the effective panel of size 𝑎𝑠 × 𝑏 with the stiffener excluded. See N.4.4.
Similarly, where 𝛼𝑐𝑟,𝑠𝑝𝑏2 is calculated, the modified critical stresses 𝜎𝑐𝑟1∗′′ , 𝜎𝑐𝑟2
∗′′ , 𝜏𝑐𝑟∗′′ shall be
calculated from:
𝜎𝑐𝑟1∗′′ = 𝛼𝑐𝑟,𝑝2𝜎1,𝑒𝑓𝑓
𝜎𝑐𝑟2∗′′ = 𝛼𝑐𝑟,𝑝2𝜎2,𝑒𝑓𝑓
𝜏𝑐𝑟∗′′ = 𝛼𝑐𝑟,𝑝2𝜏𝑒𝑓𝑓
where
𝛼𝑐𝑟,𝑝2 is the minimum load amplifier to cause elastic buckling of the combined action of component stresses 𝜎1,𝑒𝑓𝑓, 𝜎2,𝑒𝑓𝑓 and 𝜏𝑒𝑓𝑓 on the effective panel of size 𝑎𝑠 × 2𝑏 with the stiffener excluded. See N.4.4.
N.4.4 Calculation of 𝜶𝒄𝒓,𝒑𝟏 and 𝜶𝒄𝒓,𝒑𝟐
𝛼𝑐𝑟,𝑝1 and 𝛼𝑐𝑟,𝑝2 may be calculated, in order to give maximum benefit, based on a buckling mode shape which has only one half wavelength of buckling over the stiffener length, 𝑎𝑠.
NOTE 1 It is conservative to calculate 𝛼𝑐𝑟,𝑝1 and 𝛼𝑐𝑟,𝑝2 instead for the mode shape with the most critical number of half wavelengths, rather than restricting it to only 1. BS EN 1993-1-5 and the IDWR both give methods for this.
For the purpose of deriving 𝛼𝑐𝑟,𝑝1 and 𝛼𝑐𝑟,𝑝2, variation of in-plane bending stress may be considered by adding one sixth of the bending stress to the direct stress.
NOTE 1 Note that the effects of varying stress are considered differently for spb1 and spb2 than for the overall orthotropic mode, where bending stress over the whole panel would generally be considered explicitly.
148
For the purpose of deriving 𝛼𝑐𝑟,𝑝1 and 𝛼𝑐𝑟,𝑝2, variation of 𝜎1 stress along the length or of 𝜎2 stress across the width of the panels may be considered by taking the highest compressive value in the middle third.
N.5 Effective Widths of Plating N.5.1 Tangent Effective Width, 𝑲𝒃𝒕, for Stiffness
For flange stiffeners the effective width of plating for use in deriving 𝐼𝑜𝑥 (in N.4 and N.3) for stiffness shall be taken as one of the following:
1) a conservative total effective width of 0.5b for any plate slenderness or level of compression.
2) an effective width based on 𝐾𝑐′′, as an approximation for any elements acting primarily under direct stress where transverse stress or shear are negligible; or
3) for flanges under combined stresses, variation of imperfection or residual stress, conservative values of 𝐾𝑏𝑡 in accordance with N.5.3(b).
For web stiffeners the effective width of plating for use in deriving 𝐼𝑜𝑥 (in N.4 and N.3) for stiffness shall be taken as one of the following:
1) a total effective width of 32𝑡𝑤 (1 − 𝜌) but not exceeding 𝑏(1 − 𝜌) in accordance with 9.11.5.1; or
2) an effective width based on the procedure given in IDWR clause18 to derive 𝐾𝑏𝑡; or 3) for webs, under combined stresses, variation of imperfection or residual stress,
conservative values of 𝐾𝑏𝑡 in accordance with N.5.3(b).
NOTE 1 Although more accurate methods of deriving 𝐾𝑏𝑡 are available from Figure 5b and in the IDWR and could be used, generally little advantage is gained for effective stiffener stiffness.
For other elements effective widths shall be taken as those used in the effective section, such as defined in 9.13.2 (or 9.14.2) for transverse web stiffeners, 9.15.2 for flange transverse members, 9.16.4.1 for ring frames and 9.17.4.4 for diaphragm stiffeners.
N.5.2 Secant Effective Width, 𝑲𝒃𝒔, for Stress or Strength
The effective width of plating for stress shall be taken as one of the following:
1) the secant effective width, 𝐾𝑏𝑠 can be taken as equal to 𝐾𝑏𝑡 in N.5.1 as a conservative value; or
2) for element under primarily direct stress by using 𝐾𝑐′ from Figure 5a in 9.10.2.2. 3) for combined stresses a conservative value of 𝐾𝑏𝑠 can be obtained in accordance with
N.5.3(a).
NOTE 1 However the degree of conservatism could limit the strength, particularly in the case of derivation of 𝑟𝑠𝑒 and consequent benefits when considering sub-panel buckling modes or orthotropic actions, particularly for webs.
4) an effective width based on the value of 𝐾𝑏𝑠 using the procedure given in clause 18 of the IDWR.
NOTE 2 The procedure in IDWR enables full benefit of levels of plate stress to be obtained as well as allowing for any level of initial imperfections and residual stress, see N.1.5.
149
N.5.3 Effective Widths under the Action of Combined Stresses, Varying Imperfections and Residual Stresses
Where a conservative value of 𝐾𝑐′ is required from Figure 5a under the action of combined stresses, 𝐾𝑐′ shall be calculated using 𝜎𝑎′ = 𝐾𝑐′𝛾𝑚𝛾𝑓3𝜎𝑠𝑒 in Figure 5a, with 𝜎𝑠𝑒 being the equivalent effective stress taken as the greater of the values derived from N.1.3 or N.1.4.
Where adjustment is required for residual stress or imperfection (see N.1.5), this may be accounted for by use of Annex P using 𝜎𝑅 as required in place of 0.1𝜎𝑦𝑒 and Δ𝑋 as 1.2 multiplied by the initial imperfection in the plating (measured, taken from the construction specification or assumed).
Where a conservative value of 𝐾𝑐′′ is required from Figure 5b a similar procedure shall be applied as for 𝐾𝑐′, but using Figure 5b instead of Figure 5a.
N.6 Imperfection measurements for stiffened panels
Where overall buckling governs, the half-wavelengths of buckling to be adopted as the gauge length 𝐺, for use in the measurement of initial out-of-plane deformations of stiffened panels in compression shall be taken as 𝑙/𝑚.
where
𝑚 is the integer value appropriate to the values of 𝜓 and 𝛷′, within the boundaries of the dotted lines on Figure N.4.
For both sub-panel buckling modes (1 and 2), the gauge length, 𝐺, and the half wavelength of buckling shall be taken as 𝑎𝑠, the length of stiffener in direction 1 between main cross members or other points of attachment providing full restraint against buckling compatible with the implied mode of behaviour considered in N.4 resulting from the destabilising effects of transverse and/or shear stress.
NOTE 1 Thus for flanges 𝑎𝑠 is taken as 𝑙, for webs 𝑎𝑠 is taken as a and for diaphragms 𝑎𝑠 is taken as 𝑙𝑠.
150
Figure N.1
Figure N.2
Figure N.5a
151
Figure N.5b
Figure N.5c
Figure N.3 – Simply supported rectangular plates with linearly varying edge stress
152
Figure N.4 – Simply supported orthotropic plates with linearly varying edge stress
153
[BS5400-3, Add new Annex P]
Annex P – Effective width coefficients for plates unrestrained in plane along their longitudinal edges
P.1 Introduction
This Annex shall be used where necessary to calculate the coefficients 𝐾𝑐′ or 𝐾𝑐′′ for unrestrained plates with any out-of-plane deformation Δ𝑥 measured after welding in accordance with BS 5400-6 with or without welding residual stress.
Values of 𝐾𝑐′ may be derived from clauses P.2 to P.4.
NOTE 1 The Annex gives the basis for Figures 5a and 5b in 9.10.2.2.
The objective of this Annex should be to calculate 𝐾𝑐′ or 𝐾𝑐′′ by performing the following stages of calculation:
1) The out of flatness imperfection Δ𝑥 and the welding residual stress for the panel should be determined.
2) The theoretical initial imperfection value, Δ0, of the plate before welding should be calculated using the out of flatness imperfection after welding, Δ𝑥, and the welding residual stress, in accordance with P.2.
3) The magnification factor, 𝑚, of imperfections under the applied stress should be calculated in accordance with P.3.
4) The secant effective width coefficient, 𝐾𝑐′, or the tangent effective width coefficient, 𝐾𝑐′′, should then be calculated in accordance with P.4.
NOTE 2 Where plates form part of a cross section, iteration is required because 𝜎𝑎′ in P.3 depends on the value of 𝐾𝑐′.
P.2 Calculation step 1 – Calculation of initial imperfection, 𝚫𝟎
The value of Δ0 shall be obtained from Equation P.2.
NOTE 1 Equation P.2 is a quadratic equation and can be solved by the standard solution.
(𝛥𝑜
𝑡𝑓)2
+ 2.94 (𝛥𝑜
𝛥𝑥) − (
𝛥𝑥
𝑡𝑓)2
− 2.94 +𝜆2
710
𝜎𝑅
𝜎𝑦𝑒= 0 Equation P.2
where
𝛥𝑥 is the measured out of flatness imperfection of the plate
𝜆 =𝑏
𝑡𝑓√𝜎𝑦𝑒
355
𝑡𝑓 is the thickness of the plate.
𝑏 is the width of the plate.
𝜎𝑦𝑒 is as defined in 9.10.2.3. Where, for most practical cases of girder flanges, the shear is negligible, 𝜎𝑦𝑒 may be taken as equal to the nominal yield stress of the plate.
154
𝜎𝑅 is the average welding residual stress on the gross plate area.
NOTE 2 For the purpose of deriving Figures 5a and 5b, values of 𝜎𝑅 and 𝛥𝑥 are assumed such that
𝜎𝑅 = 0.1𝜎𝑦𝑒 and 𝛥𝑥𝑡𝑓=
𝜆
165.
P.3 Calculation step 2 – Calculation of magnification factor, 𝒎
The value of the magnification factor, 𝑚, shall be obtained, such that Equation P.3 is satisfied.
𝜎𝑎′
𝜎𝑦𝑒=
2088
𝜆2[(1 −
1
𝑚) + 0.34 (
𝛥𝑜
𝑡𝑓)2
(𝑚2 − 1)] −𝜎𝑅
𝜎𝑦𝑒 Equation P.3
where
𝜎𝑎′ is the average axial stress on the section using a plate effective width
coefficient 𝐾𝑐′.
Other terms are as defined for Equation P.2.
P.4 Calculation step 3 – Calculation of coefficients, 𝑲𝒄′ , 𝑲𝒄′′
The corresponding values of 𝐾𝑐′ shall be calculated from Equation P.4a.
𝐾𝑐′ =
(1−1
𝑚)+0.34(
𝛥𝑜𝑡𝑓)
2
(𝑚2−1)−𝜆2𝜎𝑅
2088𝜎𝑦𝑒
(1−1
𝑚)+0.34(
𝛥𝑜𝑡𝑓)
2
(2𝑚2−𝑚𝑟2−1)−
𝜆2𝜎𝑅2088𝜎𝑦𝑒
Equation P.4a
where
𝑚𝑟 =𝛥𝑥
𝛥𝑜
The corresponding values of 𝐾𝑐′′ shall be calculated from Equation P.4b.
𝐾𝑐′′ =
1+0.68(𝛥𝑜𝑡𝑓)
2
𝑚3
1+1.36(𝛥𝑜𝑡𝑓)
2
𝑚3
Equation P.4b
Where terms are as defined in P.2 and P.3
155
[BS5400-3, Add new Annex S]
Annex S – Shape limitations for assessment
S.1 Introduction
Where directed by clause 9.3.1, the methods in this appendix shall be used to determining the ‘lower yield stress’ 𝜎𝑦𝑠 of stiffeners for use in subsequent strength calculations.
NOTE: This method does not give a ‘lower yield stress’, 𝜎𝑦, of the plate to which the stiffener is attached. While the plate yield is significant in determining limiting proportions in some of the individual sub-clauses of 9.3, it is not relevant to this Annex.
S.2 Open Shaped Stiffeners S.2.1 General S.2.1.1 Calculation of lower yield stress, 𝝈𝒚𝒔
The lower yield stress, 𝜎𝑦𝑠, for open shaped stiffeners shall be calculated according to Equation S.2.1.1.
𝜎𝑦𝑠 = 0.5 {[𝜎𝑜 + (1 +𝜂𝑐𝑟𝐸
𝜎𝑐𝑟)𝜎𝑐𝑟] − √[𝜎𝑜 + (1 +
𝜂𝑐𝑟𝐸
𝜎𝑐𝑟) 𝜎𝑐𝑟]
2− 4𝜎𝑜𝜎𝑐𝑟}Equation S.2.1.1
where
𝜎𝑜 is the nominal yield stress of the stiffener as defined in 6.2.
𝜂𝑐𝑟 is the imperfection parameter, calculated according to S.2.1.2.
𝜎𝑐𝑟 is the critical stress of the stiffener as defined in clauses S.2.2 to S.2.3.
𝐸 is the modulus of steel, according to clause 6.6
S.2.1.2 Calculation of imperfection parameter, 𝜼𝒄𝒓
For the purpose of calculating 𝜎𝑦𝑠 in S.2.1.1, the value of the imperfection parameter 𝜂𝑐𝑟 shall be calculated from Equation S.2.1.2.
𝜂𝑐𝑟 = 1.2𝜋2𝛥𝑆𝑌𝐸𝑎𝑦
𝑙𝑠2 Equation S.2.1.2
where
𝛥𝑆𝑌𝐸 is the effective imperfection as defined in S.2.1.3, representing the lateral departure from straightness of the tip of the outstand appropriate to the half wavelength of buckling, 𝑙𝑠.
𝑎𝑦 is the greatest distance from the centroid of the stiffener alone to the extreme fibre of the outstand, as defined in Figure S.3.
156
S.2.1.3 Imperfections
For the purpose of calculating the imperfection parameter in S.2.1.2, the effective stiffener imperfection, 𝛥𝑆𝑌𝐸, shall be derived from the measured imperfection or the fabricated tolerances for the structure and the buckling length 𝑙𝑠.
The equations below may be used where the gauge length G for measurement of 𝛥𝑠𝑦 does not match the buckling length 𝑙𝑠.
Where 𝐺 is less than 𝑙𝑠, Δ𝑆𝑌𝐸 should be taken as:
𝛥𝑆𝑌𝐸 =𝛥𝑠𝑦
1−𝑠𝑖𝑛[𝜋
2(1−
𝐺
𝑙𝑠)]
Equation S.2.1.3a
Where 𝐺 is greater than 𝑙𝑠, Δ𝑆𝑌𝐸 should be taken as:
𝛥𝑆𝑌𝐸 = 𝛥𝑠𝑦 {1 − 𝑠𝑖𝑛 [𝜋
2(1 −
𝑙𝑠
𝐺)]} Equation S.2.1.3b
where
𝐺 is the gauge length for measurement of 𝛥𝑠𝑦.
𝑙𝑠 is the buckling length calculated in the relevant section of S.2.2 or S.2.3. Where the lower bound for 𝜎𝑐𝑟 from S.2.3.1 is used, 𝑙𝑠 should be taken as 𝐿.
𝛥𝑠𝑦 is the specified tolerance or measured value for lateral departure from straightness of the stiffener.
Where fabrication has been in accordance with BS5400-6, the tolerance value of Δ𝑠𝑦 and associated gauge length G may be taken from BS5400-6.
NOTE 1 The most accurate results are obtained when the measurements are made using a gauge length equal to the buckling length 𝑙𝑠.
S.2.2 Flat Stiffeners, calculation of 𝝈𝒄𝒓
For the purpose of calculating 𝜎𝑦𝑠 in S.2.1.1 for flat stiffeners, 𝜎𝑐𝑟 shall be calculated from Equation S2.2.
𝜎𝑐𝑟 = 𝑘𝜋2𝐸
12(1−𝜈2)(𝑡𝑠
ℎ𝑠)2
Equation S2.2
where
𝑘 is a factor depending on the degree of restraint given by the parent plate to the connected edge of the stiffener, as derived from Figure S.2 using a value of 𝜀 =
4 (𝑡
𝑡𝑠)3 ℎ𝑠
𝑏𝛼.
𝑡𝑠, ℎ𝑠 are as defined in Figure S.3.
𝑡 is the thickness of the parent plate.
𝑏 is the spacing of longitudinal stiffeners. Where longitudinal stiffeners are unequally spaced, 𝑏 may be taken as the mean of the spacing on either side of the stiffener under consideration.
157
𝛼 is a factor to allow for the loss of effectiveness of plate under compressive stress, calculated from the following equations, but in no instances less than zero or greater than 1.
𝛼 = 1 −𝜎𝑝1
𝜎𝑝𝑐𝑟(
2𝑙𝑠𝑏+𝑏
𝑙𝑠
)
2
−𝜎𝑝2
𝜎𝑝𝑐𝑟(
2
1+𝑏2
𝑙𝑠2
)
2
, for 𝑙𝑠 > 𝑏, or
𝛼 = 1 − (𝜎𝑝1+𝜎𝑝2
𝜎𝑝𝑐𝑟), for 𝑙𝑠 ≤ 𝑏
NOTE 1 Where 𝑙𝑠 ≥ 3𝑏, 𝛼 can be approximated to 𝛼 = 1 − 𝜎𝑝1
𝜎𝑝𝑐𝑟(2𝑏
𝑙𝑠)2− 4
𝜎𝑝2
𝜎𝑝𝑐𝑟.
𝜎𝑝1 is the compressive stress in the parent plate on the direction of the stiffener.
𝜎𝑝2 is the compressive stress in the parent plate normal to the stiffener.
𝜎𝑝𝑐𝑟 =𝜋2𝐸
3(1−𝜈2)(𝑡
𝑏)2
𝑙𝑠 is obtained from Figure S.1, but not greater than 𝐿.
𝐿 is the length between transverse supports to the stiffener. NOTE 2 Hence, the procedure is iterative, as follows:
1) Guess a value of 𝑘 (between 0.43 and 1.28 which represent simply supported edges and fully fixed long edge respectively.)
2) Determine 𝑙𝑠 from Figure S.1 (but see NOTE 3). 3) Determine 𝛼 from the expression above. 4) Determine 𝜀 from the expression above. 5) Determine 𝑘 from Figure S.2. 6) Correct the initial guess for 𝑘 and repeat as necessary until calculated 𝑘 is sufficiently
close to the original guess, and then derive 𝜎𝑐𝑟.
NOTE 3 Where 𝛼 = 0, 𝑘 tends to 0.43 and 𝑙𝑠 ℎ𝑠⁄ tends to ∞, i.e. 𝑙𝑠 tends to 𝐿.
Where 𝜎𝑝𝑐𝑟 is low and combination of 𝜎𝑝1 and 𝜎𝑝2 is high such that 𝛼 = 𝑧𝑒𝑟𝑜, a higher value of 𝛼 or 𝜎𝑐𝑟 may be derived from first principles or from tests.
S.2.3 Bulb flat, Angle and Tee Stiffeners, calculation of 𝝈𝒄𝒓 S.2.3.1 Bulb flat, Angle and Tee Stiffeners, calculation of lower bound 𝝈𝒄𝒓
Where 𝜎𝑐𝑟 is required in S.2.1.1 for bulb flat, angle or tee stiffeners, the method in S.2.3.2 shall be used except where the following lower bound method is sufficient to demonstrate adequacy.
A lower bound value for 𝜎𝑐𝑟 may be found from Equation S.2.3.1 by assuming the edge is simply supported.
𝜎𝑐𝑟 =1
𝐴𝑠(𝑟𝑋2+𝑟𝑌
2)(𝐺𝐽 +
𝜋2𝐸𝐶𝑊
𝐿2) Equation S.2.3.1
where
158
𝑟𝑋, 𝑟𝑌 are the radii of gyration of the stiffener about X-X, Y-Y axes drawn through the line of attachment, as illustrated in Figure S.3.
𝐴𝑠 is the are of section of the stiffener.
𝐽 is the torsion constant of the stiffener, taken as:
𝐽 =𝐻𝑡𝑠
3
3+𝐵𝑡𝑓
3
3(1 − 0.63
𝑡𝑓
𝐵) for bulb flat stiffeners, or
𝐽 =𝐻𝑡𝑠
3
3+𝐵𝑡𝑓
3
3 for angle stiffeners and tee stiffeners.
𝐺 is the shear modulus as defined in 6.6.
𝐶𝑊 is the warping constant of the stiffener about the line of attachment, taken as
𝐶𝑊 =1.1𝐵3𝐻2𝑡𝑓
3(
𝐵3𝑡𝑓
3𝐻2+𝐵𝑡𝑓+
𝐻𝑡𝑠3
𝐵𝑡𝑓+𝐻𝑡𝑠) for bulb flats, or
𝐶𝑊 =1.3𝐵3𝐻2𝑡𝑓
3(
𝐵3𝑡𝑓
3𝐻2+𝐵𝑡𝑓+
𝐻𝑡𝑠3
𝐵𝑡𝑓+𝐻𝑡𝑠) for angles, or
𝐶𝑊 =1.1𝐵3𝐻2𝑡𝑓
12(
𝐵3𝑡𝑓
12𝐻2+𝐵𝑡𝑓+
𝐻𝑡𝑠3
𝐵𝑡𝑓+𝐻𝑡𝑠) for tees.
𝐻, 𝑡𝑓 , 𝑡𝑠,𝐵 are as defined in Figure S.3 for the appropriate stiffener type.
𝐿 is the length between transverse supports to the stiffener.
S.2.3.2 Bulb flat, Angle and Tee Stiffeners, alternative calculation of 𝝈𝒄𝒓
Where 𝜎𝑐𝑟 is required in S.2.1.1 for bulb flat, angle or tee stiffeners and the lower bound method in S.2.3.1 is not sufficient to demonstrate adequacy, 𝜎𝑐𝑟 shall be derived to take benefit from the rotational restraint of the plate using Equation S.2.3.2.
𝜎𝑐𝑟 =1
𝐴𝑠𝑟𝑜2 (𝐺𝐽 +
𝜋2𝐸𝐶𝑊
𝑙𝑠2 +
𝑙𝑠2𝛽
𝜋2) Equation S.2.3.2
where
𝑙𝑠 is the half wavelength of buckling given by the following equation but not greater than 𝐿:
𝑙𝑠 = 𝜋 (𝐸𝐶𝑊
𝛽)0.25
𝑟𝑜 =√𝑟𝑋2 + 𝑟𝑌2
𝛽 =𝐸
(1−𝜈2)(3𝑏
𝛼𝑡3+4𝐻
𝑡𝑠3)
𝐴𝑠, 𝑟𝑋, 𝑟𝑌, 𝐺, 𝐽, 𝐶𝑊, 𝐿, 𝐻, 𝑡𝑠, 𝑏, 𝑡 are as defined in S.2.3.1.
𝛼 is as defined in S2.2, using 𝑙𝑠 as defined above for Equation S.2.3.2.
159
NOTE 1: Hence, the procedure to determine 𝜎𝑐𝑟 is iterative, similar to that for flat stiffeners:
1) Guess a value of 𝑙𝑠 (try 𝑙𝑠 = 5𝐻). 2) Check 𝑙𝑠 < 𝐿. 3) Determine 𝛼 from the expression in S2.2. 4) Determine 𝛽 from the expression above. 5) Determine 𝑙𝑠 from the expression above. 6) Correct the initial value of 𝑙𝑠 and repeat until convergence is obtained.
𝜎𝑐𝑟 is derived using the converged values of the parameters. NOTE 2 This method of allowing for the restraint to the long edge gives little benefit for the zero or
very small restraints (i.e. for 𝛼 and for 𝛽 small enough to imply the preferred half wavelength of buckling 𝑙𝑠 > 𝐿). In such cases the lower bound to 𝜎𝑐𝑟 can be used given by the equation for the simply supported case in S.2.3.1.
Figure S.1
160
Figure S.2
Note In Figure S.3, Y-Y is axis of point of attachment (taken as centre of the attached leg) but y-y
is centroidal axis of the stiffener alone. Figure S.3
161
[BS5400-3, Add new Annex T]
Annex T – Derivation of buckling coefficients for web panels
T.1 General
The methods in this Annex shall be used where necessary in order to determine the adequacy of plates under a combination of stresses and with imperfections that are different from the tolerances in BS5400-6.
NOTE 1 The basis is the well-established use of elastoplastic large deflection computer methods and checks with nominal imperfections show satisfactory agreement.
The calculation should involve the determination of the individual buckling coefficients 𝐾1, 𝐾𝑞, 𝐾𝑏 and 𝐾𝑐, and the modification of them to take into account the actual level of imperfection by means of factors 𝑘Δ1, 𝑘Δq, 𝑘Δb and 𝑘Δc.
NOTE 2 The buckling coefficients 𝐾1, 𝐾𝑞, 𝐾𝑏 and 𝐾𝑐 are given as polynomials in 𝛽 which are ‘best-fit’ curves to results obtained from large deflection elasto-plastic analysis. The basic buckling coefficients are based on a nominal imperfection 𝑤𝑜𝑠 given by Equation T.1.
𝑤𝑜𝑠 = 0.145𝛽𝑡 =𝑏
165√𝜎𝑦
355 Equation T.1
where terms are as defined in T.2
The plate directions, 1 and 2, should be assumed such that the length of the plate in direction 1, 𝑎, is greater than or equal to the length of the plate in direction 2, 𝑏.
T.2 Limiting longitudinal stress, 𝝈𝒖𝟏
For the purpose of this Annex, the limiting stress in direction 1, 𝜎𝑢1, shall be calculated using Equation T.2.
𝜎𝑢1 = 𝑘𝛥1𝐾1𝜎𝑦 Equation T.2
where
𝐾1 is the longitudinal coefficient 𝐾1 for nominal imperfection given by 𝐾1 = 0.23 +1.16
𝛽−0.48
𝛽2+0.09
𝛽3
𝛽 is the non-dimensional slenderness of the plate panel
𝛽 =𝑏
𝑡√𝜎𝑦
𝐸
𝜎𝑦 is the nominal yield stress of the panel, as defined in 6.2. 𝑘𝛥1 is the imperfection sensitivity parameter determined from Figure T.3a using the ratio, 𝛺, of the actual imperfection to the nominal and the ratio 𝛽 𝛽𝑐𝑟⁄ as defined below.
𝛽 𝛽𝑐𝑟⁄ is the ratio of the slenderness, 𝛽, to the critical slenderness, 𝛽𝑐𝑟, (for which the critical stress is equal to the yield stress. For the use of Figure T.3a, the ratio 𝛽 𝛽𝑐𝑟⁄ should be taken as the value for long panels
162
𝛽 𝛽𝑐𝑟⁄ = √𝜎𝑦
[4𝜋2𝐸𝑡2
12(1−𝜈2)𝑏2]
𝑏 is the length of the panel in direction 2 (the short direction of the panel).
𝑡 is the thickness of the panel.
𝐸,𝜈 are as defined in 6.6.
T.3 Limiting shear stress, 𝝉𝒖
For the purpose of this Annex, the limiting stress 𝜏𝑢 shall be calculated from Equation T.3.
𝜏𝑢 = 𝑘𝛥𝑞𝐾𝑞 𝜎𝑦 √3⁄ , but not greater than 𝜎𝑦
√3 Equation T.3
where
𝐾𝑞 is the shear buckling coefficient determined from the curves of Figure 23b.
𝑘𝛥𝑞 is the imperfection sensitivity parameter determined from Figure T.3b.
𝜎𝑦 is the nominal yield stress of the panel, as defined in 6.2.
T.4 Limiting bending stress, 𝝈𝒃
For the purpose of this Annex bending shall be allowed for by adding half the peak compressive bending stress to the direct stress, 𝜎1.
NOTE 1 Explicit values of the coefficient 𝐾𝑏 and the factor 𝑘Δ𝑏are not yet available for this method.
T.5 Limiting transverse stress, 𝝈𝒖𝟐
The process to determine the transverse limiting stress 𝜎𝑢2 shall first determine the limiting transverse stress for a panel based on the strength acting as a column, 𝜎𝑢𝑐, using Equation T.5a.
𝜎𝑢𝑐 = 𝑘𝛥𝑐𝐾𝑐𝜎𝑦 Equation T.5a
where
𝐾𝑐 is the transverse coefficient 𝐾1 for nominal imperfection and for column action alone, given by 𝐾1 =
0.025
𝛽+0.641
𝛽2−0.188
𝛽3
𝛽 is as defined in T.2.
𝑘𝛥𝑐 is the imperfection sensitivity parameter determined from Figure T.3c using the ratio, 𝛺, of the actual imperfection to the nominal and the ratio 𝛽 𝛽𝑐𝑟⁄ as defined below.
𝛽 𝛽𝑐𝑟⁄ is the ratio of the slenderness, 𝛽, to the critical slenderness, 𝛽𝑐𝑟, (for which the critical stress is equal to the yield stress. For the use of Figure T.3c, the ratio 𝛽 𝛽𝑐𝑟⁄ should be taken as the value for column action alone, given by:
163
𝛽 𝛽𝑐𝑟⁄ = √𝜎𝑦
[𝜋2𝐸𝑡2
12(1−𝜈2)𝑏2]
𝑏,𝑡,𝐸,𝜈 are as defined in T.2.
The transverse limiting stress 𝜎𝑢2 shall be determined from Equation T.5b using the terms calculated above.
NOTE 1 The term 𝜎𝑢2 is not used for the interaction between stresses in T.6 as it is implicit within the T.6 interaction.
𝜎𝑢2 = 𝜎𝑢𝑐 +𝑏
𝑎(𝜎𝑢1 − 𝜎𝑢𝑐) Equation T.5b
where
𝜎𝑢1 is the value calculated from T.2.
𝑎 is the panel length in direction 1.
𝑏 is the panel width in direction 2.
T.6 Interaction of limiting stresses
To evaluate the combined effect of the stresses, 𝜎1, 𝜎2 and 𝜏, on the plate two non-dimensional parameters, 𝜂 and 𝜁, shall be determined first.
𝜂 should be determined by Equation T.6a.
𝜂 = (𝐾1
𝐾𝑏𝑖𝑎𝑥)2− 2 Equation T.6a
where
𝐾1 is as defined in T.2
𝐾𝑏𝑖𝑎𝑥 =1.27
𝛽−0.89
𝛽2+0.30
𝛽3
𝜁 should be determined by Equation T.6b.
𝜁 = [1 − (𝜏
𝜏𝑢)2](1 𝑛⁄ )
Equation T.6b
where
𝜏 is the shear stress in the panel.
𝜏𝑢 is derived in T.3.
𝑛 is derived as follows:
𝑛 = 2 −𝛽
𝛽𝑐𝑟 for
𝛽
𝛽𝑐𝑟≤ 1, and
𝑛 = 1 for 𝛽
𝛽𝑐𝑟> 1.
𝛽 is as defined in T.2.
164
𝛽𝑐𝑟 = √8.34 + 6.25 (𝑏
𝑎)2
The adequacy of the panel shall then be determined using the inequality in Equation T.6c.
𝜎12 + 𝜂𝜎1𝜎2𝑒 + 𝜎2𝑒
2 ≤ (𝜁𝜎𝑢1
𝛾𝑚𝛾𝑓3)2
Equation T.6c
where
𝜎1 is the longitudinal stress in the panel, to be taken as positive if compressive and zero if tensile.
𝜎𝑢1 is the longitudinal limiting stress derived in T.2.
𝜎2𝑒 is the equivalent transverse stress, derived as follows:
𝜎2𝑒 = 𝜎2 for 𝜎2 ≤ 𝜁𝜎𝑢𝑐 or 𝑎𝑏= 1; and
𝜎2𝑒 = 𝜁𝜎𝑢𝑐 (1 −𝑎
𝑏) +
𝑎
𝑏𝜎2 otherwise.
𝜎2 is the transverse stress in the panel; to be taken as positive if compressive and zero if tensile.
𝜎𝑢𝑐 is derived in T.5
In all cases, the adequacy of the panel shall be checked additionally for yielding in accordance with Equation T.6d.
𝜎12 − 𝜎1𝜎2 + 𝜎2
2 ≤ (𝜎𝑦
𝛾𝑚𝛾𝑓3)2
Equation T.6d
where
𝜎1, 𝜎2 are the longitudinal and transverse stresses in the panel, taken as positive if compressive and negative if tensile.
𝜎𝑦 is the nominal yield stress of the panel, as defined in 6.2.
165
Figure T.3a Imperfection Sensitivity
Figure T.3b Imperfection Sensitivity
166
Figure T.3c Imperfection Sensitivity
167
[BS5400-3, Add new Annex X] Annex X – Assessment of risk levels for notch toughness
Figure X1: Identification of risk level due to low toughness 2 categories
168
Figure X.2: Assessment of risk level 2 categories
CS 456 Revision 0
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