Ultimate Strength Evaluation for Wide-Type Box Girders in Cable-Supported Bridges

Transcription

1 Ultimate Strength Evalation for Wide-Tpe Box Girders in Cable-Spported Bridges Jong Seo KIM Ph.D. Candidate Seol National Universit Seol,Korea (OK) Jong Seo Kim, born 1980, is a Ph.D andidate in department of ivil engineering, Seol National Universit, Seol, Korea. His main area of researh is related to steel strtres. Hae Sng LEE Professor Seol National Universit Seol, Korea (OK) hslee@sn.a.kr Hae Sng Lee, born 1958, reeived his Ph.D. degree in ivil engineering from Universit of Illinois at Urbana-Champaign, IL., USA. He is a professor in department of ivil engineering, Seol National Universit, Seol, Korea. His main area of researh is solid and flid analsis. Kngsik KIM Professor Cheongj Universit Cheongj, Korea (OK) kkim@j.a.kr Kngsik Kim, born 1968, reeived his Ph.D. degree in ivil engineering from Abrn Universit, AL., USA. He worked for GS E&C, Seol, Korea before beoming a professor at Cheongj Universit. His main area of researh is related to steel and omposite strtres. Smmar Wide-tpe steel box girders that have mh larger size of width than depth are widel adopted in able-spported bridges de to their sperb rigidit and advantages in aerodnamis. In design sh primar members it is inevitable to evalate nominal strengths before appling varios design parameters. As ltimate strength of wide-tpe steel box girders sbjeted to onrrent bending moment and axial fore is governed b flanges in ompression rather than in tension, separated dek panel sstem in ompression was modeled and analzed. General-prpose nonlinear finite element analsis program was sed to perform evalation of ltimate strengths of varios hpothetial stiffened plate sstems with U-ribs. The analses reslts have been ompared to expeted strengths from available design speifiations sh as Eroode 3, HWA (ederal Highwa Assoiation), and JA (Japanese oad Assoiation). New design eqations have been developed for ltimate strength as a fntion of plate and olmn slenderness parameters of the stiffened dek panel. It has been fond that the proposed eqations expet ltimate strengths reasonabl permitting a wa to more eonomi design than other design gides. Kewords: wide-tpe steel box girders; ltimate strength; stiffened plate; U-rib; able-spported bridges. 1. Introdtion Wide-tpe steel box girder has been widel sed in able-spported bridges de to their sperb torsional rigidit, etiveness in resisting lateral bending, advantages in aerodnamis, et [9]. Espeiall, this kind of girders an offer sper long span in able-spported bridges b reding the dead. In reent design pratie, losed tpe stiffeners are more preferred than open tpe stiffeners as former have high performane on wheel load distribtion and loal rigidit. In general design proedre for box girder bridges, it is one of the important steps to evalate nominal strengths of stiffened plate sstems in ompression. Objetives of present std are smmarized as: (1) investigation of ltimate ompressive strength for U-rib stiffened plate, and () proposition of strength rves based on the nmerial methodolog. Major parameters eting on ltimate strength of wide-tpe box girders sbjeted to bending and/or ompression have been reviewed from existing odes. Hpothetial models for stiffened panel plate with U-rib were seleted and analzed tilizing a ommerial pakage program ABAQUS [1]. Effets of initial imperfetion, residal stresses, and material ielding were inorporated in nonlinear inremental analsis. Strength preditor rves were derived from nmerial reslts sing linear regression method.

2 . A review on design odes.1 HWA-TS Althogh AASHTO LD bridge design speifiation [] offers general provisions for box girder setion, it reommends HWA speifiation [1] for speial prpose of design of long span box girder bridges. This speifiation was based on strt approah whih tilizes the onept of stiffener strt onsisting of one stiffener and the assoiated portion of flange plate with eqall spaed stiffener spaing. The ltimate ompressive strength of stiffened plate, P, is allated as: P = A (1) P f = f λ, λ ) () ( pl ol Where Af is the ross setional area of flange and all longitdinal stiffeners, the ield stress, the ltimate ompressive strength of a stiffener strt. This strength is an fntion of plate slenderness parameter, λ pl, and olmn slenderness parameter, λ ol, as shown in Eq. () and given b interation diagram shown in ig (A) in HWA. Slenderness parameters are defined as: λ pl = (3) 1.9 E 1 L λol = (4) π E r where w is stiffener spaing, t thikness of flange plate, L transverse stiffener spaing, r radis of gration of stiffener strt, E ong s modls. HWA speifiation onsiders onl two slenderness parameters presented in qs. (3) and (4). In order to prevent stiffener loal bkling inherentl, this speifiation provides a prereqisite reqirement for stiffeners that the strength of stiffener mst greater than that of stiffened panels.. EN or stiffened plates, Eroode 3 reommends etive setion method for allating the ltimate ompressive strength in EN [5] and gives a strength eqation as: = A (5) P, where A, is etive setion for overall redtion from sb-panel bkling and global bkling of stiffened plates, and allated as: A, = ρ A,, lo + bedge, t (6) A,, lo = Asl, + ρ lob, lot (7) where sl lo, lo A, is sm of the etive ross-setional area of all longitdinal stiffeners, ρ b t the etive ross setional area of all the sb-panels reded for loal plate bkling exept for etive part of sb-panels whih are spported b a web or a flange plate( bedge, t ), ρ the redtion fator for global bkling of the stiffened panel, ignoring loal bkling of sb-panels. The redtion fator for global bkling, ρ, is determined from an empirial interpolation between the redtion fators for olmn-like bkling and for overall stiffened plate bkling and is defined as: ρ = ( ρ χ ) ξ ( ξ ) + χ (8) As shown in Eq. (6) ~ Eq. (8) the etive area is obtained mainl b the proess of reding the

3 gross area in two steps, namel, the first step for sb-panel loal bkling and the seond step for global bkling. Conerning the first step, EN onsiders the et of stiffener loal bkling whereas HWA prevents it inherentl b the stiffener strength reqirement. In the viewpoint of the seond step, both odes onsider both the plate behavior and the olmn behavior..3 JA & JSCE gideline In JA(Japanese oad Assoiation) [7], ltimate ompressive strength have been sggested as fntions of the plate slenderness parameter onl from the general plate theor and the fntions are given as: f r / f = 1.0 ( 0. 5 ) (9a) f / f = 1. 0 ( ) (9b) r r / f < f = 0.5/ ( f f = 0.5/ ) (9) where r / b f 1(1 µ ) =, t E π k k = 4n in whih b, t, k and n are total plate width, thikness of plate panel, bkling oiient and nmber of panels divided b stiffener. Contrasted with HWA and EN , JA onsider onl plate loal bkling et sing one parameters,. In ase of JSCE gideline (for bkling design)[8], modified olmn approah is sed to allate ltimate ompressive strength of orthogonall stiffened plate,, and the strength given as b t + A l = esm (10) bl t + Al where esm is the ltimate stress of etive stiffener, A l ross-setional area of longitdinal stiffener, b l and b are fll width and etive width of plate between stiffeners. or determining esm and b, the following eqations are reqired iterativel. b e b λ l esm bl = (11) E t 3 = 0.70e 1.640e e 1 σ L = (13) π E r esm = 1.0, ( λ 0.) (14a) (1) 3 αλ + βλ γλ + δ, (0. < λ 1.) (14b) esm = where r is radis of gration of etive stiffener and L is etive length of psedo-stiffened plate. The parameters α, β, γ and δ for steel grades speified in JSHB[7] are show in Table 1. Similarl to HWA, the JSCE gideline also adopted two parameters, e and λ, in order to inorporate two different tpes of failres, namel, plate loal failre and olmn-tpe failre of stiffened plate sstem. It is also noted that the JSCE gideline provide reqirements for preventing prematre loal bkling in longitdinal stiffeners.

4 Table 1. Coiient α, β, γ and δ in JSHB[7] Steel grade ( ) σ * MPa Y σ σ α β γ δ * r / Y SM SM Nonlinear E analsis of stiffened plates 3.1 Geometr of model After varios preliminar nmerial stdies for U-rib stiffened dek panel sstems, it has been identified that failre modes at ltimate stages an be ategorized into two major modes; one is the plate loal bkling in dek panels and global (overall) bkling of panel sstems as in strt approah. These two modes of failres, than are governed b plate and olmn slenderness parameters shown in Eqs (3) and (4), respetivel, were taken into aont when hpothetial analsis models were set p. U-ribs onsidered in this std were also heked and set to prevent the stiffener loal bkling and/or stiffener tripping. Eah parameter was ontrolled b hanging the dek panel plate thikness and dek panel spaing between transverse stiffeners. U-rib shape, thikness, and the spaing in lateral diretion were nhanged. Details of hpothetial models are represented in ig. 1, and Table. a w b h h t r L ~6000 Table. Dek thikness of hpothetial model Model ID t d (mm) T08 8 T10 10 T1 1 T14 14 T16 16 T18 18 T0 0 T T4 4 T3 3 T40 40 ig. 1: Notation for U-rib stiffened plate Unit: mm ig. : Modelling b ABAQUS 3. Material properties The most freqentl adopted steel that is designated as SM490Y in Korean Speifiation for oadwa Bridges was assmed for material harateristis in present std. In partilar, SM490Y has ield stress (355MPa) and ltimate stress (490MPa) that are similar to A 709M Grade 345W in ASTM Designation. The onstittional relationship between stress and strain was assmed to be elasti-plasti with ield platea and strain-hardening rate as shown in ig. 3. The mehanial properties of the steel are smmarized in Table 3.

5 Table 3. Mehanial properties of onventional steel Tpe E (GPa) (MPa) (MPa) sh E sh (GPa) SM490Y Initial imperfetion and residal stress As ltimate ompressive strengths of stiffened plates are governed b plate loal bkling or global bkling, the magnitde and tpes of initial imperfetion (I. I.) ma signifiantl inflene on the strength. In order to evalate ets of initial imperfetions on in-plane ompressive strengths, two different tpes of initial geometri imperfetion were onsidered in this std. ig. 4 shows the first eigenmode of stiffened dek panel sstem with relativel thik dek plates while ig.5 shows that of the sstem with relativel thin dek plates. The thikness of dek panel was varied from 8 mm to 40 mm, respetivel. Aording to Sheikh s std [11], the global bkling mode shown in ig.4 is in aord with stiffener inded global bkling mode. Both the global bkling mode and plate loal bkling mode were onsidered in the present analsis for initial imperfetions. In ABAQUS, shapes of initial imperfetions an be inorporated as independent analsis reslt files. or the reason that global bkling tpe is similar to olmn behavior, the magnitde of maximm defletion (saling fator) for initial imperfetion, δmax, for global bkling tpe was assmed to be L /1000 referring to the SSC olmn rve [10]. It is noted that the assmed magnitde is a little bit in onservative side ompared to L / 0 from AISC speifiation (5) [3] and AASHTO LD bridge design speifiation (7). or the plate loal bkling tpe, the magnitde of maximm defletion was taken as w / 10 based on the Artile 3.5 of the Bridge welding Code [4]. sh E sh ig. 3: Conventional steel model ig. 4: Global bkling tpe I.I. ig. 5: Plate loal bkling tpe I.I. It is generall aepted in the analsis of steel strtres that the residal stresses de to welding shold be onsidered for possible ets on ltimate strength. ig. 6 represents assmed residal stress distribtion onsidered in this std. This model was known to be sggested b kmoto et al.[6] and Sheikh et al.[11]. ig. 6: esidal stress model.

6 4. Analsis reslts and proposed strength rve 4.1 Analsis reslts Normalized ltimate strengths, /, as fntions of the plate slenderness parameter w/t, are shown in ig. 7 along with those from other available ode preditions. In ig. 7, EA 1 and EA represent the strengths from analses inorporating global bkling tpe and plate bkling tpe, respetivel, as an initial imperfetion mode shape. It is ver interesting to note that ltimate ompressive strengths of stiffened plate sstems signifiantl depend on the shapes of initial imperfetions as identified in ig. 7. It is also noted that there is a ertain inonsisten among design ode preditions. The strength preditions b JA monotoniall derease as the vale of w/t inreases. It ma be reonfirmed from ig. 7 that the strength preditions from Eroode, HWA, and JSCE gideline have onsidered interation et of olmn behavior and plate behavior showing the optimal point for the maximm. L = 3m L = 6m EA 1 (I.I. = GB tpe) EA (I.I. = PB tpe) HWA EUOCODE JSCE gideline JA EA 1 (I.I. = GB tpe) 100 EA (I.I. = PB tpe) HWA EUOCODE 50 JSCE gideline JA ig. 7: Strength omparison with respet to plate slenderness parameter 4. Proposed strength rve Stiffened dek panel sstems have two strength rves de to two different mode shapes of initial imperfetion. The strength gb represent a strength rve from EA 1 reslts that inorporated GB tpe initial imperfetion while the strength pb represent EA reslts that inorporated PB tpe initial imperfetion. The final strength rves in normalized vales an be defined onservativel as minimm line as noted as low bond of strength rve in ig. 8 and have the following eqation form: gb pb = min[, ] (15) or normalized strength rve, basis fntion was set as seond order polnomial fntion and given as = 0 + 1λol + λ pl + 3λol + 4λ pl + 5λ plλol (16) To fit the oiients of Eq. (16), linear regression method was performed based on the least sqare 100 Low bond of strength rve 0.5GB+0.5PB Upper bond of EA 1 Upper bond of EA ig. 8: Proposed strength rve

7 errors and the oiients are smmarized in Table 4. In ig. 7, proposed strength rves are plotted as vales of w/ t varies. It seem that the proposed strength rve generall higher than existing ode preditions de to more arate evalation of stiffened plate behaviors. Table 4. Coiients for proposed strength rve L = 3m HWA EUOCODE JSCE gideline Proposed strength rve Alternative (0.5GB+0.5PB) L = 6m HWA EUOCODE JSCE gideline Proposed strength rve Alternative (0.5GB+0.5PB) ig. 7: Strength omparison with proposed method and existing odes preditions 5. Conlsion Stiffened plates b U-rib were modelled and analzed sing finite element software, ABAQUS. Two tpes of initial imperfetion were onsidered in the analses for ltimate ompressive strength, the global bkling mode and the plate loal bkling mode, respetivel. Based on nmerial reslts, strength formlas were derived sing linear regression method and the minimm envelopes were proposed for final ltimate ompressive strength rves. The proposed method was ompared with other existing ode preditions. It has been fond that the proposed method provides higher strengths than existing odes bt in the onservative side for E reslts. 6. Aknowledgement This researh was spported b the grant (09CCTI-A ) from the Ministr of Land, Transport and Maritime Affairs of Korean government throgh the Core esearh Institte at Seol National Universit for Core Engineering Tehnolog Development of Sper Long Span Bridge &D Center. 7. eferenes [1] ABAQUS In, ABAQUS standard ser s manal. V , 01. [] Amerian Assoiation of State Highwa and Transportation Offiials, AASHTO LD Bridge design speifiations, Washington, D.C, 7. [3] Amerian Institte of Steel Constrtion(AISC), Steel onstrtion manal, 5. [4] ANSI/AASHTO/AWS D1.5-96, Bridge welding ode, A joint pbliation of the Amerian Assoiation of State Highwa and Transportation offiials and the Amerian Welding Soiet, Washington(DC),. [5] EN , EUOCODE3 Design of steel strtres Part 1.5 Plated strtral elements,

8 4. [6] kmoto Y., Usami T., Okamoto Y., Ultimate ompressive strength of stiffened plates, Pro., Speialt Conf. on Metal Bridge, St. Lois, MO, [7] Japan oad Assoiation (JA), Speifiation for highwa bridges: Part I, Toko,. [8] NAKAI., A design method for orthogonall stiffened plates with or withot stringers sbjeted to niaxial ompression, JSCE jornal of strtral engineering, Vol., No., Pp [9] PETOS P. XANTHAKOS., Theor and design of bridges, JOHN WILEY & SONS, New York, 1994, pp.465. [10] Johnston, B.G., ed. Strtral Stabilit esearh Conil Gide to Stabilit Design Criteria for Metal Strtres, Third edition. John Wile & Sons, New York, [11] Sheikh IA, Grondin GY, Elwi AE, Stiffened steel plates nder niaxial ompression Jornal of Constrtional Steel esearh,. [1] Wolhk,., Marborl,.M., Proposed Design Speifiation for Steel Box Girder Bridges, eport No. HWA-TS-80-05, ederal Highwa Administraion, Washington, D.C., 1980.