STATISTICAL RESEARCH OF STEEL GRADES: DX51D, DX52D AND DX53D BADANIA STATYSTYCZNE GATUNKÓW STALI: DX51D, DX52D I DX53D

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1 TECHNICAL TRANSACTIONS CIVIL ENGINEERING CZASOPISMO TECHNICZNE BUDOWNICTWO 4-B/204 PAWEŁ ŻWIREK* STATISTICAL RESEARCH OF STEEL GRADES: DX5D, DX52D AND DX53D BADANIA STATYSTYCZNE GATUNKÓW STALI: DX5D, DX52D I DX53D Abstract This article presets the results of the statistical research of the echaical properties of sheets of Polish grades DX5D, DX52D ad DX53D, ade of low carbo steel for cold forig, cotiuously hot-dip coated. DX-type sheets, i particular DX5D, produced accordig to stadard EN 0346 [4], ca be used, iter alia, to produce corrugated etal sheets ad sadwich paels. Stadard EN 0346 [4] does ot give at all, or gives i the for of very wide itervals, stregth paraeters for sheets of DX type. Characteristic ad desig values of yield stregth ad tesile stregth have bee preseted i the article. Also, the values of partial factors for DX-type steel have bee aalyzed. Keywords: DX5D, DX52D, DX53D, steel sheets, statistical research Streszczeie W artykule przedstawioo wyiki badań statystyczych cech wytrzyałościowych dla krajowych blach gatuku DX5D, DX52D i DX53D ze stali iskowęglowych do obróbki plastyczej a zio powlekaych ogiowo w sposób ciągły. Blachy typu DX wg ory EN 0346 [4], w szczególości DX5D, ogą być stosowae.i do produkcji blach trapezowych i płyt warstwowych. Nora EN 0346 [4] ie podaje wcale lub podaje w postaci bardzo szerokich przedziałów paraetry wytrzyałościowe blach typu DX. W pracy wyzaczoo wartości charakterystycze i obliczeiowe dla graicy plastyczości i wytrzyałości a rozciągaie oraz przeaalizowao wartości częściowych współczyików bezpieczeństwa dla blach typu DX. Słowa kluczowe: DX5D, DX52D, DX53D, blachy stalowe, badaia statystycze * Ph.D. Eg. Paweł Żwirek, Faculty of Civil Egieerig, Cracow Uiversity of Techology.

2 02. Itroductio Accordig to stadard EN 0346 [4], coteporary corrugated sheets [8] ad exteral layers of sadwich paels [9] are aily ade of thi sheets of the followig steel grades S220GD, S250GD, S280GD, S320GD, S350GD (cotiuously hot-dip coated strips ad sheets of structural steel) or DX5D (cotiuously hot-dip coated strips ad sheets of low carbo steel for cold forig). The stregth paraeters for the atioal cotiuously hot-dip coated strips ad sheets of structural steel aufactured accordig to [4] have bee verified o the basis of a large statistical test i [5]. For DX-type steel, the stadard EN 0346 [4] oly specifies itervals of its echaical properties or does ot provide the iforatio at all. While coparig the tables cotaied i stadards EN 0346 [4] ad EN [3], it ca be oted that the stadard for desigig steel structures [3] defies the iiu values of the itervals specified i stadard [4] (for trasverse directio) c.f. Table. The ai of this paper is to deterie the characteristics ad desig values of the stregth paraeters ad partial safety factors for DX-type sheets o the basis of statistical research. The calculatios shall be perfored for Polish steel products. Steel grade Mechaical properties of steel grades: DX5D, DX52D ad DX53D Yield stregth R e EN 0346 [4] EN [3] Tesile stregth R Elogatio A 80 % i DX5D DX52D DX53D f yb Table f u Accordig to [3], properties of the base aterial, i particular, the oial yield stregth f yb ad ultiate tesile stregth f u ca be adopted either by assuig values f y =R eh or R p0.2 ad f u =R direct fro product stadards, by usig the values give i the tables cotaied i the stadard, or by appropriate tests, accordig to EN 990 []. This work will use the provisios of Appedix D to the stadard EN 990 []. Deteriig the desig values of aterial properties fro statistical research ay be carried out i oe of the followig ways: by assessig a characteristic value X k, which is the divided by a partial factor g ad ultiplied by a explicit coversio factorh d (ethod a), by direct deteriatio of the desig value X d, iplicitly or explicitly accoutig for the coversio of results ad the total reliability required (ethod b). The forulas specified i the desig stadard PN-EN 990 [] are based o the assuptio that all rado variables have oral or log-oral distributios ad there is o prior iforatio about their ea values. The estiatio of the desig values ca be perfored either whe there is o prior iforatio about the dispersio easureet

3 03 of the rado variable i the for of a coefficiet of variatio v x, or whe there is full iforatio about a coefficiet of variatio. I the case of ethod a, the desig value of a property X ca be calculated fro the forula: for the oral distrubutio for the log-oral distributio s X 2 y x x d X k ηd = ηd = x( kvx ) () γ γ s vx = sx / x (2) x = i= 2 2 x i x i= x i (3) = x ( ) (4) ηd Xd = exp( y ks y ) (5) γ y = i= l( x ) (6) i s = l( V + ) = v if v s is kow fro prior kowledge (7) 2 y = i y i= (l x ) if v x is ukow fro prior kowledge (8) where: h d desig value of the coversio coefficiet, g partial safety factor associated with the ucertaity of aterial properties, uber of test results, x i value of a sigle result, k value of statistics, depedig o the uber of test results accordig to Table 2. I the case of ethod b, the desig value of X is deteried fro the followig forulas: for oral distributio for log-oral distributio X = η ( k v ) (9) d d x d, x where: k d, value of statistics accordig to Table 3. Xd = ηd exp( p kd, sy) (0)

4 04 If the value of the coefficiet of variatio v x 0. (as is usually the case for the stregth properties of steel products), the differece betwee the results of the statistical aalysis for oral ad log-oral distributio is practically isigificat. While aalyzig the values of statistics i each row of Tables 2 ad 3, it ca be observed that for large saple sizes, the values of statistics ted asyptotically to the sae value, irrespective of whether the coefficiet of variatio is kow or estiated fro the test. Values of statistics k for the 5% characteristic value Table v x (kow) v x (ukow) Values of statistics k d, for the desig value Table v x (kow) v x (ukow) Statistical research I order to deterie the echaical paraeters of the DX-type sheets aufactured accordig to stadard EN 0346 [4], the data o the echaical properties of etal sheets fro the years , provided by the Quality Cotrol Departet of Arcelor Mittal, have bee used by the author. The preseted statistical test icludes properties of the sheets with a oial thickess of 0,45 2,00. The results of statistical research for the differet grades of steel have bee preseted i Table 4. The uber of the data set for each property was Particularly iterestig, fro a practical poit of view, are the results for the DX5D steel grade, which is used i the aufacturig of corrugated sheets, exteral layers of sadwich paels ad cold fored sectios. Sheets ade of grade DX52 are iteded priarily for drawig ad DX53D for deep drawig. A large uber of the results sice 2007 are due to the itroductio of the electroic archivig syste by the copay. The results of earlier years were obtaied fro the archives stored i the paper versio. A sall uber of the results for the DX52 ad DX53 steel grades are caused by a relatively sall productio volue copared to the DX5D steel. Verificatio of a type of probability distributio for rado yield stregth R e ad rado ultiate tesile stregth R, was perfored with a graphical ethod usig probabilistic grids where the statistical results have bee applied. Figure a presets a verificatio of the probability distributio of yield stregth of the DX5D grade steel sheets o the grid of oral distributio. Liear approxiatio of epirical data sees reasoable. Siilar results were also obtaied for the other two aalyzed grades of steel.

5 05 Fig.. Statistical test for the DX5D steel (years ) o the oral probability grid for: a) yield stregth R e, b) ultiate tesile stregth R The results obtaied for the ultiate tesile stregth R (c.f. Fig. b) iply a possibility of usig liear approxiatio oly for results cocetrated aroud the cetral values. The assuptio of orality of distributio of ultiate tesile stregth R is therefore satisfied i approxiatio. Figure 2 depicts sets of ipleetatio o the plae R e R, ad liear regressio lies for the DX5D grade steel. The values of the correlatio coefficiets have bee icluded i table 4, colu (9). I the case of the DX5D steel of the largest uber of data, for the joit test of years 2005 to 200, a oderate [7] depedece of the correlatio r = 0,498 < 0,4;0,6) was obtaied. Table 4 suarizes the detailed statistical research results both for the aual tests, ad for the joit tests of years Colus (3), (6) ad (0) of the table iclude:

6 06 Table 4 The results of statistical research of echaical properties of the followig steel grades: DX5D, DX52D ad DX53D Year Fig. 2. Liear regressio betwee yield stregth R e ad ultiate tesile stregth R for the DX5D grade steel Nuber of results R e Re v Re R R () (2) (3) (4) (5) (6) (7) (8) (9) (0) () DX5D DX52D DX53D v R r A % v A

7 07 ea values R, R ad A respectively for rado yield stregth R e, rado ultiate e tesile stregth R ad rado elogatio of the tested saple A calculated accordig to the forula (3). Colus (5), (8) ad () represet the values of the coefficiet of variatio deteried accordig to forula (2). Colus (4) ad (7) cotai the values of stadard deviatio obtaied fro forula (4) ( = s). 3. Characteristic ad desig values The ext stage of the aalysis was to deterie the characteristic ad desig values of the stregth properties of the aalysed grades of steel. The colus (5) ad (0) of Table 5 copare the characteristic values calculated accordig to forula (), as the lower 5% quatiles of the oral distributio (assuig the coversio coefficiet h d =,0, as i the work i [6]). O the other had, the colus (6) ad () cotai desig values of yield stregth R e ad ultiate tesile stregth R, calculated as 0.% lower quatiles of a oral distributio. No. Year Nuber of results R e Characteristic ad desig values of R e ad R v Re R e,k R e,d g 0 R v R R,k R,d Table 5 () (2) (3) (4) (6) (6) (7) (8) (9) (0) () (2) DX DX DX Accordig to the iterpretatio preseted i stadard EN 990 [] ad the work i [6], a partial safety factor g M =g g R is a product of the coefficiet g describig the ucertaity i assessig aterial properties, ad the coefficiet g R describig the ucertaity of the adopted odel i structural resistace. Coparig forulas () ad (9), ad assuig k ad k d, accordig to the saple size (c.f. Tables 2 ad 3), the value of the coefficiet g ca be calculated fro the forula (): γ v = v Values of the coefficiet g, for the differet grades of steel have bee suarized i colus (7) ad (2) of Table 5 for yield stregth R e ad ultiate tesile stregth R, x x g 2 ()

8 08 respectively. Values of the partial safety factor for the cross-sectio resistace g M0 have bee calculated by ultiplyig the value of the coefficiet g 0 (deteried fro the tests) by g R =.0. Estiates of the coefficiet g R value, describig the ucertaity of the odel of the cross-sectio resistace have bee obtaied akig use of the results of siilar studies carried out for the thi sheets aufactured accordig to the stadard EN 0346 [4]. For the S280GD ad S320GD grades of steel the values of γr = γm0 / 0. were obtaied. Thus, for DX-type sheets, the value of the partial factor is g M0 =.0 g 0. I the case of partial resistace factor g M2 of the et sectio at fasteer holes, the values of odel ucertaity factor i structural resistace are ot kow to the author. A siilar proble is etioed by the authors of the work i [6]. Startig fro the values of the coefficiet g M2 =.25 specified i stadard EN [3], estiatio of the odel ucertaity i structural resistace coefficiet for et sectios at fasteer holes ca be calculated as iterval g R =.25/(.04.3) = Coclusios The statistical data collected by the author allowed for the deteriatio of the characteristic ad desig values of the stregth properties ad the values of partial factors for the DX5D, DX52D, DX53D sheets aufactured accordig to stadard EN 0346 [4]. I the case of the Polish steel products, the obtaied results allow to adopt for the calculatios the sigificatly higher stregth paraeters tha those specified i the desig stadard EN [3]. Refereces [] PN-EN 990:2004. Eurokod. Podstawy projektowaia kostrukcji. [2] PN-EN 993--:2005. Eurokod 3. Projektowaie kostrukcji stalowych. Część.: Reguły ogóle i reguły dla budyków. [3] PN-EN :2008. Eurokod 3. Projektowaie kostrukcji stalowych. Część.3: Regóły ogóle Reguły uzupełiające dla kostrukcji z kształtowików i blach profilowaych a zio. [4] PN-EN 0346:20. Wyroby płaskie stalowe powlekae ogiowo w sposób ciągły Waruki techicze dostawy. [5] Gwóźdź M., Żwirek P., Weryfikacja statystycze współczyików częściowych ośości blach ciekich, Iżyieria i Budowictwo 9/20, [6] Medera Z., Suchodoła M., Częściowe współczyiki bezpieczeństwa w projektowaiu kostrukcji stalowych według eurokodów, Iżyieria i Budowictwo 2/203, [7] Sobczyk M., Statystyka. Aspekty praktycze i teoretycze, Wydawictwo UMCS, Lubli [8] Techical Approval ITB AT /20, Stalowe blachy profilowae Mauka, Broo, ACP-, AC-, TR-, V-, TR35, TR40, TS40, TR50, TR60, TR70, TR84, TR94, TR50, TR60, LT40, LT70, EP-, Hacierba-, Haciero-, Frequece-, Flolie-, Softlie-, Hairbable-, Papa-, Cofrasol-, PMA-, opracowaa dla ArcelorMittal Costructio. [9] Techical Approval ITB AT-5-859/200, Ściee płyty warstwowe PWS-WA Pruszyński z rdzeie z weły ieralej w okładziach z blachy stalowej pełej i perforowaej dla firy Pruszyński Spółka z o.o.