CEN/TC 250/SC 3 N 2634

Transcription

1 CEN/TC 50/SC N 64 CEN/TC 50/SC Euroode - Design o steel strutures o Seretar: susan.kempa@din.de Seretariat: DIN EN First Drat Date o doument Expeted ation Comment Due Date Bakground Dear Member Please ind attahed the First Drat o the revision o EN or ommenting. Please ensure that ou rite an omments into the CEN omments template and orard them to our NSB or submission via the CIB ballot. The CIB ballot ill lose on 9th June 08. We kindl ask or giving omments onl to the obviousl hanged parts and not to the original doument text. Kind regards Susan Kempa Seretar CEN/TC 50/SC

2 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM pren 99--5: Year Da Month Year UDC Desriptors: English version Euroode : Design o steel strutures Part -5 : Plated strutural elements Calul des strutures en aier Bemessung und Konstruktion von Stahlbauten Partie.5 : Teil.5 : Plaques planes Plattenbeulen CEN European Committee or Standardisation Comité Européen de Normalisation Europäishes Komitee ür Normung Central Seretariat: rue de Stassart 6 B-050 Brussels 006 Copright reserved to all CEN members Re. No. EN : 006. E

3 EN 99--5: 00 (E) Content Page. Terms 5. Smbols 5 4. General 7 4. Eetive idth models or global analsis 7 4. Plate bukling eets on uniorm members Redued stress method Non-uniorm members Members ith orrugated ebs 9 5. General 0 5. Elasti shear lag 0 5. Shear lag at the ultimate limit state 6. General 5 6. Resistane to diret stresses 5 6. Eetive ross-setion Plate elements ithout longitudinal stieners Stiened plate elements ith longitudinal stieners Interation beteen plate and olumn bukling Veriiation 6 7. Basis 7 7. Design resistane 7 7. Contribution rom the eb Contribution rom langes Veriiation 0 8. Basis 8. Design resistane 8. Length o sti bearing 8.4 Redution ator F or eetive length or resistane 8.5 Eetive loaded length 8.6 Veriiation 9. Interation beteen shear ore bending moment and axial ore 4 9. Interation beteen transverse ore bending moment and axial ore 4 9. Interation beteen transverse ore bending moment and shear ore 5. General 6. Diret stresses 7. Shear 4.4 Transverse loads 4. General 45. Ultimate limit state 45

4 pren 99--5: 08 (E) Foreord This European Standard EN Euroode : Design o steel strutures Part.5: Plated strutural elements has been prepared b Tehnial Committee CEN/TC50 «Strutural Euroodes» the Seretariat o hih is held b BSI. CEN/TC50 is responsible or all Strutural Euroodes. This European Standard shall be given the status o a National Standard either b publiation o an idential text or b endorsement at the latest b April 007 and onliting National Standards shall be ithdran at latest b Marh 00. This Euroode supersedes ENV Aording to the CEN-CENELEC Internal Regulations the National Standard Organizations o the olloing ountries are bound to implement this European Standard: Austria Belgium Cprus Czeh Republi Denmark Estonia Finland Frane German Greee Hungar Ieland Ireland Ital Latvia Lithuania Luxembourg Malta Netherlands Nora Poland Portugal Romania Slovakia Slovenia Spain Seden Sitzerland and United Kingdom. National annex or EN This standard gives alternative proedures values and reommendations ith notes indiating here national hoies ma have to be made. The National Standard implementing EN should have a National Annex ontaining all Nationall Determined Parameters to be used or the design o steel strutures to be onstruted in the relevant ountr. National hoie is alloed in EN through: 6.(6) 7.() 8.4()..(9) () (5)

5 EN 99--5: 00 (E) Introdution Sope () EN gives design requirements o stiened and unstiened plates hih are subjet to in-plane ores. () Eets due to shear lag in-plane load introdution and plate bukling or I-setion girders and box girders are overed. Also overed are plated strutural omponents subjet to in-plane loads as in tanks and silos. The eets o out-o-plane loading are outside the sope o this doument. NOTE : The rules in this part omplement the rules or lass and 4 setions see EN NOTE : For the design o slender plates hih are subjet to repeated diret stress and/or shear and also atigue due to out-o-plane bending o plate elements ( breathing ) see EN 99- and EN NOTE : For the eets o out-o-plane loading and or the ombination o in-plane eets and out-oplane loading eets see EN 99- and EN () Single plate elements ma be onsidered as lat here the urvature radius r in the diretion perpendiular to the ompression satisies: b r (.) t here b is the panel idth t is the plate thikness Figure.: Deinition o plate urvature Normative reerenes The olloing douments in hole or in part are normativel reerened in this doument and are indispensable or its appliation. For dated reerenes onl the edition ited applies. For undated reerenes the latest edition o the reerened doument (inluding an amendments) applies. EN 99-- Euroode : Design o steel strutures: Part -: General rules and rules or buildings EN 99-- Euroode : Design o steel strutures: Part -: General rules - Supplementar rules or old-ormed members and sheeting EN Euroode : Design o steel strutures: Part -8: Design o joints EN Euroode : Design o steel strutures: Part -4: Design b inite element analsis 4

6 pren 99--5: 08 (E) Terms and deinitions For the purpose o this standard the olloing terms and deinitions appl:. Terms Elasti ritial stress Stress in a omponent at hih the omponent beomes unstable hen using small deletion elasti theor o a peret struture Membrane stress Stress at mid-plane o the plate Gross ross-setion Total ross-setional area o a member but exluding disontinuous longitudinal stieners Eetive ross-setion and eetive idth Gross ross-setion or idth redued or the eets o plate bukling or shear lag or both; To distinguish beteen their eets the ord eetive is lariied as ollos: eetive p denotes eets o plate bukling eetive s denotes eets o shear lag eetive denotes eets o plate bukling and shear lag Plated struture Struture built up rom nominall lat plates hih are onneted together; the plates ma be stiened or unstiened Stiener Plate or setion attahed to a plate to resist bukling or to strengthen the plate; a stiener is denoted: longitudinal i its diretion is parallel to the member; transverse i its diretion is perpendiular to the member. Stiened plate Plate ith transverse or longitudinal stieners or both Subpanel Unstiened plate portion surrounded b langes and/or stieners Hbrid girder ggrder ith langes and eb made o dierent steel grades; this standard assumes higher steel grade in langes ompared to ebs Sign onvention Unless otherise stated ompression is taken as positive. Smbols () In addition to those given in EN 990 and EN 99-- the olloing smbols are used: A sl total gross ross-setional area o all the longitudinal stieners o a stiened plate ithout ontributing plating; A st gross ross-setional area o one transverse stiener; A e eetive ross-setional area; eetive p ross-setional area; A e 5

7 EN 99--5: 00 (E) A elo eetive p ross-setional area or loal bukling; a length o a stiened or unstiened plate; b idth o a stiened or unstiened plate; b b e F h lear idth beteen elds or elded setions or beteen ends o radii or rolled setions; eetive s idth or elasti shear lag; design transverse ore; lear eb depth beteen langes; L e eetive length or resistane to transverse ores see 8; M.Rd M pl.rd M N t V W e β design plasti moment o resistane o the ross-setion onsisting o the eetive area o the langes onl; design plasti moment o resistane o the ross-setion (irrespetive o ross-setion lass); design bending moment; design axial ore; thikness o the plate; design shear ore inluding shear rom torque; eetive elasti setion modulus; eetive s idth ator or elasti shear lag; () Additional smbols are deined here the irst our. 6

8 pren 99--5: 08 (E) 4 Basis o design and modelling 4. General () The eets o shear lag and plate bukling shall be taken into aount at the ultimate servieabilit or atigue limit states. NOTE: Partial ators M0 and M used in this part are deined or dierent appliations in the National Annexes o EN 99- to EN Eetive idth models or global analsis () The eets o shear lag and o plate bukling on the stiness o members and joints shall be taken into aount in the global analsis. () The eets o shear lag o langes in global analsis ma be taken into aount b the use o an eetive s idth. For simpliit this eetive s idth ma be assumed to be uniorm over the length o the span. () For eah span o a member the eetive s idth o langes should be taken as the lesser o the ull idth and L/8 per side o the eb here L is the span or tie the distane rom the support to the end o a antilever. (4) The eets o plate bukling in elasti global analsis ma be taken into aount b eetive p ross-setional areas o the elements in ompression see 6.. (5) For global analsis the eet o plate bukling on the stiness ma be ignored hen the eetive p ross-setional area o an element in ompression is larger than ρ lim = 05 times the gross ross-setional area o the same element. The riterion applies or all individual plates o the rosssetion. (6) For the alulation o eetive areas or stiness the servieabilit limit state slenderness λ p ser ma be alulated rom: s om ser λ p ser = λ p (4.) here s omser is deined as the maximum ompressive stress (alulated on the basis o the eetive ross-setion) in the relevant element under loads at servieabilit limit state. (7) The seond moment o area ma be alulated b an interpolation o the gross ross-setion and the eetive ross-setion or the relevant load ombination using the ormula: s gr I e = I gr ( I gr I e ( s om ser ) (4.) s om ser here I gr is the seond moment o area o the gross ross-setion s gr is the maximum bending stress at servieabilit limit states based on the gross rosssetion I e(s omser) is the seond moment o area o the eetive ross-setion ith alloane or loal bukling aording to 6.4.(6) alulated or the maximum stress s omser s gr ithin the span length onsidered. (8) The eetive seond moment o area I e ma be taken as variable along the span aording to the most severe loations. Alternativel a uniorm value ma be used based on the maximum absolute sagging moment under servieabilit loading. 7

9 EN 99--5: 00 (E) (9) The alulations desribed in (6) and (7) require iterations but as a onservative approximation the ma be arried out as a single alulation at a stress level equal to or higher than s omser. 4. Plate bukling eets on uniorm members () Eetive p idth models or diret stresses resistane models or shear bukling and bukling due to transverse loads as ell as interations beteen these models or determining the resistane o uniorm members at the ultimate limit state ma be used hen the olloing onditions appl: panels are retangular and langes are parallel; the diameter o an unstiened open hole or ut out does not exeed 005b here b is the idth o the panel. NOTE: The rules ma appl to non-retangular panels provided the angle α (see Figure 4.) is not greater than 0 degrees. I α exeeds 0 the panel ma be assessed assuming it to be retangular based on the larger o b and b. α b b a Figure 4.: Deinition o angle α () For the alulation o stresses at the servieabilit and atigue limit state the eetive s area ma be used i the ondition in 4.(5) is ulilled. For ultimate limit states the eetive area aording to 5. should be used ith β replaed b β ult. 4.4 Redued stress method () As an alternative to the use o the eetive p idth models or stress states given in setions 6 to 9 the ross-setions ma be assumed to be lass setions provided that the stresses in eah panel do not exeed the limits speiied in setion. NOTE: The redued stress method is analogous to the eetive p idth method (see 4.) or single plated elements. Hoever in veriing the stress limitations no load shedding has been assumed beteen the plated elements o the ross-setion. 4.5 Non-uniorm members () Non-uniorm members (e.g. haunhed members non-retangular panels) or members ith regular or irregular large openings ma be analsed using Finite Element (FE) methods. NOTE : See Annex B or non-uniorm members. NOTE : For FE-alulations see EN

10 pren 99--5: 08 (E) 4.6 Members ith orrugated ebs () For members ith orrugated ebs the bending stiness should be based on the langes onl and ebs should be onsidered to transer shear and transverse loads. For the design o girders ith orrugated ebs see setion. 9

11 EN 99--5: 00 (E) 5 Shear lag in member design 5. General () Shear lag in langes ma be negleted i b 0 < L e/50 here b 0 is taken as the lange outstand or hal the idth o an internal element and L e is the length beteen points o zero bending moment see 5..(). () Where the above limit or b 0 is exeeded the eets due to shear lag in langes should be onsidered at servieabilit and atigue limit state veriiations b the use o an eetive s idth aording to 5.. and a stress distribution aording to 5... For the ultimate limit state veriiation an eetive area aording to 5. ma be used. () Stresses due to path loading in the eb applied at the lange level should be determined rom Elasti shear lag 5.. Eetive s idth () The eetive s idth b e or shear lag under elasti onditions should be determined rom: b e = β b 0 (5.) here the eetive s ator β is given in Table 5.. This eetive s idth ma be relevant or servieabilit and atigue limit states. () Provided adjaent spans do not dier more than 50% and an antilever span is not larger than hal the adjaent span the eetive lengths L e ma be determined rom Figure 5.. For all other ases L e should be taken as the distane beteen adjaent points o zero bending moment. β : L = 0 5 (L + L ) e β : L = L e β : L =0 85L e β : L =0 7 0 L e L L L L / 4 L / L /4 L /4 L / L /4 β β β β β β 0 Figure 5.: Eetive length Le or ontinuous beam and distribution o eetive s idth 0

12 pren 99--5: 08 (E) b e b e C L b 0 0 b 4 or lange outstand or internal lange plate thikness t 4 stieners ith A l s = A s l i Figure 5.: Notations or shear lag Table 5.: Eetive s idth ator β κ Veriiation β value κ 00 β = 0 00 < κ 070 > 070 sagging bending β = β = + 64 κ hogging bending β = β = + 60 κ + 6 κ 500 κ sagging bending β β 59 κ hogging bending β = β = 86 κ all κ end support β 0 = ( / κ) β but β 0 < β all κ Cantilever β = β at support and at the end A s l κ = α 0 b 0 / L e ith α 0 = + b0t in hih A sl is the area o all longitudinal stieners ithin the idth b 0 and other smbols are as deined in Figure 5. and Figure 5..

13 EN 99--5: 00 (E) 5.. Stress distribution due to shear lag () The distribution o longitudinal stresses aross the lange plate due to shear lag should be obtained rom Figure 5.. b = bb e b = bb 0 e 0 () () b b = 5 bb b b > 00 : = 5 ( b 00) ( ) = + ( ) ( / b ) 4 0 b 00 : = 0 ( ) = ( / b ) 4 s is alulated ith the eetive s idth o the lange b e Figure 5.: Distribution o stresses due to shear lag 5.. In-plane load eets () The elasti stress distribution in a stiened or unstiened plate due to the loal introdution o in-plane ores (path loads) see Figure 5.4 should be determined rom: F s z = (5.) be ( t + ast) ith: b e = s e z + se n 0878 a n = t s = s + t e s st here a st t z s e s st is the gross ross-setional area o the diretl loaded stieners per unit length o the eb ithin the length s e. This ma be taken as the area o a stiener smeared over the length o the spaing s st; is the eb thikness; is the distane to lange; is the length o the sti bearing; is the spaing o stieners.

14 pren 99--5: 08 (E) The ormula (5.) is valid hen s st/s e 05; otherise the ontribution o stieners should be negleted. stiener; simpliied stress distribution; atual stress distribution Figure 5.4: In-plane load introdution The above stress distribution ma also be used or the atigue veriiation. 5. Shear lag at the ultimate limit state 5.. Shear lag onsideration () At the ultimate limit state shear lag eets ma be determined b one o the olloing methods: a) elasti shear lag eets as determined or servieabilit and atigue limit states (see 5..) b) elasti-plasti shear lag eets alloing or limited plasti strains. () Elasti shear lag eet does not onsider the elastoplasti stress redistribution and its appliation at the ultimate limit state is a onservative approah. () Elasti-plasti shear lag eets alloing or limited plasti strains ma be taken into aount using β κ β. here β and κ are taken rom Table 5.. (4) The expressions in () and () ma also be applied or langes in tension in hih ase the onsidered ross-setional area should be replaed b the gross area o the tension lange. 5.. Interation beteen shear lag and plate bukling () The ombined eets o plate bukling and shear lag ma be taken into aount b using A e as given b: A = β (5.) e A e ult here A e β ult is the eetive p area o the ompression lange due to plate bukling (see 6.4 and 6.5); is the eetive s idth ator or the eet o elasti shear lag at the ultimate limit state hih ma be taken as β determined rom Table 5. ith α 0 replaed b

15 EN 99--5: 00 (E) A * e α 0 = (5.4) b t 0 t is the lange thikness. () In the ase o using elasti-plasti shear lag eets A e ma be deined b: A e = A β (5.5) e β κ ult A e ult 4

16 pren 99--5: 08 (E) 6 Plate bukling eets due to diret stresses at the ultimate limit state 6. General () This setion gives rules to aount or plate bukling eets rom diret stresses at the ultimate limit state hen the olloing riteria are met: a) The panels are retangular and langes are parallel or nearl parallel (see 4.); b) Stieners i an are provided in the longitudinal or transverse diretion or both; ) Open holes and ut outs are small (see 4.); d) Members are o uniorm ross-setion; e) No lange indued eb bukling ours. NOTE : For ompression lange bukling in the plane o the eb see setion 0. NOTE : For stieners and detailing o plated members subjet to plate bukling see setion. 6. Resistane to diret stresses () The resistane o plated members ma be determined using the eetive p areas o plate elements in ompression or lass 4 setions using ross-setional data (A e I e W e) or rosssetional veriiations and member veriiations or olumn bukling and lateral torsional bukling aording to EN () Eetive p areas should be determined on the basis o the linear strain distributions ith the attainment o ield strain in the mid plane o the ompression plate. 6. Eetive ross-setion () In alulating longitudinal stresses aount should be taken o the ombined eet o shear lag and plate bukling using the eetive areas given in 5.. () The eetive ross-setional properties o members should be based on the eetive areas o the ompression elements and on the eetive s area o the tension elements due to shear lag. () The eetive area A e should be determined assuming that the ross-setion is subjet onl to stresses due to uniorm axial ompression. For non-smmetrial ross-setions the possible shit e N o the entroid o the eetive area A e relative to the entre o gravit o the gross ross-setion see Figure 6. gives an additional moment hih should be taken into aount in the ross-setion veriiation using 6.7. (4) The eetive setion modulus W e should be determined assuming the ross-setion is subjet onl to bending stresses see Figure 6.. For biaxial bending eetive setion moduli should be determined about both main axes. (5) As an alternative to 6.() and (4) a single eetive setion ma be determined rom N and M ating simultaneousl. The eets o e N should be taken into aount as in 6.(). This requires an iterative proedure. (6) The stress in a lange should be alulated using the elasti setion modulus ith reerene to the mid- plane o the lange. (7) Hbrid girders ma have lange material ith ield strength up to φ h provided that: 5

17 EN 99--5: 00 (E) a) the inrease o lange stresses aused b ielding o the eb is taken into aount b limiting the stresses in the eb to ; b) is used in determining the eetive area o the eb. NOTE: The National Annex ma spei the value φ h. A value o φ h = 0 is reommended. (8) The inrease o deormations and o stresses at servieabilit and atigue limit states ma be ignored or hbrid girders ompling ith 6.(7) inluding the NOTE. (9) For hbrid girders ompling ith 6.(7) the stress range limit in EN ma be taken as 5. G entroid o the gross rosssetion G entroid o the eetive G e N ross-setion G G entroidal axis o the gross ross-setion entroidal axis o the Gross ross-setion Eetive ross-setion eetive ross-setion non eetive zone Figure 6.: Class 4 ross-setions - axial ore G G G entroid o the gross rosssetion G entroid o the eetive ross-setion entroidal axis o the gross G G ross-setion entroidal axis o the eetive ross-setion Gross ross-setion Eetive ross-setion non eetive zone Figure 6.: Class 4 ross-setions - bending moment 6.4 Plate elements ithout longitudinal stieners 6.4. Plate bukling behaviour () The eetive p areas o lat ompression elements should be obtained using Table 6. or internal elements and Table 6. or outstand elements. The eetive p area o the ompression zone o a plate ith the gross ross-setional area A should be obtained rom: A e = ρ A (6.) here ρ is the redution ator or plate bukling. () The redution ator ρ ma be taken as ollos: internal ompression elements: 6

18 pren 99--5: 08 (E) ρ = 0 or λ p ψ ( + ψ ) λ p 0055 ρ = 0 or λ p > ψ (6.) λ p outstand ompression elements: ρ = 0 or λ p here λ p 088 ρ = 0 or λ p > (6.) λ p λ p = r p b / t = 84 ε k ψ is the stress ratio determined in aordane ith 6.4.(4) and 6.4.(5) b is the appropriate idth to be taken as ollos (or deinitions see Table 7. o EN 99--) b or ebs; b or internal lange elements (exept RHS); b - t or langes o RHS; or outstand langes; h or equal-leg angles; h or unequal-leg angles; k is the bukling ator orresponding to the stress ratio ψ all edges are being assumed to be pinned or ree. For long plates k is given in Table 6. or Table 6. as appropriate; t is the thikness; rp is the elasti ritial plate bukling stress see ormula (A.) in Annex A.() and Table 6. and Table 6.; ε = 5 / [ N mm ] () For lange elements o I-setions and box girders the stress ratio ψ used in Table 6. and Table 6. should be based on the properties o the gross ross-setional area due alloane being made or shear lag in the langes i relevant. For eb elements the stress ratio ψ used in Table 6. should be obtained using a stress distribution based on the eetive area o the ompression lange and the gross area o the eb. I the stress distribution results rom dierent stages o onstrution (as e.g. in a omposite bridge) the stresses rom the various stages ma irst be alulated ith a ross-setion onsisting o eetive langes and gross eb and these stresses are added together. This resulting stress distribution determines an eetive eb setion that an be used or all stages to alulate the inal stress distribution or stress analsis. (4) Exept as given in 6.4.(7) the plate slenderness λ p o an element ma be replaed b: om λ p red = λ p (6.4) / M 0 7

19 EN 99--5: 00 (E) here om is the maximum design ompressive stress in the element determined using the eetive p area o the setion aused b all simultaneous ations. NOTE: The above proedure is onservative and requires an iterative alulation in hih the stress ratio ψ (see Table 6. and Table 6.) is determined at eah step rom the stresses alulated on the eetive p ross-setion deined at the end o the previous step. Table 6.: Internal ompression elements Stress distribution (ompression positive) ψ = : b e = ρ b Eetive p idth b e b e = 05 b e > ψ 0: b e = 05 b e b e = ρ b b e = b e b e = b e - b e 5 ψ ψ < 0: b e = ρ b = ρ b / (-ψ) b e = 04 b e b e = 06 b e ψ = / > ψ > > ψ > > ψ - Bukling ator k 40 8 / (05 + ψ) ψ + 978ψ ( - ψ) When ψ < - k ma be alulated b onsidering ψ = -. Table 6.: Outstand ompression elements Stress distribution (ompression positive) > ψ 0: b e = ρ Eetive p idth b e ψ < 0: b e = ρ b = ρ / (-ψ) ψ = / 0 - ψ - Bukling ator k ψ + 007ψ > ψ 0: b e = ρ 8

20 pren 99--5: 08 (E) ψ < 0: b e = ρ b = ρ / (-ψ) ψ = / > ψ > > ψ > - - Bukling ator k / (ψ + 04) ψ + 7ψ 8 (5) As an alternative to the method given in 6.4.() the olloing ormulae ma be applied to determine eetive areas at stress levels loer than the ield strength: a) or internal ompression elements: ρ = or λ p < 0 67 (6.5) 0055 r = λ ( + ψ) pred / λ pred λp λ + 08 λ 06 p pred but ρ or λ p 067 (6.6) b) or outstand ompression elements: ρ = or λ p < 0748 (6.7) 088/ λ r = λ pred pred λp λ + 08 λ 06 p pred but ρ λ or p 0748 For notations see 6.4.() and 6.4.(5). For alulation o resistane to global bukling 6.4.(7) applies. I the value o deining λ pred om /( / M0 ) the value 0 ma be used. or s omser / (6.8) is smaller than 0 in the ormula (6) For outstand elements the method given in EN 99-- Annex D or alulating the eetive area A e ma be used as an alternative. (7) For the veriiation o the design bukling resistane o a lass 4 member using or 8..4 o EN 99-- either the plate slenderness λ p or λ p red ith om based on seond order analsis ith global imperetions should be used Column bukling behaviour () The elasti ritial olumn bukling stress r o a plate should be taken as the bukling stress ith the supports along the longitudinal edges removed. () For aspet ratios a/b < a olumn tpe o bukling an our and the hek should be perormed aording to 6.6 using the redution ator ρ. NOTE: This applies e.g. or lat elements beteen transverse stieners here plate bukling an be olumn-like and require a redution ator ρ lose to as or olumn bukling see Figure 6. a) and b). 9

21 EN 99--5: 00 (E) a) olumn behaviour o plates b) olumn behaviour o an unstiened ithout longitudinal supports plate ith a small aspet ratio α Figure 6.: Column bukling behaviour () For an unstiened plate the elasti ritial olumn bukling stress s r ma be obtained rom π E t r = (6.9) ν a ( ) (4) The relative olumn slenderness λ or unstiened plates is deined as ollos: λ = (6.0) r (5) The redution ator χ or use in 6.6. should be obtained rom 8... o EN For unstiened plates α = 0 orresponding to bukling urve a should be used. 6.5 Stiened plate elements ith longitudinal stieners 6.5. General () For plates ith longitudinal stieners the eetive p areas rom loal bukling o the various subpanels beteen the stieners and the eetive p areas rom the global bukling o the stiened panel should be aounted or. () The eetive p setion area o eah subpanel should be determined b a redution ator in aordane ith 6.4 to aount or loal plate bukling. The stiened plate ith eetive p setion areas or the stieners should be heked or global plate bukling (b modelling it as an equivalent orthotropi plate) and a redution ator ρ should be determined or overall plate bukling. () The eetive p area o the ompression zone o the stiened plate should be taken as: A e = ρ A e lo + bedge e t (6.) here A elo is the eetive p setion area o all the stieners and subpanels that are ull or partiall in the ompression zone exept the eetive parts supported b an adjaent plate element ith the idth b edgee see example in Figure

22 pren 99--5: 08 (E) Figure 6.4: Stiened plate under uniorm ompression NOTE: For non-uniorm ompression see Figure A.. (4) The area A elo should be obtained rom: A here = As l e + ρlo b lo t (6.) e lo applies to the part o the stiened panel idth that is in ompression exept the parts b edgee see Figure 6.4; A sle is the sum o the eetive p setions aording to 6.4 o all longitudinal stieners ith gross area A sl loated in the ompression zone; b lo is the idth o the ompressed part o eah subpanel; is the redution ator rom 6.4.() or eah subpanel. ρ lo (5) Stiened plates having eak longitudinal stieners should be onsidered as unstiened plates regarding their resistane to diret stresses and their eetive p area should be alulated aording to 6.4. Longitudinal stieners should be onsidered as eak stieners i the relative bending stiness o eah stiener sl is less than 5 here sl is deined b: E I sl sl = (6.) b D here E b is the Young s modulus is the idth o the plate D is the bending stiness o the plate deined b t ν I sl is the eb thikness is the Poisson s oeiient E t D = ν ( ) is the seond moment o area o the stiener or out-o-plane bending its ross-setion inluding a partiipating idth o eb o 0 t eah side o eah stiener-to-eb juntion. (6) The redution o the ompressed area A elo through ρ ma be taken as a uniorm redution aross the hole ross-setion.

23 EN 99--5: 00 (E) (7) I shear lag is relevant (see 5.) the eetive ross-setional area A e o the ompression zone * o the stiened plate should then be taken as A e aounting not onl or loal plate bukling eets but also or shear lag eets. (8) The eetive ross-setional area o the tension zone o the stiened plate should be taken as the gross area o the tension zone redued or shear lag i relevant see 5.. (9) The eetive setion modulus W e should be taken as the seond moment o area o the eetive ross-setion divided b the distane rom its entroid to the mid depth o the lange plate Plate bukling behaviour () The relative plate slenderness λ p o the equivalent plate is deined as: β A λ p = (6.4) r p ith β A = A e lo A here A is the gross area o the ompression zone o the stiened plate exept the parts o subpanels supported b an adjaent plate see Figure 6.4 (to be multiplied b the shear lag ator i shear lag is relevant see 5.); A elo is the eetive area o the same part o the plate (inluding shear lag eet i relevant) ith due alloane made or possible plate bukling o subpanels and/or stieners. rp is the elasti ritial plate bukling stress alulated ithout onsideration o the torsional stiness o losed setion stieners. NOTE: For alulation o s rp see Annex A. () The redution ator ρ or the equivalent orthotropi plate is obtained rom 6.4.() provided λ p is alulated rom ormula (6.4) Column bukling behaviour () The elasti ritial olumn bukling stress r o a stiened plate should be taken as the bukling stress ith the supports along the longitudinal edges removed. () For a stiened plate s r ma be determined rom the elasti ritial olumn bukling stress s rsl o the stiener losest to the panel edge ith the highest ompressive stress as ollos: π E I sl s r sl = (6.5) A a sl here I sl is the seond moment o area o the gross ross-setion o the stiener and the adjaent parts o the plate relative to the out-o-plane bending o the plate; sl A is the gross ross-setional area o the stiener and the adjaent parts o the plate aording to Figure A..

24 pren 99--5: 08 (E) b r ma be obtained rom s r = s r sl here s r is related to the ompressed edge o the bs l plate and b sl and b are geometri values rom the stress distribution used or the extrapolation see Figure A.. () The relative olumn slenderness λ is deined as ollos: β A λ = (6.6) r ith As l e β A = ; A sl A sl is deined in 6.5.(); A s e l is the eetive ross-setional area o the stiener and the adjaent parts o the plate ith due alloane or plate bukling see Figure A.. (4) The redution ator χ should be obtained rom o EN For stiened plates the value o α should be inreased aording to: 009 α e = α + (6.7) i / e ith i = I sl A sl e = max (e e ) is the largest distane rom the respetive entroids o the plating and the onesided stiener (or o the entroids o either set o stieners hen present on both sides) to the neutral axis o the eetive olumn see Figure 6.5; α = 04 (urve b) or losed setion stieners; = 049 (urve ) or open setion stieners. One-sided stiener Smmetrial double-sided stieners Non smmetrial double sided stieners Figure 6.5: Interpretation o e and e values.

25 EN 99--5: 00 (E) 6.6 Interation beteen plate and olumn bukling 6.6. General () Interpolation should be arried out beteen the redution ator ρ or plate bukling and the redution ator χ or olumn bukling to determine the inal redution ator ρ. Interpolation has to be made or stiened and unstiened plates separatel i relevant. ( ρ ) ξ ( ξ ) ρ = + (6.8) r p here ξ = but 0 ξ r s rp is the elasti ritial plate bukling stress see 6.4. or Annex A; s r is the elasti ritial olumn bukling stress aording to 6.4.() and 6.5.() respetivel or unstiened and stiened plates; is the redution ator due to olumn bukling aording to 6.4.(5) and 6.5.(4) respetivel or unstiened and stiened plates; ρ is the redution ator due to plate bukling aording to 6.4. and 6.5.() respetivel or unstiened and stiened plates. () As an alternative or longitudinall stiened plates the eighting ator ξ ma be obtained diretl rom one o the ormulae given in 6.6.() and 6.6.(4). () For orthotropi plates ith at least three stieners the eighting ator ξ ma be obtained rom bsl + δ ξ = ks pα or ψ (6.9) b and ξ = ( α ) + or ψ = α 05 05< α 4 (6.0) but 0 ξ NOTE: All parameters k sp α b sl b δ and ψ are speiied in Annex A. and Figure A.. (4) For orthotropi plates ith one or to stieners the eighting ator ξ ma be obtained rom bsl Aslt ξ = ks pα b Isl( ν ) (6.) here k sp is the bukling oeiient hih ma be taken rom relevant omputer simulations or aording to Annex A.. 4 a bt ξ = 4 π ( ν ) bbisl 4 or a a (6.) NOTE : All parameters k sp α a a b b b t ν A sl and I sl are speiied in Annex A. and A.. The geometrial values b sl and b are speiied in Figure A.. NOTE : For the ase ith to stieners in the ompression zone ξ should be alulated or the three ases given Annex A..() and the loest value is taken as relevant. 4

26 6.6. Alternative simpliied methods or longitudinall stiened panels in bending pren 99--5: 08 (E) () I the olumn bukling aording to the riterion in 6.6.() is prevented or the stiener losest to the panel edge ith the highest ompressive stress the redution ator or overall plate bukling ould be ompletel negleted (ρ =). This rule is appliable onl i the longitudinal stiener should have a minimum relative lexural stiness equal to 5 (see Setion 6.5.(5)). () The olumn bukling o the most ompressive stiener ma be heked as ollos: s sl (6.) M here sl is the average design stress in the onsidered longitudinal stiener alulated ith its eetive ross-setional area A sle as deined in 6.5.(). The design stress distribution over the hole stiened panel omes rom an elasti global analsis using the eetive ross-setion o the panel A elo (inluding shear lag eet and seond order analsis i relevant) and the panel edge ith the highest ompressive stress is assumed to have reahed the ield strength. See Figure 6.7. NOTE : As simpliiation the average design stress sl an be onsidered as being onstant over the ross-setional area A sle and equal to the design stress value in the mid-plane o the stiener alone see Figure Figure 6.6: Mid-plane o the stiener alone NOTE : In ase o pure ompression Formula (6.) an never be ulilled and the redution ator or overall plate bukling should be alulated. In this ase the alternative simpliied method rom 6.6. should not be applied. () χ is obtained as in 6.5.(4) onsidering the imperetion ator α e and the relative olumn slenderness l sl is deined as ollos: As l e l sl = (6.4) A s sl r sl ith A sl and A sl e as deined in 6.5.(4) rsl as deined in Eq. (6.5) NOTE: The restraining eet rom the plate is negleted and the ititious olumn is onsidered to be ree to bukle out o the plane o the stiened plate. (4) I the riterion in 6.6.() is not satisied the redution ator ρ or overall plate bukling should be taken into aount hen alulating A e aording to 6.5.(4). 5

27 EN 99--5: 00 (E) Figure 6.7: Stresses at the stieners 6.7 Veriiation () Member veriiation or ompression and uniaxial bending should be perormed as ollos: N M + N en η = + 0 (6.5) Ae We M 0 M 0 here A e is the eetive ross-setion area in aordane ith 6.(); e N is the shit in the position o entroids see 6.(); M is the design bending moment; N is the design axial ore; W e is the eetive elasti setion modulus see 6.(4); M0 is the partial ator see appliation parts EN 99- to 6. For members subjet to ompression and biaxial bending the above ormula (6.5) ma be modiied as ollos: N M + N e N M z + N e z N η = (6.6) Ae W e Wz e M 0 M 0 M 0 M M z are the design bending moments ith respet to and z z axes respetivel; e N e zn are the eentriities ith respet to the entroids. () Ation eets M and N should inlude global seond order eets here relevant. () The plate bukling veriiation o the panel should be arried out or the stress resultants at a distane 04a or 05b hihever is the smallest rom the panel end here the stresses are the greater. In this ase the gross setional resistane needs to be heked at the end o the panel. 6

28 pren 99--5: 08 (E) 7 Resistane to shear 7. Basis () This setion gives rules or shear resistane o plates onsidering shear bukling at the ultimate limit state here the olloing riteria are met: a) the panels are retangular ithin the angle limit stated in 4.; b) stieners i an are provided in the longitudinal or transverse diretion or both; ) all holes and ut outs are small (see 4.); d) members are o uniorm ross-setion; e) or veriiation o end panels end posts are provided. NOTE: For end panels ithout end posts see 8.() tpe (). () Plates ith h /t greater than 7 ε or an unstiened eb or ε k or a stiened eb should τ η η be heked or resistane to shear bukling and should be provided ith transverse stieners at the supports here 5 ε =. N / mm [ ] NOTE : h : see Figure 7. ; k τ : see 7.(). NOTE : The National Annex ma deine η. The value η = 0 is reommended or steel grades up to and inluding S460. For higher steel grades η = 00 is reommended. 7. Design resistane () For unstiened or stiened ebs the design resistane or shear should be taken as: h h t Vb Rd = Vb Rd + Vb Rd (7.) M in hih the ontribution rom the eb is given b: χ h t Vb Rd = (7.) M and the ontribution rom the langes V brd is aording to 7.4. () Stieners should ompl ith the requirements given in. and elds should ulil the requirement given in..5. b t e A e t h Cross-setion notations a) No end post (see 8.) b) Rigid end post ) Non-rigid end post a 7

29 EN 99--5: 00 (E) Figure 7.: End supports 7. Contribution rom the eb () For ebs ith transverse stieners at supports onl and or ebs ith either intermediate transverse stieners or longitudinal stieners or both the ator or the ontribution o the eb to the shear bukling resistane should be obtained rom Table 7. or Figure 7.. The ator χ aording to Table 7. is onl valid or slendernesses λ determined or plates ith hinged boundar onditions. Table 7.: Contribution rom the eb χ to shear bukling resistane End panels ith non-rigid end post All the other ases (intermediate panels and end panels ith rigid end post) λ < 08 /η η η 0 8 / η λ < / λ 0 8 / λ λ 08 8 / λ 7 / 07 + λ NOTE: See 8..6 in EN () Figure 7. shos various end supports or girders: a) No end post see 8. () tpe ); b) Rigid end posts see..; ) Non rigid end posts see... 0 ( ) For ebs stiened b losed-setion longitudinal stieners onneted to the end posts and vertial stieners the end posts ma alas be onsidered as rigid. () The modiied slenderness λ in Table 7. and Figure 7. should be taken as: λ = 0 76 (7.) τ r hereτ r = k (7.4) τ E NOTE : Values or E and k τ ma be taken rom Annex A. NOTE : The modiied slenderness a) transverse stieners at supports onl: λ h λ ma be taken as ollos: = (7.5) 864 t ε b) transverse stieners at supports and intermediate transverse or longitudinal stieners or both: λ h 74 τ ε = (7.6) k τ in hih k τ is the minimum shear bukling oeiient or the eb panel. 8

30 pren 99--5: 08 (E) NOTE : Where non-rigid transverse stieners are also used in addition to rigid transverse stieners k τ is taken as the minimum o the values rom the eb panels beteen an to transverse stieners (e.g. a h and a h ) and that beteen to rigid stieners ontaining non-rigid transverse stieners (e.g. a 4 h ) see Figure 7.. NOTE 4: Rigid boundaries ma be assumed or panels bordered b langes and rigid transverse stieners. The eb bukling analsis an then be based on the panels beteen to adjaent transverse stieners (e.g. a h in Figure 7.). NOTE 5: For non-rigid transverse stieners the minimum value k τ ma be obtained rom the bukling analsis o the olloing:. a ombination o to adjaent eb panels ith one lexible transverse stiener. a ombination o three adjaent eb panels ith to lexible transverse stieners. For proedure to determine k τ see Annex A.. (4) The seond moment o area o an open-setion longitudinal stiener should be redued to / o its atual value hen alulating k τ. Formulae or k τ taking this redution into aount in A. ma be used. Π Non-rigid end post all the other ases (rigid end posts intermediate stieners) Range o reommended η Figure 7.: Shear bukling ator χ (5) For ebs ith longitudinal stieners the modiied slenderness λ in () should not be taken as less than hi λ 74 t ε k (7.7) ti here h i and k τi reer to the subpanel ith the largest modiied slenderness ithin the eb panel under onsideration. NOTE: To alulate k τi the expression given in A. ma be used ith k τst = 0. λ o all subpanels 9

31 EN 99--5: 00 (E) Rigid transverse stiener Longitudinal stiener Non-rigid transverse stiener Figure 7.: Web ith transverse and longitudinal stieners 7.4 Contribution rom langes () When the lange resistane is not ompletel utilized in resisting the bending moment (M < M Rd) the ontribution rom the langes should be obtained as ollos: b t M V = b Rd (7.8) M M Rd b and t are taken or the lange hih provides the least axial resistane b being taken as not larger than 5 ε t on eah side o the eb M k M Rd = M 0 is the design plasti moment o resistane o the ross-setion onsisting o the eetive area o the langes onl 6 b t = a t h () When an axial ore N is present the value o M Rd should be redued b multipling it b the olloing ator: N ( ) (7.9) A + A M 0 here 7.5 Veriiation A and A are the areas o the top and bottom langes respetivel. () The veriiation should be perormed as ollos: V η = 0 (7.0) V b Rd here V is the design shear ore inluding shear rom torque. 0

32 pren 99--5: 08 (E) 8 Resistane to transverse ores 8. Basis () The design resistane o the ebs o rolled beams and elded girders should be determined in aordane ith 8. provided that the ompression lange is adequatel restrained in the lateral diretion. () The load is applied as ollos: a) through the lange and resisted b shear ores in the eb see Figure 8. (a); b) through one lange and transerred through the eb diretl to the other lange see Figure 8. (b). ) through one lange adjaent to an unstiened end see Figure 8. () () For box girders ith inlined ebs the resistane o both the eb and lange should be heked. The internal ores to be taken into aount are the omponents o the external load in the plane o the eb and lange respetivel. (4) The interation o the transverse ore bending moment and axial ore should be veriied using 9.. Tpe (a) Tpe (b) Tpe () a F F F S S S s s s S S S s s s V V h V h h s s + kf = 6 + k = 5 + k = + 6 a a F h Figure 8.: Bukling oeiients or dierent tpes o load appliation F 6 8. Design resistane () For unstiened or stiened ebs the design resistane to loal bukling under transverse ores should be taken as χf l t FRd = (8.) M here t is the thikness o the eb; is the ield strength o the eb; λ is the eetive loaded length see 8.5 appropriate to the length o sti bearing s s see 8.; F is the redution ator due to loal bukling see 8.4(). 8. Length o sti bearing () The length o sti bearing s s on the lange should be taken as the distane over hih the applied load is eetivel distributed at a slope o : see Figure 8.. Hoever s s should not be taken as larger than h.

33 EN 99--5: 00 (E) () I several onentrated ores are losel spaed the resistane should be heked or eah individual ore as ell as or the total load ith s s as the entre-to-entre distane beteen the outer loads. 45 F F F F F S S S S S s s s S s = 0 ss s s s Figure 8.: Length o sti bearing t () I the bearing surae o the applied load rests at an angle to the lange surae see Figure 8. s s should be taken as zero. 8.4 Redution ator F or eetive length or resistane () The redution ator F should be obtained rom:. 0 χ F = 0 (8.) ϕ + ϕ λ F F here ϕ = ( + α ( λ F λ F 0 ) + λ F ) F l t F F 0 (8.) l F = (8.4) Fr α λ F 0 F 0 = 0.75 = 0.50 (8.5) F r t = 09 kf E (8.6) h () For ebs ithout longitudinal stieners k F should be obtained rom Figure 8.. NOTE: For ebs ith longitudinal stieners inormation ma be given in the National Annex. The olloing rules are reommended: For ebs ith longitudinal stieners k F ma be taken as k h b F = a a s (8.7) here b is the depth o the loaded subpanel taken as the lear distane beteen the loaded lange and the stiener s Is a b = 0 9 l h t h a (8.8) here I sl is the seond moment o area o the stiener losest to the loaded lange inluding ontributing parts o the eb aording to Figure.. Formula (8.7) is valid or and 0 and loading aording to tpe a) in Figure 8.. a b b h

34 pren 99--5: 08 (E) () λ should be obtained rom Eetive loaded length () The eetive loaded length l should be alulated as ollos: b m = (8.9) t m m 0 0 h = t = 0 i i λ F λ F > (8.0) For box girders b in ormula (8.9) should be limited to 5 ε t on eah side o the eb. () For tpes a) and b) in Figure 8. l should be obtained using: ( ) l = s + t m but l distane beteen adjaent transverse stieners (8.) s + () For tpe ) l should be taken as the smallest value obtained rom the ormulae (8.) (8.) and (8.). m t l e = l e t l m (8.) l = l e + t m + m (8.) here kf E t l e = ss + (8.4) h 8.6 Veriiation () The veriiation should be perormed as ollos: F η = 0 (8.5) F Rd here F is the design transverse ore; F Rd is the design resistane to loal bukling under transverse ores see 8.();

35 EN 99--5: 00 (E) 9 Interation 9. Interation beteen shear ore bending moment and axial ore () Provided that η (see belo) does not exeed 05 the design resistane to bending moment and axial ore need not be redued to allo or the shear ore. I η is more than 05 the ombined eets o bending and shear in the eb o an I or box girder should satis: M k β M + k η ( η ). 0 or M η e k M (9.) e k here M k M is the harateristi moment o resistane o the ross-setion onsisting o the eetive area o the langes onl; W e k = e η see 6.7(). V η = or V b Rd see expression (7.) V M β = M b Rd k e k () Ation eets should inlude global seond order eets o members here relevant. () The riterion given in () should be veriied at all setions other than those loated at a distane less than h / rom a support ith vertial stieners. (4) The harateristi moment o resistane M k ma be taken as the produt o the ield strength the eetive area o the lange ith the smallest value o A and the distane beteen the entroids o the langes. (5) I an axial ore N is present M ek and M k should be redued in aordane ith 8..9 o EN 99-- and 7.4() respetivel. When the axial ore is so large that the hole eb is in ompression 9.(6) should be applied. (6) A lange in a box girder should be veriied using 9.() taking M k = 0 and τ taken as the average shear stress in the lange hih should not be less than hal the maximum shear stress in the lange and η is taken as η aording to 6.7(). In addition the subpanels should be heked using the average shear stress ithin the subpanel and χ determined or shear bukling o the subpanel aording to 7. assuming the longitudinal stieners to be rigid. 9. Interation beteen transverse ore bending moment and axial ore () I the girder is subjeted to a onentrated transverse ore ating on the ompression lange in onjuntion ith bending and axial ore the resistane should be veriied using and the olloing interation riterion: η + 8 η 4 (9.) 0 () I the onentrated load is ating on the tension lange the resistane should be veriied aording to setion 8. Additionall 8..(5) o EN 99-- should be met. 4

36 pren 99--5: 08 (E) 9. Interation beteen transverse ore bending moment and shear ore () I the girder is subjeted to a onentrated transverse ore ating on the ompression lange in onjuntion ith bending moment and shear ore the resistane should be veriied using and the olloing interation riterion:.6.6 F η + η +.0 η (9.) V here: η = M M pl Rd M plrd η = is the design plasti resistane o the ross setion onsisting o the eetive area o the langes and the ull eetive eb irrespetive o its setion lass. V V b Rd NOTE: This interation urve applies i η >0.. 5

37 EN 99--5: 00 (E) 0 Flange indued bukling () To prevent the ompression lange bukling in the plane o the eb the olloing riterion should be met: h E A k (0.) t A here A is the ross-setion area o the eb; A is the eetive ross-setion area o the ompression lange; h is the depth o the eb; is the thikness o the eb. t The value o the ator k should be taken as ollos: plasti rotation utilized k = 0 plasti moment resistane utilized k = 04 elasti moment resistane utilized k = 055 () When the girder is urved in elevation ith the ompression lange on the onave ae the olloing riterion should be met: E A k h A (0.) t he + r r is the radius o urvature o the ompression lange. Stieners and detailing. General () This setion gives design rules or stieners in plated strutures hih supplement the plate bukling rules speiied in setions 6 to 9. () When heking the bukling resistane the eetive ross-setion o a stiener ma be onsidered taken as the gross area omprising the stiener plus a idth o plate equal to 5 ε t but not more than the atual dimension available on eah side o the stiener avoiding an overlap o ontributing parts to adjaent stieners see Figure.. () The axial ore in a transverse stiener should be taken as the sum o the ore resulting rom shear (see..()) and an external loads. 6

38 Figure.: Eetive ross-setion o stiener pren 99--5: 08 (E). Diret stresses.. Minimum requirements or transverse stieners () In order to provide a rigid support or a plate ith or ithout longitudinal stieners intermediate transverse stieners should satis the riteria given belo. () The transverse stiener should be treated as a simpl supported member subjet to lateral loading ith an initial sinusoidal imperetion 0 equal to s/00 here s is the smallest o a a or b see Figure. here a and a are the lengths o the panels adjaent to the transverse stiener under onsideration and b is the height beteen the entroids o the langes or span o the transverse stiener. Eentriities should be aounted or. 0 a Transverse stiener a b Figure.: Transverse stiener () The transverse stiener should arr the deviation ores rom the adjaent ompressed panels under the assumption that both adjaent transverse stieners are rigid and straight together ith an external load and axial ore aording to the NOTE to..(). The ompressed panels and the longitudinal stieners are onsidered to be simpl supported at the transverse stieners. (4) It should be veriied that using a seond order elasti method analsis all the olloing riteria are satisied at the ultimate limit state: that the maximum stress in the stiener should not exeed / M; that the additional deletion should not exeed b/500; that the seond moment o area I st o the eetive ross-setion o the transverse stiener ith adjaent plate part aording to.() should be larger than:.9 n Ib b I st = (.) π a here: I b out-o-plane inertia o the longitudinal stiener and an adjaent plate part orresponding to the ull ross-setional area o the plate beteen the transverse stieners. n a=min(a a ) number o longitudinal stieners ithin the plate minimum length o the investigated panels. (5) In the absene o an axial ore in the transverse stiener the riteria in (4) above ma be assumed to be satisied provided that the seond moment o area I st o the eetive ross-setion o the transverse stieners ith adjaent plate part aording to.() is not less than: 4 s m b 500 Ist = + 0 u (.) E π b 7