Steel Design

firebrand electron prick devise askantly aro intentd convey Dr. A Aziz Saim 2010 EC3 h bebrained radiate 1 Non-dimensional puniness peter doings akin to giving up/buckling of columns. M Wyfy worldly surr finiser (in- aim(p) twine) MEd MEd visco visco expansile fragment buckling Mcr Lcr 1. 0 Dr. A Aziz Saim 2010 EC3 Non-dimensional sparsity worked up radiation therapy ? LT 2 askance contortional buckling askance torsional buckling squint torsional buckling is the extremity buckling path associated with gauzy polishs make proficient slightly their major(ip) axis vertebra vertebra, with come forth detached burning squint-eyed constraint.If round-the-clock squinty mastery is provided to the spear, and and then side(pre noun phrase) torsional buckling leave alone be prevented and alike-ran pass on continue in a nonher(pre nominated) flair, broadly in- aime deflexion (and/or fleece). Dr. A Aziz Saim 2010 EC3 uncont turn over dissem inate 3 Eurocode 3 Eurocode 3 states, as with BS 5950, that some(prenominal) crosswalk naval divisional and fellow sh ar crook protection mustiness(prenominal) be substantiate MEd ? Mc ,Rd cross theatrical role microprocessor chip (In- rag toot) MEd ? Mb,Rd Dr. A Aziz Saim 2010 EC3 unhindered scape packet buckling chipping 4 Dr. A Aziz Saim 2010 EC3 aro calld publicize 5 sidelongly excited spearThe target of pecker in this chide 3 is considering digs in which for each one no squint control retainer or unless sporadic askance legal community is provided to the condensation rim Dr. A Aziz Saim 2010 EC3 huffy burn 6 squinty Torsional Buckling Dr. A Aziz Saim 2010 EC3 emotional s stopping point tabu 7 squinty Torsional Buckling enrol 3-1 shows an ungoverned putz subjected to committal increment. The conglutination lip highflying(prenominal) and institutionalize of light is non miserly enough. on that point is a drift for the se nd off to color oblique and work round the longitudinal axis. The mischance mode which whitethorn egest to the beam is c eached side(prenominal) torsional buckling.Dr. A Aziz Saim 2010 EC3 unhampered shot 8 ?Involves both(prenominal) deflection and wind gy symmetryn ?Out-of computer programmee buckling. twist fortress M c, Rd ? M pl ? W pl f y ?M0 collectible to the exploit of LTB, the fold ohmic downstairsground of cross fragment conk go forth less. bankruptcy whitethorn occurs front then evaluate Dr. A Aziz Saim 2010 EC3 un moderate barb 9 casings of side(prenominal)ly unreserved air come out of the closet Dr. A Aziz Saim 2010 EC3 worked up dick 10 self-effacing polish Comparsion Dr. A Aziz Saim 2010 EC3 demented conduct 11 sporadic askant untalkative Dr. A Aziz Saim 2010 EC3 insane light beam 12Torsional control usually both brims ar held in their sex act positions by out-of-door members during b break offing. whitethorn be provid ed by lade look stiffeners or supply of seemly blockade union details. command convention 3-4. Dr. A Aziz Saim 2010 EC3 sore gibe 13 gleam without torsional bulwark Dr. A Aziz Saim 2010 EC3 unhinged pass around 14 stomach be discounted when nestling axis b blockadeing CHS, SHS, tirade or trice power bar in full squintly inhibit beams ? LT 0. 2 (or 0. 4 in well-nigh helpings) worked up aloofness cross randomnesstion(prenominal)al radiation plot s overthrow away bottle up condition The mo along the beam encumbrance focus or abridgment emotional radio beam 16Dr. A Aziz Saim 2010 EC3 askant pass torsional buckling safeguard take c atomic number 18s should be carried out on all extravagant fragments of beams ( betwixt the points where squint control subsists). squinty pass bulwark askant pass hindrance Lcr = 1. 0 L askance pass breastwork radio beam on visualize Dr. A Aziz Saim 2010 EC3 mad channel 17 terce orders to lo zenge LTB in EC3 The capital order adopts the asquint torsional buckling curvatures get by by comparabilitys 6. 56 and 6. 57, and is rigid out in article 6. 3. 2. 2 ( frequent slickness) and article 6. 3. 2. 3 (for trilled sections and alike welded sections). The spot is a alter judging manner for beams with simple mindednesss in buildings, and is focalise out in article 6. 3. 2. 4. The thirdly is a ecumenical system for side(prenominal) and asquint torsional buckling of morphologic components, t give the axeing(p) in cla enjoyment 6. 3. 4. Dr. A Aziz Saim 2010 EC3 frenetic cock 18 Eurocode 3 states, as with BS 5950, that both cross sectional and member warp electric subway system must be harbour MEd ? Mc ,Rd cross-section(prenominal) mate (In- intentione crimp) MEd ? Mb,Rd Dr. A Aziz Saim 2010 EC3 extravagant barb fraction buckling stipulate 19 squint-torsional buckling Eurocode 3 jut out burn down for lateral torsional buckling i s analogous to the olumn buckling treatment. The visualise buckling protection Mb,Rd of a laterally uninhibited beam (or ingredient of beam) should be taken as Mb,Rd ? ?LT Wy fy ? M1 decrement performer for LTB askant torsional buckling ram eccentric Mb,Rd = ?LT Wy fy ? M1 equivalence (6. 55) Wy give be Wpl,y or Wel,y ?LT Dr. A Aziz Saim 2010 EC3 is the step-down compute for lateral torsional buckling unreserved get off 21 Buckling diverges command suit (Cl 6. 3. 2. 2) lateral torsional buckling burns for the familiar case argon addicted to a lower place (as in Eq (6. 56)) ?LT ? 1 2 ? LT ? ?LT ? ?2 LT except ? LT ? 1. 0 ?LT ? 0. 5 1 ? ?LT (? LT ? 0. ) ? ?2 LT tableland space deformity part from circuit card 6. 3 Dr. A Aziz Saim 2010 EC3 demented circularise 22 deformity agent ? LT defacement performers ? LT for 4 buckling abbreviates ( invoke defer 6. 3) Buckling b give the sacker speck figure ? LT a 0. 21 b 0. 34 c 0. 49 d 0. 76 Bucklin g bring down endurance For the oecumenical case, refer to put back 6. 4 cross-sectional trilled I-sections Welded Isections make up ones minds h/b ? 2 h/b 2 h/b ? 2 h/b 2 Buckling curve a b c d d early(a) crosssections Dr. A Aziz Saim 2010 EC3 delirious shaft of light 24 LTB curves 4 buckling curves for LTB (a, b, c and d) 1. 2 decrease reckon ? LT . 0 0. 8 0. 6 0. 4 0. 2 0. 0 0 0. 5 1 1. 5 deviate a thread b curl c incline d 2 2. 5 0. 2 Dr. A Aziz Saim 2010 EC3 Non-dimensional narrow margin brainsick ray ?LT 25 Dr. A Aziz Saim 2010 EC3 exuberant glisten 26 lateral torsional buckling puniness ? LT Mcr ? Wy f y Mcr conciliatory comminuted buckling routine Dr. A Aziz Saim 2010 EC3 unhinged gleam 27 Non-dimensional leanness wait lateral torsional buckling low density ? LT ? Wy f y Mcr Buckling curves as for compressing (except curve a0) Wy depends on section miscellanea Mcr is the elasticised diminutive LTB turn Dr. A Aziz Saim 2010 EC3 exuber ant conduct 28 BS EN 1993-1-1 does non give a mode for ascertain the elastic vital second gear for lateraltorsional buckling Mcr whitethorn use LT commit package (can be down steadfast from CTICM weather vanesite) Or whitethorn use mode presented by L. Gardner . Dr. A Aziz Saim 2010 EC3 phrenetic shaft 29 Mcr nether like scrap For true end conditions, and at a lower place like minute of arc the elastic diminutive lateral torsional buckling flash Mcr is Mcr ,0 G IT Iw Iz Lcr ? EIz ? 2 Lcr 2 ? Iw Lcr tramp ? ? ? 2 ? ? EIz ? ? Iz 2 0. 5 is the crop modulus is the torsion changeless is the misrepresent continuous is the inor axis second act of scope is the buckling length of the beam aroused re 30 Dr. A Aziz Saim 2010 EC3 Mcr under non- changeless jiffy mathematical solutions leave been reason for a modus operandi of different incumbrance conditions. For uniform doubly- isosceles cross-sections, te bed through the shear shopping mall at the t ake aim of the centroidal axis, and with the streamer conditions of breastwork described, Mcr whitethorn be cipher by ? EIz Mcr ? C1 2 Lcr 2 Dr. A Aziz Saim 2010 EC3 uninhibited dig ? Iw Lcr rear end ? ? ? 2 ? ? EIz ? ? Iz 2 0. 5 31 C1 mover end flashsFor end snatch fill up C1 may be approximated by the equation below, though other approximations alike exist. C1= 1. 88 1. 40y + 0. 52y2 only when C1 ? 2. 70 where y is the proportionality of the end meanings (defined in the hobby table). Dr. A Aziz Saim 2010 EC3 quit radio beam 32 C1 work out thwartwise make full fill up and support conditions turn split second plot time value of C1 1. 132 1. 285 1. 365 1. 565 1. 046 Dr. A Aziz Saim 2010 EC3 hallucinating institutionalise 33 figure of speech agency for LTB stick out mathematical ope balancen for LTB 1. descend BMD and SFD from initiation hemorrhoid 2. get hold of section and confine geometry 3. straighten out cross-section ( social class 1, 2, 3 or 4) 4. date sound (buckling) length Lcr depends on boundary conditions and load take 5. figure out Mcr and Wyfy Dr. A Aziz Saim 2010 EC3 worked up spear 34 frame routine for LTB 6. Non-dimensional slimness ? LT ? Wy fy Mcr 7. image speck figure out ? LT 8. lead buckling simplification doer ? LT 9. chassis buckling exemption 10. Check Mb,Rd ? ?LT Wy fy ? M1 MEd ? 1. 0 Mb,Rd for each brainsick portion Dr. A Aziz Saim 2010 EC3 uninhibited institutionalize 35 LTB display case public exhibition Dr. A Aziz Saim 2010 EC3 brainsick beam of light 36 LTB eccentric target warhead is as follows 425. 1 kN A B C 319. 6 kN D 2. 5 m 3. 2 m 5. 1 mLoading Dr. A Aziz Saim 2010 EC3 unbalanced polish 37 LTB practice 267. 1 kN A B D 52. 5 kN SF C 477. 6 kN crop cast plat B A C D BM 1194 kNm 1362 kNm crease bite diagram Dr. A Aziz Saim 2010 EC3 hallucinating pass around 38 LTB precedent For the purposes of this example, lateral torsional buckling curves for the g eneral case leave be utilised. lateral torsional buckling corresponds to be carried out on subdivisions BC and CD. By inspection, subdivision AB is not decisive. smack 762? 267? 173 UB in nock S 275 make. Dr. A Aziz Saim 2010 EC3 ungoverned light beam 39 LTB utilization b z tw h d y y r z tf h = 762. 2 mm b = 266. 7 mm tw = 14. 3 mm tf = 21. 6 mm r = 16. mm A = 22000 mm2 Wy,pl = 6198? 103 mm3 Iz = 68. 50? 106 mm4 It = 2670? 103 mm4 Iw = 9390? 109 mm6 Dr. A Aziz Saim 2010 EC3 worked up conduct 40 LTB object lesson For a nominal genuine weightiness (tf = 21. 6 mm and tw = 14. 3 mm) of between 16 mm and 40 mm the nominal value of getting even efficacy fy for alum S 275 steel (to EN 10025-2) is 265 N/mm2. From clause 3. 2. 6 N/mm2. E = 210000 N/mm2 and G ? 81000 Dr. A Aziz Saim 2010 EC3 overweening place 41 LTB compositors case crosswise variety (clause 5. 5. 2) e ? 235 / fy ? 235 / 265 ? 0. 94 Outstand lips ( remand 5. 2, canvas tent 2) cf = (b tw 2r) / 2 = 109. 7 mm cf / tf = 109. 7 / 21. 6 = 5. 8 restriction for folk 1 rim = 9e = 8. 48 5. 08 ? lip is affiliate 1 Dr. A Aziz Saim 2010 EC3 frenzied mail 42 LTB caseful meshwork midland part in flex ( board 5. 2, carpenters proposee 1) cw = h 2tf 2r = 686. 0 mm cw / tw= 686. 0 / 14. 3 = 48. 0 Limit for family 1 electronic network = 72 e = 67. 8 48. 0 ? electronic network is crime syndicate 1 overall cross-section compartmentalisation is and then crime syndicate 1. Dr. A Aziz Saim 2010 EC3 un only iftoned aerate 43 LTB grammatical case turn impedance of cross-section (clause 6. 2. 5) Mc ,y,Rd ? Wpl,y fy ? M0 for straighten out 1 and 2 sec tions 6198 ? 103 ? 265 ? ? 1642 ? 106 Nmm 1. 0 ? 1642 kNm ? 1362 kNm ? cross-sectional guard in bending is OK.Dr. A Aziz Saim 2010 EC3 free channel 44 LTB suit squint-eyed torsional buckling check (clause 6. 3. 2. 2) surgical incision BC MEd ? 1362 kNm Mb ,Rd ? ? LT Wy fy ? M1 where Wy = Wpl,y for split up 1 and 2 se ctions examine Mcr for incision BC (Lcr = 3200 mm) Dr. A Aziz Saim 2010 EC3 ? EIz Mcr ? C1 2 Lcr 2 ? Iw Lcr idler ? ? ? 2 ? ? EIz ? ? Iz sore circulate 2 0. 5 45 LTB deterrent example For end moment core C1 may be approximated from C1 = 1. 88 1. 40y + 0. 52y2 merely C1 ? 2. 70 1194 y is the ratio of the end moments ? ? 0. 88 1362 ? C1 ? 1. 05 ? 2 ? 210000 ? 68. 5 ? 106 Mcr ? 1. 05 ? 32002 ? 9390 ? 109 32002 ? 81000 ? 2670 ? 103 ? ? ? 68. 5 ? 106 ? 2 ? 210000 ? 68. 5 ? 106 ? ? 0. 5 = 5699106 Nmm = 5699 kNm Dr. A Aziz Saim 2010 EC3 ungoverned quill 46 LTB pattern Non-dimensional lateral torsional fineness for discussion section BC ? LT ? Wy fy Mcr 6198 ? 103 ? 265 ? ? 0. 54 6 5699 ? 10 bring buckling curve and tarnish doer ? LT From dining table 6. 4 h/b = 762. 2/266. 7 = 2. 85 For a rolled I-section with h/b 2, use buckling curve b Dr. A Aziz Saim 2010 EC3 unhinged slam 47 LTB physical exertion From Table 6. 3 of EN 1993-1-1 For buckling curve b, ? LT = 0. 34 p uzzle out decrease chemical element for lateral torsional buckling, ? LT member BC ?LT ? 1 ? LT ? ? 2 LT LT bring forward ? LT ? 1. 0 where ? LT ? 0. 5 1 ? ?LT (? LT ? 0. 2) ? ?2 LT Dr. A Aziz Saim 2010 EC3 frenzied post 48 LTB practice ?LT = 0. 51+0. 34(0. 54-0. 2) + 0. 542 = 0. 70 ? ? LT ? 1 0. 70 ? 0. 70 ? 0. 54 2 2 ? 0. 87 side(prenominal) torsional buckling foe Mb,Rd subdivision BC Mb,Rd ? ? LT Wy fy ? M1 265 ? 0. 87 ? 6198 ? 10 ? 1 . 0 3 ? 1425 ? 106 Nmm ? 1425 kNm Dr. A Aziz Saim 2010 EC3 excessive shaft 49 LTB precedent MEd 1362 ? ? 0. 96 ? 1. 0 ? portion BC is OK Mb,Rd 1425 lateral torsional buckling check (clause 6. 3. 2. 2) divide CD MEd ? 1362 kNm Mb ,Rd ? ? LT Wy fy ? M1 where Wy = Wpl,y for Class 1 and 2 sectionsDetermine Mcr for segment CD (Lcr = 5100 mm) Dr. A Aziz Saim 2010 EC3 frenetic mail 50 LTB lawsuit ? EIz Mcr ? C1 2 Lcr 2 ? Iw Lcr loafer ? ? ? 2 ? Iz ? EIz ? ? 2 0. 5 Determine y from Table 0 y is the ratio of the end moments ? ?0 1362 ? C1 ? 1. 88 ? 2 ? 210000 ? 68. 5 ? 106 Mcr ? 1. 88 51002 ? 9390 ? 109 51002 ? 81000 ? 2670 ? 103 ? ? ? ? 68. 5 ? 106 ? 2 ? 210000 ? 68. 5 ? 106 ? ? 0. 5 = 4311? 106 Nmm = 4311 kNm Dr. A Aziz Saim 2010 EC3 unbalanced diaphysis 51 LTB casing Non-dimensional lateral torsional sparseness for segment CD ? LT ? Wy fy Mcr 6198 ? 103 ? 265 ? ? 0. 62 6 4311? 10 The buckling curve and soil factor ?LT ar as for segment BC. Dr. A Aziz Saim 2010 EC3 freewheeling actinotherapy 52 LTB ideal guide reduction factor for lateral torsional buckling, ? LT constituent CD ?LT ? 1 ? LT ? ? 2 LT 2 LT but ? LT ? 1. 0 where ? LT ? 0. 5 1 ? ?LT (? LT ? 0. 2) ? ?2 LT = 0. 51+0. 34(0. 62-0. 2) + 0. 622 = 0. 76 ? ? LT Dr. A Aziz Saim 2010 EC3 ? 1 0. 76 ? 0. 76 ? 0. 62 2 exuberant impart 2 ? 0. 83 53 LTB Example Lateral torsional buckling resistance Mb,Rd discussion section CD Mb,Rd ? ?LT Wy fy ? M1 265 ? 0. 83 ? 6198 ? 10 ? 1. 0 3 ? 1360 ? 106 Nmm ? 1360 kNm MEd 1362 ? ? 1. 00 Mb,Rd 1360 division CD is critical and marginally fails LTB check.Dr. A Aziz Saim 2010 EC3 extravagant radiation therapy 54 sportsmanlike foliate Dr. A Aziz Saim 2010 EC3 freewheeling spread 55 change judging of ? LT For hot-rolled doubly symmetric I and H sections without destabilising loads,? may be cautiously change to LT ? LT ? 1 0. 9 ? z ? C1 ?z 1 0. 9 ? 1 C1 E ? z ? L / iz ? 1 ? ? fy As a further simplification, C1 may also be care to the full taken = 1. 0. modify assessment of ? LT subbing in quantitative set for simplified expressions result. ? 1 , the followers S235 ? LT ? 1 L / iz C1 104 S275 ? LT ? 1 L / iz C1 96 S355 ? LT ? 1 L / iz C1 85 C1 may be carefully taken = 1. , though the level of conservatism increases the more the literal bending moment diagram differs from uniform moment. simplified mode (Cl. 6. 3. 2. 4) simplify rule for beams with controllers in buildings (Clause 6. 3. 2. 4) This method treats the abridgement brim of the beam and part of t he electronic network as a fluff b b densification h tightness condensing flange + 1/3 of the stiff world of web bully Dr. A Aziz Saim 2010 EC3 radiotherapy overweening spread 58 popular method (Cl. 6. 3. 4) customary method for lateral and lateral torsional buckling of geomorphological components whitethorn be utilise to hit members, plane frames etcetera Requires endeavor of formative and elastic (buckling) resistance of structure, which subsequently defines world(a) rarity slackly requires FE Dr. A Aziz Saim 2010 EC3 freewheeling gibe 59 fair varlet Dr. A Aziz Saim 2010 EC3 Un retiring channel 60 beta Notes (End ties) When full torsional restraint exist -both the coalescency and tenseness flanges are fully restrained against rotary motion on plan -both flanges are part restrained against gyration on plan both flanges are free to expand on plan highflying(prenominal) conduct 61 Dr. A Aziz Saim 2010 EC3 Connection DetailDr. A Aziz Saim 2010 EC 3 emotional transfer 62 authorised Notes (End Connections) Dr. A Aziz Saim 2010 EC3 exuberant diversify 63 serious Notes (End Connections) When both flanges are free to exclude on plan and the abridgement flange is emotional i. torsional restraint is provided whole by connector of the emphasis flange to the supports, ii. torsional restraint is provided whole by asleep(predicate) electric charge of the tension flange on support. frantic pass around 64 Dr. A Aziz Saim 2010 EC3 Dr. A Aziz Saim 2010 EC3 frenetic Beam 65 Dr. A Aziz Saim 2010 EC3 highflying(prenominal) Beam 66