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- 1. | BS 8100-3:1999BRITISH STANDARD | | | | Incorporating | | Corrigendum No. 1 | | | | | | | | | | |Lattice towers and | | | | | |masts Ð | | | | | | | | |Part 3: Code of practice for strength | | |assessment of members of lattice towers | | |and masts | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |ICS 91.080.10 | | | | | | | | | NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW | | | |
- 2. BS 8100-3:1999 Committees responsible for this British Standard The preparation of this British Standard was entrusted by Technical Committee B/525, Building and civil enginnering structures, to Subcommittee B/525/32, Towers and masts, upon which the following bodies were represented: British Telecommunications plc Department of Trade and Industry (Electricity Department) Institution of Civil Engineers Meteorological Office Ministry of Defence National Transcommunications Ltd Steel Construction Institute UK Steel AssociationThis British Standard, havingbeen prepared under thedirection of the Building and Civil Amendments issued since publicationEngineering Sector Committee,was published under the Amd. No. Date Commentsauthority of the StandardsCommittee and comes into effecton 15 September 1999 12097 March 2001 Indicated by a sideline Corrigendum© BSI 03-2001 No. 1The following BSI referencesrelate to the work on thisstandard:Committee reference B/525/32Draft for comment 97/10168 DCISBN 0 580 33033 8
- 3. BS 8100-3:1999 Contents Page Committees responsible Inside front cover Foreword ii Introduction 1 1 Scope 1 2 Normative references 1 3 Definitions and symbols 1 4 Axes of members 3 5 Structural configurations, system length and effective slenderness 3 6 Calculation of design strength for members in compression 15 7 Calculation of resistance of members in tension 17 8 Bolted connections 17 9 Mast guy assemblies 20 Annex A (informative) Design of battens 24 Annex B (informative) Terminations commonly used for guys 24 Annex C (informative) Erection tolerances for guyed masts 25 Bibliography 26 Figure 1 Ð Typical cable construction 2 Figure 2 Ð Dimensions and axes of sections 4 Figure 3 Ð Cruciform angle sections 5 Figure 4 Ð Typical bracing patterns 6 Figure 5 Ð Use of secondary bracing systems 7 Figure 6 Ð Typical plan bracing 9 Figure 7 Ð K bracing horizontals without plan bracing 9 Figure 8 Ð Cranked K bracing 10 Figure 9 Ð Portal frame 10 Figure 10 Ð Location of bolts 19 Table 1 Ð Applied force as percentage of leg load, F 11 Table 2 Ð Effective slenderness factor K for leg members 13 Table 3 Ð Effective slenderness factor K for bracing members 14 Table 4 Ð Factor K1 for horizontal of K brace (without plan bracing) 15 Table 5 Ð Imperfection factors 15 Table 6 Ð Reduction factors x 16 Table 7 Ð Selection of buckling curve for a cross-section 18 Table 8 Ð Relationships between flange, tube and bolts 19 Table 9 Ð Range of modulus of elasticity for steel wire guys 21 Table B.1 Ð Static tensile efficiencies of terminations 25© BSI 03-2001 i
- 4. BS 8100-3:1999 Foreword This part of BS 8100 has been prepared under the direction of Technical Committee B/525, Building and civil engineering structures. BS 8100 is a series of standards combining codes of practice with a guide covering the loading and design of lattice towers and masts of metallic construction. It comprises the following parts: Ð Part 1: Code of practice for loading; Ð Part 2: Guide to the background and use of Part 1: ªCode of practice for loadingº; Ð Part 3: Code of practice for strength assessment of members of lattice towers and masts; Ð Part 4: Code of practice for loading of guyed masts. This part of BS 8100 incorporates clauses to complement BS 8100-4. The need for this code of practice to give guidance on the determination of the strength of lattice towers and masts arises out of the difficulty in applying consistently the general structural strength codes to these often tall, slender three dimensional lattice structures. The document is based upon DD 133:1986, which in turn brought together the collective experience of the European transmission line tower industry, where each new design of structure was subjected to full-scale ªtypeº testing. It was considered invaluable to have such relatively unique data built into a code as well as enabling the limit state loading rules to be accurately calibrated. The additional clauses dealing with the special aspects of guyed masts represent the collective extensive experience of the drafting committee. It is considered that they will provide efficient solutions to the strength assessment problem, whilst avoiding some of the causes of problems which have occurred on this type of structure. By liaison with the relevant Eurocode drafting team, the rules drafted into this code of practice have been based upon a common approach and should result in the minimum amount of variation when the National Application Document is prepared following the issue of the ENV. This part of BS 8100 does not apply to other metallic structures. Other British Standards exist for some of those structures. It has been assumed in the drafting of this British Standard that the execution of its provisions will be entrusted to appropriately qualified and experienced people. As a code of practice, this British Standard takes the form of guidance and recommendations. It should not be quoted as if it were a specification and particular care should be taken to ensure that claims of compliance are not misleading. Annex A, annex B and annex C are informative. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 26, an inside back cover and a back cover. The BSI copyright notice displayed in this document indicates when the document was last issued. Sidelining in this document indicates the most recent changes by amendment.ii © BSI 03-2001
- 5. BS 8100-3:1999Introduction BS 4429, Specification for rigging screws and turnbuckles for general engineering, lifting purposesThe strengths given in this part of BS 8100 are and pipe hanger applications.characteristic (95 % probability) values for use withBS 8100-1 and -4. The design strengths are obtained BS 5950-1:1990, Structural use of steelwork inby dividing the characteristic strengths by the building Ð Part 1: Code of practice for design inappropriate partial factor gm defined in this part. simple and continuous construction: hot rolled sections.Connection eccentricities assumed in this part ofBS 8100 are those that are traditionally applied to BS 6994, Specification for steel shackles for liftinglattice masts and towers in the UK. and general engineering purposes: grade M(4). BS 7035, Code of practice for socketing of stranded steel wire ropes.1 ScopeThis part of BS 8100 provides guidance on the 3 Definitions and symbolsassessment of the strength of members andconnections for masts and towers of lattice 3.1 Definitionsconstruction consisting mainly of bolted, rivetted or For the purposes of this part of BS 8100 thewelded steel angle or tubular or solid round sections. following definitions apply.The recommendations given are valid for both equal 3.1.1and unequal angles, either rolled or cold formed,compound members fabricated from these sections, leg memberstubular members and solid rounds. members forming the main load bearing chords ofThe specific components covered in this part of the structureBS 8100 are: 3.1.2 a) compression members and bolted and/or primary bracing members welded connections which are specific to typical members other than legs carrying the shear force mast and tower configurations and which are not due to imposed loads on the structure comprehensively covered in general strength 3.1.3 codes; secondary members b) mast guys, their fittings and assemblies. For such components their strength is closely related members used to reduce the effective length of the to practical considerations, and such guidance is main legs and sometimes that of the bracing. They included where relevant. are normally considered unstressed and are only loaded due to deformation of the structure (see 5.4.)NOTE 1 Information on all other aspects of strength assessmentcan be obtained from BS 5950-1. Information for fatigue NOTE Secondary members are sometimes referred to asassessment can be obtained from BS 7608. redundant members. 3.1.42 Normative references system lengthThe following normative documents contain taken as the geometric length of a member betweenprovisions which, through reference in this text, intersection points providing restraint in the relevantconstitute provisions of this part of this British planeStandard. For dated references, subsequent 3.1.5 mast guy assembliesamendments to, or revisions of, any of these 3.1.5.1publications do not apply. For undated references,the latest edition of the publication referred to guyapplies. tension only member which provides horizontalBS 302 (all parts), Stranded steel wire ropes. support to the mast column at discrete levels. The lower end of the guy assembly is anchored to theBS 443, Specification for testing zinc coatings on ground and normally incorporates a means ofsteel wire and for quality requirements. adjusting the tension in the guyBS 463, Specification for sockets for steel wire ropes. NOTE The terms ªstayº and ªguyº are interchangeable but in thisBS 643, Specification for white metal ingots for British Standard the word ªguyº has been used throughout.capping steel wire ropes. 3.1.5.2BS 1554, Specification for stainless and wireheat-resisting steel round wire. individual filament of steel, forming the smallestBS 2763, Specification for round carbon steel wire single tension component in a cable, usually circularfor wire ropes. in cross section with a diameter between 3 mm and 8 mm, with a high strength that is usually obtained by cold drawing or cold rolling© BSI 03-2001 1
- 6. BS 8100-3:19993.1.5.3 3.1.5.7spiral strand parallel wire strandassembly of round wires formed helically around a assembly of wires laid side by side in parallel andcentre wire in one or more symmetrical layers either bound tightly together or with the spacesNOTE Each successive layer is wound in alternate directions between the wires held constant by spacer elements[see Figure 1a)].3.1.5.4 3.1.5.8wire rope coreassembly of spiral strands wound helically around a central foundation for the strands, providing supportcentre core, normally in the opposite direction to the and keeping them in their proper positionouter layer of the strands [see Figure 1b)] throughout the life of the rope3.1.5.5 NOTE Fibre cores impregnated with grease are used to provide internal lubrication of moving ropes. However, only steel wirecable cores should be used for mast guys.assembly of one or more strands or ropes of the 3.1.5.9types described in 3.1.5.3 and 3.1.5.4NOTE The strands may be bound in tight contact or kept apart terminationby spacers. [See Figure 1c).] device fixed to the ends of a cable, strand or wire to3.1.5.6 enable the loads to be transferred between it and thelocked coil mast column or the steelwork attached to the guystrand comprising a central core of round wires, foundationspirally bound with layers of shaped wiresNOTE The inner layers of shaped wires are sometimes of atrapezoidal cross section, but more usually all layers are ofZ section wires which overlap and provide a relatively watertightenvelope. Each successive layer is wound in alternate directions.[See Figure 1d).] a) Spiral-strand b) Wire ropes c) Cables d) Locked-coil Figure 1 Ð Typical cable construction2 © BSI 03-2001
- 7. BS 8100-3:19993.2 Symbols 4 Axes of membersFor the purposes of this part of BS 8100 the For the purposes of this part of BS 8100 the axes offollowing symbols apply. members are shown in Figure 2.NOTE They are based on those given in BS 8100-1 and -4 but ithas not been possible to follow those conventions in all cases. 5 Structural configurations, systemA cross-sectional area of the member length and effective slendernessAs cross-sectional area of bolt in shear plane 5.1 General (shank or threaded section as relevant) There are a number of different configurations that (in mm2) are commonly used in lattice towers and masts. EachB leg length of angle, i.e. breadth requires separate consideration. Some popular arrangements are dealt with in 5.2 and 5.3.C length of individual angle between stitch In order to determine the buckling resistance of a bolts lattice member it is necessary first to derive theD bolt, solid round or tube diameter; depth of appropriate geometric length of the member between section intersection points providing restraint, defined as theE modulus of elasticity of steel ªsystemº length. The relevant slenderness ratio basedF leg load on the system length and appropriate radius of gyration is calculated and the effective slendernessj reduction factor determined appropriate to the end conditions of theK effective slenderness factor member (see 5.5). NOTE KL is effective slenderness and Kl is effective 5.2 Leg members slenderness ratio. 5.2.1 Single membersL length Single angles, tubular sections or solid rounds mayLd system length of diagonal member be used for leg sections. The capacity of the leg willLh system length of horizontal member be dependent on the pattern and connections ofN the design buckling resistance of a member bracings used to stabilize the leg. For legs or chordsP1 compressive force in horizontal of K brace with axial compression load braced symmetrically in two normal planes or planes 608 apart, for exampleP2 tensile force in horizontal of K brace in the case of triangular structures, the slendernessQu ultimate resistance of bolt should be determined from the system lengthrvv radius of gyration about axis vv between nodes, i.e. intersections of bracings. Effective slenderness factors are given in Table 2.rxx radius of gyration about axis xx When this bracing is staggered in two normal planesryy radius of gyration about axis yy or planes 608 apart in the case of triangulart thickness of angle leg, thickness of tube wall structures, the system length should be taken as thex distance from centre line of bolt to end of length between nodes on one face. Modified effective member slenderness parameters are given for angle legs iny distance from centre line of bolt to edge of Table 2 to allow for their torsional instability in such member cases. NOTE A maximum effective slenderness ratio of 120 for legz spacing between bolts members is good practice.a imperfection factor 5.2.2 Compound membersb ratio of effective to gross area Compound members for legs may be built up withl slenderness ratio, i.e. system length divided two angles in cruciform section and then taken as by radius of gyration fully composite if welded continuously [see Figure 3a)]. When intermittently connected [seeL relative slenderness (l/l1) Figure 3b)] the possible additional deformations dueLeff effective slenderness (non- dimensional to shear should be taken into account by modifying parameter incorporating K) the slenderness ratio, l, in accordance with thesb specified minimum yield strength of bolt following: steel l2 = l02 + l12sr reference stress of member wherest specified minimum tensile strength of bolt l0 is the slenderness ratio of the full member;sy specified minimum yield strength of steel l1 is the slenderness ratio of one component member angle (C/rvv).su specified minimum tensile strength of steel NOTE It is good practice to have l0 $ l1 and l1 # 50 member A method for determining the size of battens is givenx reduction factor for relevant buckling mode in annex A.© BSI 03-2001 3
- 8. BS 8100-3:1999 t t y y y y u v v u v v u u B B B B x x x x x x x x u t t y u v v y v u u v B y y B Note: See 6.3(a) for value of B for angles connected through one leg only at both ends of the element under consideration y y y t B x x x x x x y y y Note: B is taken as the D D longest length of the individual angle, if unequal angles are used (see 6.3(a) ) Commonly used sections y y y tf tw tf y y t x x x x x x x x x x tw tw tw y y y y y tf tf Other sections Figure 2 Ð Dimensions and axes of sections4 © BSI 03-2001
- 9. BS 8100-3:1999 ,, y ,,, y x ,, ,, x ,, ,,, ,,, x x ,, y y C a) b) Figure 3 Ð Cruciform angle sections5.3 Primary bracing members When the load is not equally split into tension and compression and provided both members are5.3.1 General continuous, the compression members should beTypical primary bracing patterns are shown in checked for the worst compressive load. In addition,Figure 4. it should be checked that the sum of the loadSecondary bracings can be used to subdivide the carrying capacities of both members in compressionprimary bracing or main leg members as shown, for is at least equal to the algebraic sum of the loads inexample, in Figures 4 and 5. the two members. For the calculations of these loadNOTE A maximum effectiveness slenderness ratio of 180 for carrying capacities, the system length is the wholeprimary bracing members is good practice. length Ld and the radius of gyration is that about the rectangular axis parallel to the plane of the bracing.5.3.2 Single lattice The value of the slenderness ratio, l, should beA single lattice is commonly used where the loads taken as one of the following:are light and the length relatively short, as forinstance near the top of towers or in light guyed l = Ld/rxx or l = Ld/ryy for angles;masts [see Figure 4a) and g)]. The slenderness ratio,l, should be taken as: l = Ld/rxx for tubes or solid rounds. l = Ld/rvv for angles; 5.3.3.2 Cross bracing with secondary members l = Ld/rxx for tubes or solid rounds. Where secondary members are inserted [see Figure 4h) and Figure 5a) and b)], they reduce the5.3.3 Cross bracing systems system length of the bracing member on the minimum axis to Ld1. The slenderness ratio, l,5.3.3.1 Cross bracing without secondary members should be taken as:Provided that: a) the load is equally split into tension and l = Ld1/rvv for angles; compression; and l = Ld1/rxx for tubes or solid rounds b) both members are continuous [see Figure 4b)]; (normally not critical). and c) the members are adequately connected where Buckling should also be checked over the system they cross, then the centre of the connection may length Ld2 on the rectangular axis for buckling be considered as a point of restraint both transverse to the bracing and, when the load is not transverse to and in the plane of the bracing and equally split into tension and compression, over the the critical system length becomes length Ld2 on system length Ld for the algebraic sum of the loads the minimum axis. The slenderness ratio, l, should (see 5.3.3.1). be taken as: l = Ld2/rvv for angles; l = Ld2/rxx for tubes. NOTE Where either member is not continuous, the centre of the connection may only be considered as a restraint in the transverse direction if the detailing of the centre connection is such that the effective lateral stiffness of both members is maintained through the connection and the longitudinal axial stiffness is similar in both members.© BSI 03-2001 5
- 10. BS 8100-3:1999 Figure 4 Ð Typical bracing patterns6 © BSI 03-2001
- 11. BS 8100-3:1999 Ld Ld2 Ld1 Ld2 Ld3 Ld Ld4 Ld1 Corner stay (of limited effect if both braces are in compression) a) b) Ld3 Ld3 Lh Ld2 Ld4 Ld1 Fully triangulated hip bracing c) Figure 5 Ð Use of secondary bracing systems [See also patterns g) to k) in Figure 4]© BSI 03-2001 7
- 12. BS 8100-3:19995.3.3.3 Discontinuous cross bracing with Buckling over system length Ld2 of the face bracingcontinuous horizontal at centre intersection on the rectangular axis should also be checked ifThe diagonal members should be designed in secondary bracing, but no hip bracing, has beenaccordance with 5.3.3.2. The horizontal member provided. Thus the slenderness ratio, l, should beshould be sufficiently stiff in the transverse direction taken as:to provide restraints for the load cases where thecompression in one member exceeds the tension in l = Ld2/rxx or Ld2/ryy as appropriate, for allthe other or both members are in compression [see sections.Figure 4d) and k)]. This criterion will be satisfied byensuring that the horizontal member without plan Where triangulated hip bracing has been provided,bracing withstands (as a strut over its full length Lh then the appropriate length between such hipon the rectangular axis) the algebraic sum of the members Ld4 should be used for checking bucklingload in the two members of the cross brace resolved transverse to the face bracing on the appropriatein the horizontal direction. rectangular axis. Thus the slenderness ratio, l,NOTE A maximum effective slenderness ratio for the horizontal should be taken as:of 180 is good practice (as a strut over its full length on therectangular axis). l = Ld4/rxx or Ld4/ryy for all sections.5.3.3.4 Cross bracing with diagonal corner stays 5.3.4.2 Horizontal members with plan bracingIn some patterns of cross bracing a corner stay is Where the length of the horizontal edge membersinserted to reduce the system length transverse to becomes large, it is normal to subdivide them as partthe plane of bracing [see Figure 5b)]. A similar of the plan bracing which provides a convenientprocedure to that used for 5.3.3.1 may be used to basis to do this. (See 5.3.5.)determine whether the members are adequate withthis restraint. The system length of the horizontal members is taken between intersection points in the plan bracingIn this case five buckling checks should be carried for buckling transverse to the face of the structure,out, related to the appropriate system length: and between supports in plane for buckling in the a) buckling of member against the maximum load plane of the frame. over Ld1 on the minimum axis; Care is needed in the choice of the vv or rectangular b) buckling of member against the maximum load axes for single angle members. The vv axis should over Ld2 on the transverse rectangular axis; be used unless suitable restraint by bracing is c) buckling of two members in cross brace against provided in one plane at or about the mid-point of the algebraic sum of loads in cross brace over Ld3 the system length. In this case buckling should be on the transverse axis; checked about the vv axis over the intermediate d) buckling of two members (one in each of two length and about the appropriate rectangular axis adjacent faces) against the algebraic sum of the over the full length between restraints on that axis. loads in the two members connected by the 5.3.4.3 Horizontal members without plan bracing diagonal corner brace over Ld4 on the transverse For small widths of towers and for masts, plan axis; bracing may sometimes be omitted. [See also 5.5.1d) e) buckling of four members (each member of for reduction factor K1.] cross brace in two adjacent faces) against the The rectangular radius of gyration should be used algebraic sum of loads in all four members over Ld for buckling transverse to the frame over system on the transverse axis. length Lh (see Figure 7). In addition for single angle5.3.4 K bracing systems [see Figure 4c), j) and 5c)] members, the radius of gyration about the vv axis should be used over Lh2 [see Figure 7a)] unless5.3.4.1 Diagonal members restraint by secondary bracing at intervals along theThe critical system length without secondary length is provided in which case the system length ismembers is Ld2 on the minimum axis and the Lh1 [see Figure 7b)]. However, buckling about theslenderness ratio, l, should be taken as: rectangular axis will be critical except in the case of an unequal angle. l = Ld2/rvv for angles; Additional allowance should be made for the l = Ld2/rxx for tubes and solid rounds. bending stresses induced in the edge members by loads transverse to the frame, e.g. wind which canIf secondary members are used then the system produce significant point loads.length is Ld1 on the minimum axis, and theslenderness ratio, l, should be taken as: l = Ld1/rvv8 © BSI 03-2001
- 13. BS 8100-3:1999 If both ways, ties may be used Triangulated Not fully triangulated (not recommended for design unless careful attention is given to bending effects) Figure 6 Ð Typical plan bracing Lh Lh L h2 L h1 a) b) Figure 7 Ð K bracing horizontals without plan bracing© BSI 03-2001 9
- 14. BS 8100-3:19995.3.4.4 Cranked K bracing Where the plan is not fully triangulated, additionalFor large tower widths, a crank or bend may be allowance should be made for the bending stressesintroduced into the main diagonals (see Figure 8). induced in the edge members by loads, e.g. wind,This has the effect of reducing the length and size of transverse to the frame whereby the main diagonalthe redundant members but produces high stresses can impose a point load arising from the summationin the members meeting at the bend and necessitates of the distributed loading on the various facefully triangulated transverse support at the joint. members.Diagonals and horizontals should be designed as Attention should be given to vertical bending due tofor K bracing, with the system lengths for diagonals the self weight of plan bracing. Support from hipbased on their lengths to the knee joint. bracing can be used to reduce long spans. The design should be detailed to eliminate any face slope5.3.4.5 Portal frame effect which promotes downward displacement ofA horizontal member is sometimes introduced at the inner plan brace members.bend to turn the panel into a portal frame (seeFigure 9). The main disadvantage of this is the lack 5.3.6 Multiple lattice bracingof articulation present in the K brace. This system is Multiple lattice bracing members should be designedsensitive to foundation settlement or movement and under the applied load on the minimum system Ld1special consideration should be given to this for the slenderness ratio l = Ld1/rvv. The anglepossibility. bracing members of a multiple lattice configurationThis example also shows special secondary bracing should be checked on a system length from leg towhich is less sensitive to loads resulting from such leg with the appropriate radius of gyration rxx or ryymovement. [see Figure 4e)] such that the overall effective slenderness ratio is limited to 350. For the stability of the panel rxx/rvv should be greater than 1.50, where rxx is the radius of gyration about the axis parallel to the plane of the lattice. 5.3.7 Tie systems Great care is needed with the use of tie systems particularly if used on large masts or towers, on masts or towers with sloping legs or in conjunction with secondary members. Each diagonal member of a pair of cross bracing members [see Figure 4f)] Figure 8 Ð Cranked K bracing should be capable of carrying the full bracing shear load in tension. Detailing to give an initial tension within the bracing and to provide mutual support at the central cross will be required to minimize deflection. It will also be necessary to pay special attention to possible fatigue problems. The horizontal members should be designed as horizontal strut members with or without plan bracing as appropriate for compression along their whole length. NOTE 1 Tension systems are very sensitive to methods of erection and to modification or relative movements. Special attention should be paid to possible excessive deflections and fatigue. To ensure their effectiveness measures should be taken to Figure 9 Ð Portal frame ensure that these matters are carefully considered. NOTE 2 A maximum effective slenderness ratio of 350 for tension members is good practice.5.3.5 Plan bracingPlan bracings are required at bend lines of the leg, toprovide lateral restraint to long horizontal membersand to distribute local loads from ancillaries, etc.Plan bracing is also required to maintain the shapeof square towers, particularly where K bracing isused, and to distribute eccentric loads. Thenon-triangulated systems shown in Figure 6 do notsatisfy the first requirement.10 © BSI 03-2001
- 15. BS 8100-3:19995.3.8 Compound members a) Values of this percentage of the leg load for5.3.8.1 Double angles various values of the slenderness of the leg shouldCompound members consisting of a pair of identical be taken from Table 1. The slenderness ratio to beangles back to back (forming a T), separated by a used should be that of the restrained member,small distance and connected at intervals by spacers which will normally be L/rvv, where L is the lengthand stitch bolts, may be used for bracing. They between nodes and rvv is the minimum radius ofshould be checked for buckling about both gyration.rectangular axes as follows. (See also 5.5.1.) The effect of applying this force in the plane of the a) For buckling about the xx axis (see Figure 2) bracing at each node in turn should be calculated. the two angles should be assumed to act b) When there is more than one intermediate node compositely for the purpose of calculating stiffness in a panel then the secondary bracing systems and radius of gyration. should be checked separately for 2.5 % of the leg b) For buckling about the yy axis (see Figure 2) load shared equally between all the intermediate the additional deformation due to shear should be node points. These loads should be assumed to act taken into account by modifying the slenderness together and in the same direction, i.e. at right ratio, l, in accordance with the following: angles to the leg and in the plane of the bracing system. l2 = l02 +l12 taking a maximum value of In both cases a) and b) the distribution of forces l1 = 0.75l0 within the triangulated secondary bracing panel where should then be determined by stress diagrams or linear elastic analysis. l0 is the slenderness ratio of the full compound member; Table 1 Ð Applied force as percentage of leg l1 is the slenderness ratio of one component load, F angle (l1 = C/rvv). Slenderness ratio, l Applied force (percentage of leg load, F)In order to keep the effect of this interaction to a %minimum, the spacing between stitch bolts should be 0 to 40 1.02limited to give a maximum value l1 of 90. 45 1.15When only stitch bolts and packs are used,composite section properties should be based on 50 1.28either: 55 1.42 1) the actual space between the individual angle 60 1.52 members, or 65 1.60 2) a space taken as 1.5 times the thickness of one 70 1.65 of the angle members, 75 1.70whichever is the smaller. If batten plates are used, 80 1.75composite section properties may always be used 85 1.80based on the actual space between the individual 90 1.85angle members. 95 1.925.3.8.2 Other compound members 100 2.00For other compound member configurations and the 105 2.08sizing of battens and stitch bolts or welds, refer 110 2.16to 5.2.2. 115 2.235.4 Secondary members 120 2.30Typical secondary bracing arrangements are shown 125 2.38in Figures 4 to 9. 130 2.46NOTE A maximum effective slenderness ratio of 240 for >132 2.50secondary bracing members is good practice. The use of highslenderness can lead to the possibility of individual members NOTE 1 The tabulated values assume minimum axis restraint ofvibrating, and can make them vulnerable to damage due to the leg by two such forces each in the plane of the bracing.bending from local loads. Where the critical direction is in the plane of the bracingIn order to design secondary members it is necessary (e.g. round or cruciform sections) the values should be multiplied by a factor of √2.to apply a hypothetical force acting transverse to theleg member (or other chord if not a leg) being NOTE 2 These loads are not additive to the existing forces on the tower or mast. If the main member is eccentrically loaded orstabilized at the node point of the attachment of the the angle between the main diagonal of a K brace and the leg issecondary member. This force varies with the less than 258 then this figure may be unsafe and a more refinedslenderness of the leg member being stabilized and is value should be obtained by taking into account the eccentricityexpressed as a percentage of the leg load, F for moment and secondary stresses arising from leg deformation.which the following two checks should be carried NOTE 3 In general if the bracing strength requirements are met,out. the stiffness requirements should be sufficient.© BSI 03-2001 11
- 16. BS 8100-3:1999 5.5 Calculation of effective slenderness Leff c) Compound bracing members buckling 5.5.1 General about the yy axis of the compound member In order to calculate the design buckling resistance of the member, the effective slenderness Leff should K is taken as 1.0. be determined. d) Horizontal bracing members in K The effective slenderness Leff should be derived bracing without plan bracing from: Horizontal members of K bracing without Leff = KL plan bracing (see 5.3.4.3) usually have compression in one half of their length where and tension in the other. In such cases the L is the relative slenderness of the member effective slenderness factor K of the about the appropriate axis for which the horizontal normal to the plane of the strength is required and is given by: frame, determined from Table 3 ignoring continuity, should be multiplied by the L = l/l1 factor K1 given in Table 4, depending on where the ratio of tension load P2 to the l is the slenderness ratio obtained compression load P1. from 5.3; E 0.5| l1 = p sr 2750.5| = 85.8 when E = 205 000 Mpa sr | sr is a reference stress given in 6.3; K is an effective slenderness factor depending on the structural configurations and is given as follows. a) Leg members K is given in Table 2. b) All bracing members except where c) and d) below are applicable K is dependent on both the bracing pattern (see Figures 4 and 5) and the connections of the bracing to the legs. K is dependent on the relative stiffness of the adjoining members, of the bolt or weld group and of the connecting gusset plate if relevant. Values of K for typical configurations are given in Table 3. For welded connections in particular, the factors depend on continuity of the weld all round the joined member(s). 12 © BSI 03-2001
- 17. BS 8100-3:1999 Table 2 Ð Effective slenderness factor K for leg members© BSI 03-2001 13
- 18. BS 8100-3:1999 Table 3 Ð Effective slenderness factor K for bracing members14 © BSI 03-2001
- 19. BS 8100-3:1999 Table 4 Ð Factor K1 for horizontal of K brace For hot rolled steel members with the types of (without plan bracing) cross-section commonly used for compression members, the relevant buckling mode is general Ratio P2/P1 Factor K1 ªflexuralº buckling. 0.00 0.73 In some cases the ªtorsionalº or ªflexural-torsionalº 0.20 0.67 modes may govern. For information on the design buckling resistance of compression members for 0.40 0.62 those sections not covered in this part of BS 8100, 0.60 0.57 reference may be made to BS 5950-5. 0.80 0.53 6.2 Reduction factor x 1.00 0.50 For constant axial compression in members of constant cross-section, the value of x for the appropriate effective slenderness Leff, should be6 Calculation of design strength for determined from:members in compression 1 x= 2 2 L 2]0.56.1 General f + [f effThe design buckling resistance, N, of a compression wheremember should be taken as: N = jxAsr/gm f is 0.5 [1 + a (Leff 2 0.2) + Leff2];where a is an imperfection factor; Leff is obtained from 5.5.1. j is 0.8 for single angle members connected by one bolt at each end, 0.9 for single angle and where members connected by one bolt at one end x#1 and continuous at the other end and 1.0 in all other cases; The imperfection factor a corresponding to the appropriate buckling curve should be obtained from A is the cross-sectional area of the member; Table 5. x is the reduction factor for the relevant buckling mode, given in 6.2; Table 5 Ð Imperfection factors sr is a reference stress given in 6.3; Buckling curve Imperfection factor a gm is the partial factor on strength, as given in a 0.21 BS 8100-1 and -4, appropriate to the quality b 0.34 class of the structure, subject to the following. c 0.49 a)For untested structures: d 0.76 gm is 1.1 for Class A structures; Values of the reduction factor x for the appropriate gm is 1.2 for Class B structures; effective slenderness Leff may be obtained from Table 6. gm varies from about 1.3 to 1.45 for Class C structures depending on the 6.3 Calculation of reference stress performance requirements. The reference stress sr required to derive the ultimate stress of a member depends on the b)For angle section towers which have slenderness of the section. Most hot rolled sections successfully been subjected to fullscale are at least semi-compact. Values of m and the tests under the equivalent factored loading limiting B/t and D/t ratios are given below, together or where similar configurations have been with formulae for the reference stress sr which is type tested: used in place of the yield stress sy for the design of slender sections. gm is 1.0 for Class A structures; a) Hot rolled angle sections gm is 1.1 for Class B structures; gm varies from about 1.2 to 1.35 for sr = sy if B/t # m Class C structures depending on the sr = sy(2 2 B/mt) if m < B/t < 1.33m performance requirements. sr = π2E/(5.1B/t)2 if B/t $ 1.33m© BSI 03-2001 15
- 20. BS 8100-3:1999 Table 6 Ð Reduction factors x Leff Buckling curve a b c d0.2 1.0000 1.0000 1.0000 1.00000.3 0.9775 0.9641 0.9491 0.92350.4 0.9528 0.9261 0.8973 0.85040.5 0.9243 0.8842 0.8430 0.77930.6 0.8900 0.8371 0.7854 0.71000.7 0.8477 0.7837 0.7247 0.64310.8 0.7957 0.7245 0.6622 0.57970.9 0.7339 0.6612 0.5998 0.52081.0 0.6656 0.5970 0.5399 0.46711.1 0.5960 0.5352 0.4842 0.41891.2 0.5300 0.4781 0.4338 0.37621.3 0.4703 0.4269 0.3888 0.33851.4 0.4179 0.3817 0.3492 0.30551.5 0.3724 0.3422 0.3145 0.27661.6 0.3332 0.3079 0.2842 0.25121.7 0.2994 0.2781 0.2577 0.22891.8 0.2702 0.2521 0.2345 0.20931.9 0.2449 0.2294 0,2141 0.19202.0 0.2229 0.2095 0,1962 0.17662.1 0.2036 0,1920 0,1803 0,16302.2 0.1867 0.1765 0.1662 0.15082.3 0.1717 0.1628 0.1537 0.13992.4 0.1585 0.1506 0.1425 0.13022.5 0.1467 0.1397 0.1325 0.12142.6 0.1362 0.1299 0.1234 0.11342.7 0.1267 0.1211 0.1153 0.10622.8 0.1182 0.1132 0.1079 0.09972.9 0.1105 0.1060 0.1012 0.09373.0 0.1036 0.0994 0.0951 0.0882 where b) Hot rolled tubular sections sy is the specified minimum yield stress of sr = sy if D/t # m material of member; E if D/t > m sr = 0.10 B is the leg length of the angle. For unequal D/t angles and compound angles, B is the longer length, except for single angles connected by where bolts or welding through one leg only at both ends of the element under consideration for sy is the specified minimum yield stress of which B should be taken as the length of the material of member; connected leg; D is the diameter of tubular section; t is the thickness of angle leg; t is the wall thickness of tubular section; E √ m is 0.10 ; E m is 0.567 ; sy sy E is the modulus of elasticity. E is the modulus of elasticity.16 © BSI 03-2001
- 21. BS 8100-3:1999 c) Cold formed angle sections 8 Bolted connections sr = sy if B/T # m 8.1 Angle bolted connections 5 2 2 B/mt if m < B/t < 1.5m Bolted connections should be designed in sr = sy accordance with BS 5950-1 but with the 3 3 modifications that the design resistance of a bolt Qu, sr = π2E/(5.1 B/t)2 if B/t $ 1.5m should be the least of the following (see Figure 10). In 8.1a) to 8.1f) the partial factor on strength gm for where both tested and untested structures should be taken as given in 6.1a) for untested structures (i.e. no sy is the specified minimum yield stress of advantage can be taken for structures which have material of member after forming; been tested). B is the leg length of the angle as defined a) Design shear resistance in 6.3a). For ultimate loads this is related to the minimum t is the thickness of angle leg; tensile strength st or the yield strength of the bolt √ E steel sb and the relevant cross-sectional area As: m is 0.503 ; sy Qu = 0.65stAs/gm or 0.95sbAs/gm whichever is E is the modulus of elasticity. the lesser. b) Design bearing resistance d) Cold formed tubular sections The design bearing resistance is normally related to the acceptable amount of deformation in the sr = sy if D/t # m hole and whilst values up to three times yield can E if D/t > m be used without failure, it is recommended that sr = 0.10 the stress is limited to twice the yield strength of D/t the member steel, sy, to reduce the deformation to where acceptable limits, i.e: Qu = 2.0Dtsy/gm sy is the specified minimum yield stress of c) Design tensile resistance material of member; When prying is ignored: D is the diameter of tubular section; Qu = 0.56stAs/gm but not greater than 0.8sbAs/gm t is the wall thickness of tubular section; When prying is taken into account in accordance m is 0.10 ; E with Table 8: sy Qu = 0.7stAs/gm but not greater than sbAs/gm E is the modulus of elasticity. d) End distance of bolt x6.4 Selection of buckling curves Qu = 1.33 sy xt/gm for x > 1.5DFor flexural buckling the appropriate buckling Qu = 2.0 sy (x 2 D/2) t/gm for x # 1.5Dcurves should be determined from Table 7. e) Centres of bolts for multiple bolt connections7 Calculation of resistance of members Qu = sy (z 2 D/2) t/gmin tension f) Edge distance of boltThe resistance of a member in tension is the product Qu = 2.67 sy (y 2 D/2) t/gmof the yield strength and the net sectional area. NOTE 1 To utilize a design bearing resistance of 2.0 Dtsy requires x $ 1.5D and y $ 1.25D and z $ 2.5D. This is after allowance hasThe net sectional area of an angle connected through been made for fabrication tolerances in sizes.one leg should be taken as the net area of the NOTE 2 The design bearing resistance given in b) above may alsoconnected leg, i.e. gross area minus holes, plus half be used when the thread is in bearing.the area of the unconnected leg.The net sectional area of an angle suitably connectedthrough both legs should be taken as the sum of thenet areas of both legs, i.e. gross area minus holes.© BSI 03-2001 17
- 22. BS 8100-3:1999 Table 7 Ð Selection of buckling curve for a cross-section Buckling Buckling Cross section Limits about axis curve Angle sections hot rolled any b cold rolled any c - using fyb (See NOTE 1) cold formed any c - using fya (See NOTE 1) Commonly used sections ,, C, T, and solid sections any c Hollow sections hot rolled any a cold rolled any b - using fyb (See NOTE 1) cold formed any c - using fya (See NOTE 1) Rolled I sections x-x a D/B ≤ 1.2: y-y b tf t f ≤ 40 mm y x-x b 40 mm < t f ≤ 100 mm y-y c x x Other sections D D/B ≤ 1.2: b y x-x B t f ≤ 100 mm y-y c t f > 100 mm x-x d y-y d NOTE 1 fyb is the basic yield of the material before cold forming ; fya is the average yield stress of the material after cold forming as calculated using BS 5950-518 © BSI 03-2001
- 23. BS 8100-3:1999 D = bolt diameter x z t y Figure 10 Ð Location of bolts Table 8 Ð Relationships between flange, tube and bolts Ratio of flange to tube wall thickness b for Blank flanges 2.0 1.9 1.8 1.7 1.6 1.5 Ring flanges 3.0 2.8 2.6 2.4 2.2 2.0 Ratio of tensile design strength Increase in direct tension to allow for prying in the flange required to maximum tensile bolts (bolts prying factor) capacity of tubea 1.0 1.2 Do not use in 0.9 1.1 1.2 shaded zone 0.8 1.0 1.1 1.2 0.7 1.0 1.0 1.1 1.2 0.6 1.0 1.0 1.0 1.1 1.2 0.5 1.0 1.0 1.0 1.0 1.1 1.2 a The relationship between flange thickness ratio and bolt prying factor is a function of the extent to which the tube is loaded in tension. In permissible stress terms this is ft /pt or Fγ m /Aσy in accordance with this part of BS 8100. b Where different grades of steel are used in the tube and flange, the minimum ratio of flange to tube wall thickness should be varied in accordance with the ratio of the square root of their respective yields, within the range shown in the table.8.2 Tubular and solid round bolted a) The relationships between flange thicknessconnections expressed as a ratio of tube wall thickness, boltWhere connections are formed with gusset plates prying factor, and extent to which the tube isand bolts in shear, the rules in 8.1 should be used. loaded in tension are shown in Table 8.Details which are not covered in 8.1 should be For the required tube design tensile strengthdesigned in accordance with BS 5950-1. expressed as a proportion of its maximum tensileWhere round flange joints are used on tubular capacity, the combination of bolt prying factormembers, the following design recommendations along the line in the table, and flange thicknessshould be followed. ratio above this value should be provided as a minimum.© BSI 03-2001 19

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