Overall stability of multi-span portal sheds at right-angles to the portal spans

Transcription

1 Overall stability of multi-span portal seds at rigt-angles to te portal spans SCI s Senior Manager for Standards, Carles M King, explains te approac for design of long-span portal seds. 1. Introduction As portal seds become wider and longer, te overall stability of te buildings at rigt-angles to te span of te main portals becomes increasingly sensitive. Tis article considers te issue and describes approaces for design for stability in tis direction. Figure 1 sows te mode of deformation considered. One issue tat made te 2000 revision of BS necessary was te need for rules to ensure te in-plane stability of portal frames. Te metods available to ensure Figure 1: Sway at rigt-angles to te span of te stability of te buildings at rigtangles to te main portal frames te main portals. were not so clearly defined. 2. Stability systems Every building must ave a structural system tat provides stability. In BS 59501:2000 clause 5.5 Portal frames, clause states explicitly tat frames sould be stabilised against sway out-of-plane and refers to clause Te common structural arrangements are: Vertical bracing in te walls and in all of te planes of te valleys. Tis system gives te simplest metod of resisting sway. Vertical bracing in te walls + plan bracing in te roof (wind bracing) Vertical bracing in te walls + portal frames in te plane of te valleys Tere will be plan bracing in te roof to resist wind on te gable ends and to stabilise te portal rafters but it is used only in item 2 above to provide stability in te plane of te valley. 2.1 Vertical bracing in walls and te planes of te valleys Figure 2 sows a sed wit vertical bracing to provide stability in te walls and in te plane of te valley. 2.2 Vertical bracing in walls plus plan bracing in te roof Figure 3 sows a sed wit vertical bracing to provide stability in te walls but no vertical bracing in te plane of te valley. Stability in te plane of te valley is provided by te plan bracing in te roof connected to te vertical bracing in te walls. Te plan bracing is commonly formed as a truss in wic te cords are te rafters of one portal and te member along te top of te gable wall. It is often found tat were te truss dept is only one bay, as sown in Figure 3, te truss is very flexible and may be insufficient to stabilise te valley columns. Te dept of te plan bracing may need to be increased to two (or more) bays of te frame as sown in Figure 4. Tis plan bracing migt develop major additional axial forces in te members forming te cords. It is possible tat te member along te top of te gable wall will need rater more demanding detailing tan is commonly provided to avoid aving many connections tat migt allow a significant accumulation of slip. Figure 2: Vertical bracing in te walls and in te planes of te valleys (plan bracing omitted for clarity). Figure 3: Vertical bracing in walls plus plan bracing in te roof. Figure 4: Plan bracing in te roof wit 2 bay dept. 28 NSC May 2007

2 2.3 Vertical bracing in walls + portals in te plane of te valleys Portals, often called wind-portals, are used in te plane of te valley if diagonal bracing interferes wit te use of te sed. Tis is sown in Figure Requirements of te stability system Te frames may ave a valley column at every portal, or may be it and miss or it-miss-miss frames. Figure 6 sows a section troug a typical sed sowing te axial load F v in te valley column wic includes te vertical reaction from any miss frames in te structure. Figure 7 sows te sway mode tat te stability system is designed to resist. Important features of te stability system are: 1 Te stability system as to stabilise all of te columns 2 Stability systems often ave relatively low sway stiffness, especially in seds tat are large and ig. Te consequences of tese two features are discussed below. 3.1 Te stability system as to stabilise all of te columns Te stability system as to stabilise te total vertical load in te building, wic is te sum of all te axial compression in all of te columns. Terefore, te design loads on te system in Load Combination 1 include te notional orizontal forces from all te columns tat are stabilised by te system, including any office areas or oter structures stabilised by te main sed. In oter combinations, usually tere are wind loads. Tere may also be orizontal forces from cranes and/or orizontal impact forces. To calculate te internal forces and moments in te stability system, te analysis must be made wit te columns supporting te total factored design load including te axial load from te analysis of te main portal frames as sown in Figures 6 and 7. Oterwise, te second-order effects in te plane of te system caused by tese vertical loads will not be calculated. 3.2 Some stability systems ave relatively low sway stiffness Te forces resisted by te stability system are generally small, so te members are small, resulting in a relatively low stiffness. Because of te low sway stiffness, te designer sould expect to account for second-order effects in te plane of te valley frame. Often te design of te main portal frames also as to allow for second-order effects. It is important tat were second-order effects arise, tey are fully accounted for. Tis is required by BS 59501:2000 clause , Sway stiffness, to wic designers are referred by clause Terefore, if tere are secondorder effects in two directions, te effects in bot directions must be considered. Large buildings will often ave large tonnages of steel in te stability systems. For tese frames, it is probable tat te most economical structures will be obtained by using second-order analysis software. Indeed, te stability systems will often be so flexible tat tey will be below te limit of for wic BS allows simplified metods to be used. BS does not define a minimum Figure 5: Vertical bracing in walls + portals in te plane of te valleys (plan bracing omitted for clarity). Figure 6: Section sowing vertical load, F v, in valley column. Figure 7: Valley frame sway mode sowing column loads F v. 30 NSC May 2007

3 value of for second-order analysis, but it is recommended tat designers sould be cautious were < 4 and tat frames sould not ave < 2. Tis is because any connection slip or flexibility reduces below te value sown by frame design software, as also does any plasticity (especially in moment resisting frames), and te frame will collapse at = 1 unless tere is someting else to old it up. If second-order software is not available, te designer needs to coose anoter way to allow for any second-order effects. Guidance on te use of te simplified metods in BS is given below. 4. Modelling and design To understand te stability of a building, it needs to be considered initially as a 3D structure, even if it is modelled as several 2D frames. If tere is more tan one stability system, te orizontal loads sould be sared between te systems in proportion to te sway stiffness of eac system. Te most common example of tis is were tere is vertical bracing at bot ends of a line of columns. If te bracing is te same at eac end, only alf of te columns are stabilised by eac bracing. It migt be simplest to model te entire line of columns and all te bracing. 4.1 Vertical bracing in te walls and in eac plane of valley-columns Te frame can be modelled as separate 2D frames in wic te total vertical load in te plane of te frame must be stabilised by te bracing in tat plane. 4.2 Vertical bracing and plan bracing Were valley columns depend on plan bracing for stability, te flexibility of te complete system of vertical bracing plus plan bracing must be included in te calculation. If te vertical and orizontal bracing are analysed as separate models, te lateral deflection of te vertical bracing must be added to te lateral deflection of te plan bracing. 4.3 Portals in eac plane of te valley columns As in te case of vertical bracing in eac valley plane, te structure may be modelled in 2D provided tat te advice above about calculating secondorder effects in te plane of te valley frame is followed (ie including all te loads in all te columns wen calculating te internal forces and moments to allow for te destabilising effects). It is recommended tat te main portal frames are analysed witout te valley portals because in te normal orientation, sown in Figure 8, te valley portal leg as insignificant effect on te stiffness of te main portal valley column in te plane of te main portal. Were te main portal valley column and te valley portal leg are welded togeter, tey will act as a compound member. In te plane of te valley portal, tis as a significant effect on te column stiffness wic may be wort calculating to obtain te maximum column stiffness. Because many large seds are very ig, base stiffness is often very elpful in providing stability to te frame. Guidance on base stiffness is given in BS 59501:2000 clause Plastic design is not recommended for tese stability frames because 1 in frames supporting major loads on te valley beam, suc as miss frames, tere is commonly significant sway after formation of te first plastic inge 2 extensive plasticity reduces te sway stiffness 3 special care is needed to avoid forming inges at te beam-column connections, wic do not ave adequate ductility. Figure 8: Valley column and valley portal leg. NSC May

4 Figure 9: Elevation of sway mode sowing vertical bracing. 5 Simplified metods to allow for second-order effects 5.1 Vertical bracing in te walls and in eac plane of valley-columns Te stability can be cecked using BS 59501:2000 clause as if eac 2D frame is an ordinary braced frame. Figure 9 sows an elevation of te bracing system. In te figure, SNHF denotes te sum of te Notional Horizontal Forces from te columns in tat plane tat are stabilised by te bracing system sown. Te figure also sows te deflection, δ, at te top of te columns arising from te Notional Horizontal Forces. Te procedure is as follows: 1 Calculate te total notional orizontal force from te total vertical load in te plane of te bracing 2 Apply te total notional orizontal force to te bracing in te plane 3 Calculate as BS 59501:2000 clause If is less tan 4.0, te metod sould not be used. 4 If < 10, calculate k amp as BS 59501:2000 clause and amplify te orizontal forces applied to te bracing. Te calculation may be done independently for eac 5.2 Vertical bracing and plan bracing Were valley columns depend on plan bracing for stability, te flexibility of te complete system of vertical bracing plus plan bracing must be included in te calculation. Figure 10 sows a perspective view of te bracing system in te sway mode. Figure 11 sows a plan view and Figure 12 sows an elevation. In tese figures, ΣNHF denotes te sum of te Notional Horizontal Forces from te columns in tat plane tat are stabilised by te bracing system sown. Te figures also sow te deflections arising from te Notional Horizontal Forces δ V is te deflection at te top of te vertical bracing δ P is te maximum plan bracing deflection at te top of any column δ (= δ V + δ P ) is te maximum total deflection at te top of any column. If a 3D model is used, δ is found directly. Te procedure is as follows: Figure 12: Elevation of sway mode at valley columns. 1 Calculate te total notional orizontal forces in eac plane of columns from te total vertical loads in eac plane of columns (0.5% of te sum of te column loads). 2 Apply te total notional orizontal force in eac plane to te bracing system at eac plane. 3 Calculate as BS 59501:2000 clause using δ (= δ V + δ P ). If is less tan 4.0, te metod sould not be used. 4 If < 10, calculate kamp as BS 59501:2000 clause and amplify te orizontal forces applied to te bracing. Te calculation may be done independently for eac 5.3 Portals in eac plane of te valley columns Figure 13 sows a section troug te sed sowing te elevation of te valley frame and a potential sway failure in te plane of te valley columns Figure 13: Valley frame sway mode sowing column loads F v. Valley portals are single storey frames wit moment resisting joints, for wic BS clause requires tat reference is made to clause 5.5. Tis gives metods of calculating te resistance of frames. In addition to second-order analysis in clause , tere are two simplified metods in wic second-order effects are allowed for by te additional load factor λ r being greater tan 1.0 for frames in wic tese effects are significant. Tese are: 1 te Sway-ceck metod 2 te Amplified moments metod Figure 10: Perspective view of sway mode. Figure 11: Plan view of sway mode sowing plan bracing Te Sway-ceck metod Te Sway-ceck metod is in clause Wen applying tis metod, only te i /1000 approac sould be used and te L b /D formula approac sould not be used because it cannot allow for te loads on all te valley columns. Te notional orizontal forces applied sould be calculated from te total load on all te valley columns stabilised by te portal. Tis ensures tat te destabilising effects of all te column loads ave been included in te calculation. 32 NSC May 2007

5 Te procedure is as follows: 1 Ceck tat te geometry of te portal is witin te limits of clause Tis is true for most common valley portals. 2 Calculate te total notional orizontal force from te total vertical load in te plane of te portal 3 Apply te total notional orizontal force to te portal 4 Calculate te deflections δ i and ceck tat δ i i /1000. If tis condition is not fulfilled te metod sould not be used. 5 Ceck te frame for te gravity load case (= gravity loads plus Notional Horizontal Forces) 6 Calculate λ sc and λ r as and ceck te portal for te orizontal load case (= gravity loads + orizontal loads, eg wind) Te Amplified Moments metod Te Amplified Moments metod is in clause In applying tis metod, te calculation of must be made using a model tat includes te vertical loads on all te valley columns stabilised by te portal. Tis metod requires tat te value of includes te effect of any axial load in te valley beam. Tis will be very small if tere is a valley column in eac portal frame, but it migt be significant in it & miss frames or it-miss-miss frames. Tis is because te vertical loads applied by te miss frames produce a orizontal sear at te bases and tus an axial force in te valley beam. If software is not available to calculate, ten it may be calculated using te formula: λcr δ were 200δ is as defined in BS 59501:2000 clause is te axial compression at ULS in te valley beam in te relevant load case is te valley beam Euler buckling load in te plane of te portal in wic L is taken as te span of te valley portal and I is I x if te web of te beam is vertical. Te procedure is as follows: 1 Calculate te total notional orizontal force from te total vertical load in te plane of te portal 2 Apply te total notional orizontal force to te portal in te plane 3 Calculate λcr δ. If < 4.6, te metod sould not be used. 4 Calculate λ r as BS 59501:2000 clause If using elastic design of te portal, follow clause wic requires tat te output forces from te analysis are multiplied by λ r. (Note tat te same result is acieved by multiplying all te applied forces by λ r, wic migt be more convenient as a design procedure.) Te calculation may be done independently for eac 6 Effective lengt of valley columns Valley columns potentially fall into two categories: 1 Columns stabilised by an independent structural system 2 Columns forming te stabilising system 6.1 Columns stabilised by an independent structural system Columns tat are stabilised by an independent bracing system may be designed as non-sway, as clause Tis means tat non-sway effective lengts may be used for tese columns even if for te stabilising structure is less tan 10. It is recommended tat an effective lengt of 1.0 is taken 6.2 Columns forming te stabilising system Were te stabilising system is a truss system as sown in Figures 10, 11, 12 and 13, te effective lengts are tose appropriate to normal truss design. Were te stabilising system is a portal system wic is cecked using te metods in BS :2000 clause 5.5, tere is no requirement to consider te in-plane stability of te individual members forming te portal because tese metods allow for te in-plane buckling effects troug te factor λ r. Only out-of-plane member stability need be cecked. 7 Compound columns in valley portals Te compound section created by welding te valley portal leg to te valley column of te main portal as ig gross inertia in te plane of te valley frame, but it is susceptible to torsionalflexural buckling wic is not covered by BS :2000. To avoid te complications of design for torsional-flexural buckling, it is simplest to observe te common practice of considering te main portal and te valley portal as independent frames for te strengt calculations. If te designer cooses to calculate te strengt of te compound section, guidance on torsional and torsional-flexural buckling is available in references 1 and 2 below. It is important to remember tat te load from te main portal is not concentric wit te centroid of te compound section. References 1 Design of cruciform sections using BS 59501:2000, New Steel Construction, Vol 14, No 4, April Design of mono-symmetric and asymmetric sections in compression using BS 59501:2000 New Steel Construction, Vol 14, No 6, June NSC May 2007