Initial Imperfections of Steel and Steel-Concrete Circular Columns

Transcription

1 Recent dvnces n Contnuum echncs, Hdrolog nd colog Intl Imperectons o Steel nd Steel-Conete Crculr Columns RCL KRZÍOVÁ nd JIDRICH LCHR Fcult o Cvl ngneerng Brno Unverst o Technolog Veveří St. 33/95, 6 Brno CZCH RPUBLIC krmznov.m@ce.vutbr.cz; melcher.j@ce.vutbr.cz; bstrct: - The pper s ocused on the problems o the lod-crrng cpct o steel nd steel-conete members subjected to compresson. The ttenton s mnl pd to the bucklng strength n the connecton wth the member mperectons, whch re usull covered b the equvlent ntl geometrcl mperecton expressed s the mxml ntl member curvng n the md-length o the buckled member subjected to compresson. The pper s orented to the nltcl soluton o the ntl eccentrct bsed on the concepton o the bucklng strength nd to the possbltes how to ver the ntl mperecton expermentll. The problem nlss s shown on the exmples o steel nd steel-conete composte columns represented b steel crculr tubes nd steel tubes lled b norml-strength nd hgh-strength conete. Usng test results o the specmens subjected to compresson the comprson o the ctul vlues o the ntl mperectons wth the correspondng theoretcl vlues s presented here. Ke-Words: - Bucklng strength, lod-crrng cpct, ntl mperecton, eccentrct, steel, conete, crculr column, theoretcl nlss, expermentl vercton, test results, Southwell s lne. Introducton ccordng to the most o current normtve rules (see e.g. [3], [4], [5]), the bucklng resstnce o compresson members cn be usull determned bsed on two bsc pproches: () the second order method consderng the ntll curved member subjected to the centrc compresson, tht mens the member s subjected b the centrc compresson orce combned wth the bendng moment cused b member curvng, or () the method consderng the reducton ctor, so tht the ull plstc compresson resstnce s reduced pplng the bucklng ctor expressng the nluence o dded bendng moment. In the cse () t s necessr to know the ntl member curvng substtutng ll mperectons o the member,.e. geometrcl, structurl nd mterl mperectons. To substtute ll essentl member mperectons, lmost o the stndrds recommend the equvlent geometrcl mperecton, usull s prt o the member bucklng length, but t s queston, whether ths vlue o the mperecton sucentl corresponds wth the relt. In the cse () the bucklng resstnce s nluenced b the reltve ntl eccentrct, whch s one o the most mportnt determnng prmeters. The reltve ntl eccentrct cn be gven usng the bsolute ntl eccentrct, whch cn be determned rom the tests, or exmple. Intl ccentrct o Compresson embers Theoretcl nlss The concepton o compresson member bucklng covered b the normtve rules or the desgn o steel structures rses rom the model o the rel members wth the equvlent ntl curvng, whch s smlr to the orm o the stblt lost o the del member see, or exmple, [3], [4], [5].. Steel Columns The mxml stress o the slender member wth the oss-secton re o, subjected to the xl orce, s gven b the known ormul o + m /, () = mx where the xl stress s =, () the tcl stress o the del member s = π (3) nd the reltve ntl eccentrct m s e m =, (4) j ISB:

2 Recent dvnces n Contnuum echncs, Hdrolog nd colog j = W / nd e s the mxml ntl eccentrct n the md-length o the member snusodl curved. Denng the bucklng strength s xl stress, when the eld strength s reched n the most loded edge o the oss-secton o curved member,.e. mx, then the bucklng strength ccordng to () s explctl gven b the ormul = 4 [ + ( + m ) ] [ + ( + m ) ] (5) nlogcll to the condton or the structurl members subjected to tenson γ = d (6) wth the prtl set ctor or mterl γ, the condton or bucklng strength o the compresson member cn be wrtten n the orm o γ d = = χ, (7) d where the reducton bucklng ctor χ s χ=, (8) nd usng the equton (5) the reducton bucklng ctor χ s expressed b the ormul o χ = ( + m ) ( + m ). (9) Wthn the ccepted concept, the reltve ntl eccentrct m onl s undetermned quntt. B the sutble choosng eccentrct m, t s possble to dene the level o conventon bucklng strength n the structurl desgn process, to respect the test results o rel compresson members. The generl equton or the reltve ntl eccentrct coverng the nluence o mperectons o the rel member s ecent to choose n the orm o m = = α α () where α s the mperecton ctor, nd mterl slenderness chrcterstcs s gven s. () γ d The ormul or the reducton bucklng ctor χ n dependence on the slenderness cn be moded to the generl orm o π χ= + α + π + α + 4 π. () For the determnton o the relble dependence χ (), the essentl queston s to choose the reltve ntl eccentrct m. Test result nlss cn gve sgncnt knowledge or the vercton o the rghtness o the conventon normtve vlues o the equvlent ntl curvng coverng the mperecton nluence on the compresson bucklng cpct. I the equtons (4) nd () re consdered, then the ollowng dependence must be vld e = α, (3) j rom where the mxml ntl eccentrct e n the mddle o the member length s L e j = α = α, (4) π z where z s the dstnce o the oss-secton edge rom the grvt centre.. Steel-Conete Columns cceptng the pproch or steel slender columns desbed bove, then or columns composed o two mterls wth derent mechncl propertes the concept o substtute (del) steel oss-secton cn be used, tht mens geometrcl prmeters,.e. the re nd the second moment o re I o the substtute oss-secton must be ppled s ollows: c =, (5) n + I c I = I +, (6) n where n s the rto o steel-to-conete Young s modulus o elstct n=. (7) c The mxml stress mx o steel-conete slender column wth the oss-secton re consstng o steel prt nd conete prt c nd wth eld ISB:

3 Recent dvnces n Contnuum echncs, Hdrolog nd colog strength nd conete clndrcl strength c cn be gven b the ormul (), where the xl stress s =, (8) the tcl stress o the del member s the reltve ntl eccentrct m cn be clculted = π, (9) e m = () j nd the bucklng strength cn be gven b (5). nlogcll to the members n tenson see (6), the condton or bucklng lod-crrng cpct o steel-conete compresson column cn be wrtten s γ d = = χ () d wth the reducton bucklng ctor ccordng to (8), nd subsequentl ccordng to (9). Then, the reltve ntl eccentrct m cn be consdered ccordng to the orm o m = = α, α, () where the chrcterstcs o mterl slenderness s,. (3) γ d The reducton bucklng ctor χ n dependence on the slenderness cn be wrtten s π χ= + α+ π + α+ 4 π. (4) The mxml ntl eccentrct e n the mddle o the member length cn be gven, s n the cse o crculr steel columns, b the ormul (5). For the selected steel nd steel-conete crculr columns, whch hve been expermentll vered (see [6], [7], [8], []), the ctul vlues o ntl mperectons hve been derved evlutng test results. The specmens o vrous geometrcl nd mterl prmeters hve been tested, to ver ther ctul behvour, lure mechnsm nd bucklng lod-crrng cpct, subjected to compresson. Usng the ormul (5) the theoretcl vlues o ntl mperectons hve been clculted or the propertes o tested columns. For the comprson, lso the recommended vlues o ntl eccentrctes ccordng to the rules gven n stndrd documents, the bucklng resstnce s vered pplng the second order theor. 3. ctul Vlues o Intl Imperecton Determned xpermentll The expermentl vercton hs been relzed wth the specmens represented b steel crculr tubes nd steel crculr tubes lled b conete composed o norml-strength mterls nd hgh-strength ones. The nvestgted columns were smpl supported on both ends wth the structurl length o L = 3 7 mm or L = 3 mm, respectvel, tht the bucklng length ws L = 3 7 mm nd L = 3 mm, respectvel. Vrous mterl propertes ncludng ther combntons n prtculr oss-sectons hve been used: () steel grde o S 35 nd S 355, () conete clss o C /5, C55/67 nd C 8/95. 3 Intl Imperectons o Steel nd Steel-Conete Crculr Columns For crculr tubes, the dstnce z n (4) s hl o the dmeter,.e. d /, so tht e L = α. (5) π d Fg. Illustrton o test rrngement nd relzton The overvew o the tested specmens, ncludng ther geometrcl prmeters nd mesured phscl mechncl propertes, s lsted n Tble. Some llustrtons presentng the test rrngement nd relzton re shown b photogrphs n Fg.. ISB:

4 Recent dvnces n Contnuum echncs, Hdrolog nd colog,-5,8-5,6-5,4-5,-5,-5 8,-6 6,-6 4,-6 e w / [mm - ],-6 w [mm], ,-5,8-5,6-5,4-5,-5,-5 8,-6 6,-6 4,-6 Fg. Illustrton o Southwell s lnes: tubes TR Ø5/4.5 wthout conete llng e w / [mm - ],-6 w [mm], Fg. 3 Illustrton o Southwell s lnes: tubes TR Ø5/4.5 lled b norml-strength S conete,-5,8-5,6-5,4-5,-5,-5 8,-6 6,-6 4,-6 e w / [mm - ],-6 w [mm], Fg. 4 Illustrton o Southwell s lnes: tubes TR Ø5/4.5 lled b hgh-strength HS conete Tble Overvew o nvestgted columns: geometrcl prmeters (nomnl vlues) nd mechncl propertes (men vlues) Cross-secton [P] steel [GP] conete c [P] c [GP] TR Ø5/ ) TR Ø5/4.5 + S conete TR Ø5/4.5 + HS conete ) ) 87. ) 49. TR Ø59/4.5-I TR Ø59/4.5-I + S conete TR Ø59/4.5-I + HS conete TR Ø59/4.5-II TR Ø59/4.5-II + S conete TR Ø59/4.5-II + HS conete S conete norml-strength conete; HS conete hgh-strength conete; 3 test specmens perormed or ech group excludng ) test onl; mechncl prmeters mesured excludng ) not mesured The ctul vlues o the ntl eccentrctes hve been derved usng Southwell s lnes, exmples o whch re llustrted b the grphs n Fgs., 3 nd 4. On the horzontl xs there re the vlues o the trnsverse deormton,.e. delecton w n the mdlength o the member. On the vertcl xs there re the vlues o the rto o delecton w to xl orce,.e. w /. The ntl eccentrct e, tht mens the equvlent ntl geometrcl mperecton, s such vlue o the delecton, or whch w / =. 3. Theoretcl Vlues o Intl Imperecton Clculted nltcll ccordng to the ormul (5), the theoretcl vlue o equvlent ntl mperecton e, lso so-clled equvlent geometrcl mperecton, depends on eld strength nd Young s modulus o steel, nd on bucklng length nd tube dmeter, both n the cse o steel tubes nd n the cse o steel-conete tubes. It s becuse steel-conete oss-secton hs been trnsormed to the substtute steel oss-secton. The mportnt quntt or the clculton s the mperecton prmeter α usull recommended n normtve documents ccordng to the bucklng ISB:

5 Recent dvnces n Contnuum echncs, Hdrolog nd colog curve, whch depends on the oss-secton tpe nd ts senstvt to the mperecton nluence [9]. For crculr hot-rolled tubes [] the bucklng curve o wth the mperecton prmeter α =. s vld, s well s or crculr tubes lled b conete []. The member mperectons ccordng to [], [] re consdered n dependence on the member length s e = L / 3, or n the orm o e / L = / Comprson o Theoretcl nd ctul Vlues o Intl Imperectons In Tble, the ctul ntl mperectons derved expermentll evlutng test results re lsted n comprson wth the ntl mperectons clculted nltcll usng the ormul (5), ncludng the rtos o e / L to compre these ones wth the vlue o / 3 recommended n stndrds [], []. Tble Comprson o ntl mperectons: ctul vlues vs. theoretcl vlues Cross-secton TR Ø5/4.5 TR Ø5/4.5 + S conete TR Ø5/4.5 + HS conete TR Ø59/4.5-I TR Ø59/4.5-I + S conete TR Ø59/4.5-I + HS conete TR Ø59/4.5-II TR Ø59/4.5-II + S conete TR Ø59/4.5-II + HS conete e [mm] ctul e / L [-] /649 /894 /86 /355 /74 /836.7 / /3 /6 /6 /3 /3 /3 /3 /75 /5 /75 /3 /75 /3 /6 / /3 /3 /3 theoretcl e [mm] e / L [-] Concluson B the exmples o steel nd steel-conete crculr columns mentoned bove t s shown: The ctul vlues o the ntl mperectons obtned usng test results re much less thn those ones clculted usng nltcll derved ormul, usull n the rnge rom to 5 tmes, both n the cse o steel tubes, nd n the cse o steel-tubes, lled b norml-strength nd hgh-strength conete. Thus, the mperecton prmeter, hereto gven s α =., shows, tht the mperecton mportnce or the bucklng strength o ths column tpe cn be sgncntl lower thn consdered n stndrd rules. The vlues o ntl mperectons recommended n the normtve documents or the needs o the second order clculton, re bout tmes lrger thn the theoretcl vlue clculted nltcll, even respectng the ct, tht lso ths theoretcl vlue s probbl too hgh compred to the ctul vlues o the ntl mperectons. cknowledgement: The pper hs been elborted wthn the soluton o the specc reserch project o the Czech nstr o ducton, Youth nd Sports FST S--3/5 nd the Czech Scence Foundton grnt project o. 3/9/597. Reerences: [] urocode 3: Desgn o steel structures, Prt -: Generl rules nd rules or buldngs, C: Brussels, 8. [] urocode 4: Desgn o steel nd conete composte structures, Prt -: Generl rules nd rules or buldngs, C: Brussels, 8. [3]. Chlup, Strength o slender members nd webs (n Czech lnguge), Techncl Report on Steel Structures, Vítkovce, Vol. 3, 976. [4] J. elcher,. Chlup, Problems o mperectons nd derentton o bucklng curves o compresson steel members (orgn n Czech lnguge), Journl o Cvl ngneerng, Vol., 975. [5] J. elcher, The problems o nltcl nterpretton nd derentton o lmt bucklng stresses or centrcll compressed members, In Proceedngs o Regonl Colloquum on Stblt o Steel Structures, TU: Budpest, 977. [6] P. Bukovská,. Krmzínová, Behvour o the tubulr columns lled b conete ISB:

6 Recent dvnces n Contnuum echncs, Hdrolog nd colog subjected to bucklng compresson, Proced ngneerng, Issue 4,, pp do:.6/j.proeng [7] P. Bukovská, Inluence o conete strength on the behvor o steel tubulr columns lled b conete, Interntonl Journl o echncs, Vol. 6, o.3,, pp ISS [8] Z. Kl, L. Puklcký,. Omshore,. Krmzínová, J. elcher, Stblt problems o steel-conete members composed o hghstrength mterls, Journl o Cvl ngneerng nd ngement,, 6(3), pp do:.3846/jcem..4. [9] Z. Kl,. Krmzínová, J. elcher, L. Puklcký,. Omshore, Senstvt nlss o steel-conete structurl members, In Proceedngs o the 9 th Interntonl Conerence on Steel-Conete Composte nd Hbrd Structures SCCS 9 n Leeds, Reserch Publshng Servces: Sngpore, 9, pp ISB []. Krmzínová, J. J. elcher, Desgn sssted b testng ppled to the determnton o the desgn resstnce o steel-conete composte columns, In Proceedngs o the 3 th WSS Interntonl Conerence on themtcl nd Computtonl ethods n Scence nd ngneerng CS ', WSS, Ctn,, pp ISB []. Krmzínová, J. elcher, V. Röder, Lodcrrng cpct o steel-conete compresson members composed o hgh-strength mterls, In Proceedngs o the 9 th Interntonl Conerence on Steel-Conete Composte nd Hbrd Structures SCCS 9, Leeds, Reserch Publshng Servces: Sngpore, 9, pp ISB ISB: